EllipticalParabolicHyperbolic.ipynb

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   "source": [
    "import math\n",
    "import numpy as np"
   ]
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   "source": [
    "# Elliptical orbits using the Euler method"
   ]
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   "source": [
    "In the simple_two_body.ipynb notebook I implemented circular orbits with arbitary starting positions and confirmed that the truncation error converged linearly with timestep for the Euler method.  In this notebook I have begun to implement elliptical orbits. "
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   "source": [
    "It would be meaningless to evaluate the L0 error for a hyperbolic or parabolic orbit since there is no cycle and the L0 error is found after one or more cycles when the system returns to its starting point. However, it would be possible to evaluate it for the elliptical orbit system, and I intend to check that the convergence of the L0 error with dt is linear as it should be for the Euler method. "
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the convergence can be tested for ellipses only and because ellipses are closed so make it clear if they are not working correctly graphically, I will begin with ellipses then proceed to parabolas and hyperbolas. "
   ]
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    "def getfocus(a,ecc):\n",
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1\"},\"renderers\":[{\"id\":\"1052\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1062\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1027\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1011\",\"type\":\"LinearScale\"},{\"attributes\":{\"callback\":null,\"end\":15,\"start\":-15},\"id\":\"1005\",\"type\":\"Range1d\"},{\"attributes\":{},\"id\":\"1060\",\"type\":\"Selection\"},{\"attributes\":{\"items\":[{\"id\":\"1048\",\"type\":\"LegendItem\"},{\"id\":\"1062\",\"type\":\"LegendItem\"},{\"id\":\"1078\",\"type\":\"LegendItem\"}],\"location\":\"bottom_right\"},\"id\":\"1047\",\"type\":\"Legend\"},{\"attributes\":{},\"id\":\"1028\",\"type\":\"HelpTool\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"1023\",\"type\":\"PanTool\"},{\"id\":\"1024\",\"type\":\"WheelZoomTool\"},{\"id\":\"1025\",\"type\":\"BoxZoomTool\"},{\"id\":\"1026\",\"type\":\"SaveTool\"},{\"id\":\"1027\",\"type\":\"ResetTool\"},{\"id\":\"1028\",\"type\":\"HelpTool\"}]},\"id\":\"1029\",\"type\":\"Toolbar\"},{\"attributes\":{\"formatter\":{\"id\":\"1042\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1014\",\"type\":\"BasicTicker\"}},\"id\":\"1013\",\"type\":\"LinearAxis\"},{\"attributes\":{\"fill_color\":{\"value\":\"#1f77b4\"},\"line_color\":{\"value\":\"red\"},\"line_width\":{\"value\":15},\"x\":{\"value\":-5.0},\"y\":{\"value\":0.0}},\"id\":\"1064\",\"type\":\"Circle\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"line_width\":{\"value\":15},\"x\":{\"value\":-5.0},\"y\":{\"value\":0.0}},\"id\":\"1065\",\"type\":\"Circle\"},{\"attributes\":{\"fill_color\":{\"value\":\"#1f77b4\"},\"line_color\":{\"value\":\"green\"},\"line_width\":{\"value\":15},\"x\":{\"value\":5.0},\"y\":{\"value\":0.0}},\"id\":\"1050\",\"type\":\"Circle\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1046\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"1014\",\"type\":\"BasicTicker\"},{\"attributes\":{\"formatter\":{\"id\":\"1044\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1019\",\"type\":\"BasicTicker\"}},\"id\":\"1018\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1089\",\"type\":\"Selection\"},{\"attributes\":{\"data_source\":{\"id\":\"1063\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1064\",\"type\":\"Circle\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1065\",\"type\":\"Circle\"},\"selection_glyph\":null,\"view\":{\"id\":\"1067\",\"type\":\"CDSView\"}},\"id\":\"1066\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1019\",\"type\":\"BasicTicker\"},{\"attributes\":{\"text\":\"Ellipse\"},\"id\":\"1003\",\"type\":\"Title\"},{\"attributes\":{\"ticker\":{\"id\":\"1014\",\"type\":\"BasicTicker\"}},\"id\":\"1017\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1042\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"source\":{\"id\":\"1063\",\"type\":\"ColumnDataSource\"}},\"id\":\"1067\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1044\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1075\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"1019\",\"type\":\"BasicTicker\"}},\"id\":\"1022\",\"type\":\"Grid\"},{\"attributes\":{\"label\":{\"value\":\"Focus 2\"},\"renderers\":[{\"id\":\"1066\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1078\",\"type\":\"LegendItem\"},{\"attributes\":{\"callback\":null,\"data\":{},\"selected\":{\"id\":\"1089\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1088\",\"type\":\"UnionRenderers\"}},\"id\":\"1063\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1076\",\"type\":\"Selection\"},{\"attributes\":{\"label\":{\"value\":\"Circle\"},\"renderers\":[{\"id\":\"1039\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1048\",\"type\":\"LegendItem\"},{\"attributes\":{\"data_source\":{\"id\":\"1036\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1037\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1038\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1040\",\"type\":\"CDSView\"}},\"id\":\"1039\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"1036\",\"type\":\"ColumnDataSource\"}},\"id\":\"1040\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1038\",\"type\":\"Line\"},{\"attributes\":{\"line_color\":\"blue\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1037\",\"type\":\"Line\"},{\"attributes\":{\"callback\":null,\"data\":{},\"selected\":{\"id\":\"1076\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1075\",\"type\":\"UnionRenderers\"}},\"id\":\"1049\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1023\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"1088\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"line_width\":{\"value\":15},\"x\":{\"value\":5.0},\"y\":{\"value\":0.0}},\"id\":\"1051\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1024\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1026\",\"type\":\"SaveTool\"},{\"attributes\":{\"data_source\":{\"id\":\"1049\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1050\",\"type\":\"Circle\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1051\",\"type\":\"Circle\"},\"selection_glyph\":null,\"view\":{\"id\":\"1053\",\"type\":\"CDSView\"}},\"id\":\"1052\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[103]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[103]}},\"selected\":{\"id\":\"1060\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1059\",\"type\":\"UnionRenderers\"}},\"id\":\"1036\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"overlay\":{\"id\":\"1046\",\"type\":\"BoxAnnotation\"}},\"id\":\"1025\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"callback\":null,\"end\":15,\"start\":-15},\"id\":\"1007\",\"type\":\"Range1d\"},{\"attributes\":{\"source\":{\"id\":\"1049\",\"type\":\"ColumnDataSource\"}},\"id\":\"1053\",\"type\":\"CDSView\"}],\"root_ids\":[\"1002\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"73fb529f-e15c-4515-b04f-287a16057a16\",\"roots\":{\"1002\":\"ebb1f25a-d3f7-4062-8261-1ed0cef45955\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1002"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "radius=10\n",
    "t=2*math.pi*0.01*np.arange(103)\n",
    "a=10\n",
    "ecc=.5\n",
    "b=a*np.sqrt(1-ecc**2)\n",
    "centerx=0\n",
    "centery=0\n",
    "focusx=centerx+getfocus(a,ecc)\n",
    "focusy=centery+0.0\n",
    "p = figure(title=\"Ellipse\", plot_width=400, plot_height=400, x_range=[-15,15], y_range=[-15,15])\n",
    "p.line(centerx+a*np.cos(t),centery+b*np.sin(t),line_width=3,line_color=\"blue\",legend=\"Circle\")\n",
    "p.circle(focusx,focusy,line_width=15,line_color=\"green\",legend=\"Focus 1\")\n",
    "p.circle(centerx-getfocus(a,ecc),focusy, line_width=15, line_color=\"red\", legend=\"Focus 2\")\n",
    "p.legend.location=\"bottom_right\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler(h,t, x,y,z,f,debugprint):\n",
    "    xstep = (f(t, x, y,z)+f(t+h,x+h,y,z))/2*h\n",
    "    xnew=x+xstep\n",
    "    if(debugprint):\n",
    "        print(h,t,x,xstep,xnew)\n",
    "    return t+h,xnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "def InitialDataEqualMassConic(radius,ecc,angle,initmass):\n",
    "    orbitalangle=angle\n",
    "    print(\"angle\",angle)\n",
    "    phi=np.array([math.pi+orbitalangle,orbitalangle])\n",
    "    orbitalradius=radius #semimajor axis\n",
    "    eccentricity=ecc\n",
    "    print(eccentricity)\n",
    "    mass=np.ones(2)\n",
    "    masses=initmass*mass #*masssun (natural units)\n",
    "    return phi,orbitalangle,orbitalradius,eccentricity, masses\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "angle 0.0\n",
      "0.5\n",
      "(array([3.14159265, 0.        ]), 0.0, 50, 0.5, array([1., 1.]))\n"
     ]
    }
   ],
   "source": [
    "import random,numpy as np\n",
    "rad0=50\n",
    "ecc0=0.5\n",
    "theta0=0. #math.pi/6.\n",
    "mass0=1.0\n",
    "initdateqellipse=InitialDataEqualMassConic(rad0,ecc0,theta0,mass0)\n",
    "print(initdateqellipse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getxyuveqtwoellipses(initdat):\n",
    "    phi,orbitangle,orbitalradius,eccentricity, masses=initdat\n",
    "    print(\"initdat\", orbitalradius, phi, eccentricity, np.cos(phi), np.sin(phi))\n",
    "    metersperAU=1\n",
    "    Gconstant=1\n",
    "    #fix x0 y0 at one star, disregard initial data, use orbital radius as separation between stars\n",
    "    #this is consistant with choice in previous part\n",
    "    cosphi=np.cos(phi)\n",
    "    sinphi=np.sin(phi)\n",
    "    coordsep=orbitalradius #/2.\n",
    "    print(\"coordsep\",coordsep)\n",
    "    #x0=orbitalradius/2.*np.cos(phi)*metersperAU\n",
    "    #y0=orbitalradius/2.*np.sin(phi)*metersperAU\n",
    "    count=0\n",
    "    for phi0 in phi:\n",
    "        if phi0==0:\n",
    "            print(\"zero\")\n",
    "            #x0[count]=orbitalradius[count]/2.\n",
    "            #y0[count]=0\n",
    "            cosphi[count]=1.0\n",
    "            sinphi[count]=0.0\n",
    "        if phi0==math.pi:\n",
    "            cosphi[count]=-1.0\n",
    "            sinphi[count]=0.0\n",
    "            print(\"pi\")\n",
    "            #x0[count]=-orbitalradius[count]/2.\n",
    "            #y0[count]=0\n",
    "        if phi0==math.pi/2.:\n",
    "            cosphi[count]=0.0\n",
    "            sinphi[count]=1.0\n",
    "            #x0[count]=0\n",
    "            #y0[count]=orbitalradius[count]/2.\n",
    "        if phi0==3*math.pi/2.:\n",
    "            cosphi[count]=0.0\n",
    "            sinphi[count]=-1.0\n",
    "            #x0[count]=0\n",
    "            #y0[count]=-orbitalradius[count]/2.\n",
    "        count+=1\n",
    "    x0=coordsep*cosphi\n",
    "    y0=coordsep*sinphi\n",
    "    #x0[1]=0.0\n",
    "    #y0[1]=0.0\n",
    "    z0=np.zeros(2)\n",
    "    print(x0)\n",
    "    print(y0)\n",
    "    v=np.zeros(2)\n",
    "    a=np.zeros(2)\n",
    "    ux0=0.\n",
    "    uy0=0.\n",
    "    uz0=0.\n",
    "    ax0=0.\n",
    "    ay0=0.\n",
    "    az0=0.\n",
    "    vx0=0.\n",
    "    vy0=0.\n",
    "    vz0=0.\n",
    "    print(eccentricity)\n",
    "    #masses=np.zeros(2)\n",
    "    #masses[0]=masses[1]+masses[0]\n",
    "    #masses[1]=(masses[1]*masses[0])/(masses[1]+masses[0])\n",
    "    if eccentricity<1 and eccentricity>0:\n",
    "        #elliptical\n",
    "        orbitalr=orbitalradius #NO REDUCED MASS \n",
    "        #focusdisp=getfocus(orbitalr,eccentricity) #displacement of the center due to the focus being at the center\n",
    "        coordsep=orbitalr*(1+eccentricity) #start at aphelion\n",
    "        x0=(coordsep)*cosphi\n",
    "        y0=(coordsep)*sinphi\n",
    "        starsep=np.sqrt((x0[0]-x0[1])**2+(y0[0]-y0[1])**2) #two stars, at opposite ends of the orbit\n",
    "        Fapastron=masses[1]*masses[0]/starsep**2\n",
    "        #print('xycomp',coordsep,focusdisp,x0,y0)\n",
    "        #x0[0]=0.0\n",
    "        #y0[0]=0.0\n",
    "        v=np.zeros(2)\n",
    "        #v= np.sqrt(masses[1]*masses[0]/masses*(2./coordsep-1./(orbitalr)))\n",
    "        v= np.sqrt(masses[1]*masses[0]/masses*(2./starsep-1./(2.*orbitalr)))\n",
    "        ux0=-v*sinphi\n",
    "        uy0=v*cosphi #initial data in y only \n",
    "        uz0=np.zeros(2)\n",
    "    \n",
    "        print(\"vstuff\", coordsep,orbitalr, 2./coordsep, 1./orbitalr, (2./starsep-1./(2.*orbitalr)), 1./(coordsep))\n",
    "        \n",
    "        a=np.zeros(2)\n",
    "        a=Fapastron/masses\n",
    "    \n",
    "        ax0=-a*cosphi\n",
    "        ay0=-a*sinphi\n",
    "        az0=np.zeros(2)\n",
    "    elif eccentricity[0]==0.0: #circular\n",
    "        #start at perihelion for both (eliptical, doesn't generalize to three body)\n",
    "        #actually start with circular orbit\n",
    "        ux0=np.zeros(2) #*149597870700\n",
    "        #centrepital force balances gravitational force\n",
    "        metersperAU=1 #natural units\n",
    "        #G=1\n",
    "        Gconstant=1\n",
    "        #Fcentripital=mass1*v**2/rphys\n",
    "        #centF=accel\n",
    "        #Faccel=G*m1*m2/r^2\n",
    "        r0=2.*orbitalradius #Mystery factor of 2\n",
    "        print(\"r0\", r0)\n",
    "        v=np.zeros(2)\n",
    "        for i in np.arange(2):\n",
    "            v[i]=np.sqrt(Gconstant*masses[(i+1)%2]/np.abs(r0[i]))\n",
    "        print(v)\n",
    "        #r0=orbitalradius #np.sqrt(x0**2+y0**2)\n",
    "        ux0=-v[0]*sinphi\n",
    "        uy0=v[1]*cosphi #initial data in y only \n",
    "        uz0=np.zeros(2)\n",
    "    \n",
    "        a=np.zeros(2)\n",
    "        a=Fapastron/masses\n",
    "    \n",
    "        ax0=-a[0]*cosphi\n",
    "        ay0=-a[1]*sinphi\n",
    "        az0=np.zeros(2)\n",
    "\n",
    "    \n",
    "    \n",
    "    return masses,x0,y0,z0, ux0, uy0,uz0, ax0, ay0,az0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initdat 50 [3.14159265 0.        ] 0.5 [-1.  1.] [1.2246468e-16 0.0000000e+00]\n",
      "coordsep 50\n",
      "pi\n",
      "zero\n",
      "[-50.  50.]\n",
      "[0. 0.]\n",
      "0.5\n",
      "vstuff 75.0 50 0.02666666666666667 0.02 0.003333333333333334 0.013333333333333334\n",
      "(array([1., 1.]), array([-75.,  75.]), array([0., 0.]), array([0., 0.]), array([-0., -0.]), array([-0.05773503,  0.05773503]), array([0., 0.]), array([ 4.44444444e-05, -4.44444444e-05]), array([-0., -0.]), array([0., 0.]))\n"
     ]
    }
   ],
   "source": [
    "xyuvaeqtwoellipses=getxyuveqtwoellipses(initdateqellipse)\n",
    "print(xyuvaeqtwoellipses)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(array([1., 1.]), array([ 50., -50.]), array([0., 0.]), array([0., 0.]), array([-0., -0.]), array([ 0.07071068, -0.07071068]), array([0., 0.]), array([-2.5e-05,  2.5e-05]), array([-0., -0.]), array([0., 0.]))\n",
    "Circular"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def timestep(step,t,dt,mtotal, mass,xi,yi,zi, vxi, vyi, vzi, axi, ayi, azi):\n",
    "    xii=np.zeros(np.size(xi))\n",
    "    vxii=np.zeros(np.size(vxi))\n",
    "    yii=np.zeros(np.size(yi))\n",
    "    vyii=np.zeros(np.size(vyi))\n",
    "    zii=np.zeros(np.size(vzi))\n",
    "    vzii=np.zeros(np.size(vzi))\n",
    "    rii=np.zeros(np.size(xi))\n",
    "    axii=np.zeros(np.size(axi))\n",
    "    ayii=np.zeros(np.size(ayi))\n",
    "    azii=np.zeros(np.size(azi))\n",
    "    \n",
    "\n",
    "    Gconstant=1\n",
    "    for star1 in np.arange(len(mass)):\n",
    "        for star2 in np.arange(len(mass)):\n",
    "            if star1!=star2:\n",
    "                #Depends on the separation vector's magnitude, rsepjk, because gravity is a central force, \n",
    "                #not because it moves in a circle. \n",
    "                #This should be true even if it moves in an ellipse. This is Newton's Force Law.\n",
    "                #Newton's force law applies in the non-relativisitic limit. \n",
    "                # In this limit, the orbits are stable and no inspiral or outspiral occurs and \n",
    "                # no gravitational waves are emitted.\n",
    "                #In vector form, broken into its components\n",
    "                \n",
    "                \n",
    "                #BECAUSE ACCELERATION IS DECREASING WHILE RADIUS IS INCREASING FOR AN APHELION START, THE PROBLEM \n",
    "                #HAS TO BE BETWEEN HERE AND \n",
    "                xvec=xi[star2]-xi[star1]\n",
    "                yvec=yi[star2]-yi[star1]\n",
    "                zvec=zi[star2]-zi[star1]\n",
    "                rvecsq=xvec**2+yvec**2+zvec**2\n",
    "                rvec3halves=rvecsq**(1.5)\n",
    "                if step < 10:\n",
    "                    print(xvec,yvec,zvec,rvecsq,rvec3halves)\n",
    "                #xhat=xvec/rvec #projection in the x direction\n",
    "                #yhat=yvec/rvec #projection in the y direction\n",
    "                #zhat=zvec/rvec #projection in the z direction\n",
    "                #if step< 10:\n",
    "                #    print(xhat,yhat,zhat)\n",
    "                NewtonF=mass[star1]/rvec3halves\n",
    "                axii[star2]=-NewtonF*xvec\n",
    "                ayii[star2]=-NewtonF*yvec\n",
    "                azii[star2]=-NewtonF*zvec\n",
    "                #HERE\n",
    "                #print(yi[star2],yi[star1],yvec,rvec,yhat,NewtonF,ayii[star2])\n",
    "    if step<10:\n",
    "        print(\"ax\",axii)\n",
    "        print(\"ay\",ayii)\n",
    "        print(\"az\",azii)\n",
    "        print(\"a\",axii**2+ayii**2)\n",
    "    for m in np.arange(len(mass)):\n",
    "        #m represents choices of mass\n",
    "        i=step\n",
    "        dx_by_dt=vxi[m]\n",
    "        dy_by_dt=vyi[m]\n",
    "        dz_by_dt=vzi[m]\n",
    "        dx_by_dt_initial=dx_by_dt\n",
    "        dy_by_dt_initial=dy_by_dt\n",
    "        dz_by_dt_initial=dz_by_dt\n",
    "        d2x_by_dt2=axi[m]\n",
    "        d2y_by_dt2=ayi[m]\n",
    "        d2z_by_dt2=azi[m]\n",
    "        yinitial=yi[m]\n",
    "        xinitial=xi[m]\n",
    "        zinitial=zi[m]\n",
    "        \n",
    "        xfinal = xinitial + dt*dx_by_dt\n",
    "        dx_by_dt_final = dx_by_dt_initial + dt*d2x_by_dt2\n",
    "        yfinal= yinitial + dt*dy_by_dt\n",
    "        dy_by_dt_final = dy_by_dt_initial + dt*d2y_by_dt2\n",
    "        zfinal= zinitial + dt*dz_by_dt\n",
    "        dz_by_dt_final = dz_by_dt_initial + dt*d2z_by_dt2\n",
    "        #rfinal=np.sqrt(xfinal**2+yfinal**2+zfinal**2)\n",
    "        \n",
    "        xii[m]=xfinal\n",
    "        yii[m]=yfinal\n",
    "        zii[m]=zfinal\n",
    "        vxii[m]=dx_by_dt_final\n",
    "        vyii[m]=dy_by_dt_final\n",
    "        vzii[m]=dz_by_dt_final\n",
    "        #rii[m]=rfinal\n",
    "   \n",
    "\n",
    "\n",
    "    return mass, xii,yii,zii,vxii,vyii,vzii,axii,ayii,azii\n",
    "                    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getPotentialEnergy(x1,y1,x2,y2, mass1,mass2):\n",
    "    diffx=x1-x2\n",
    "    diffy=y1-y2\n",
    "    r=np.sqrt(diffx**2+diffy**2)\n",
    "    return -mass1*mass2/r**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getKineticEnergy(vx,vy, mass):\n",
    "    return 1/2*mass*(vx**2+vy**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getAngularMomentum(x,y,vx,vy,mass):\n",
    "    return mass*(vx*y-vy*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-75.  75.]\n",
      "150.0 0.0 0.0 22500.0 3375000.0\n",
      "-150.0 0.0 0.0 22500.0 3375000.0\n",
      "ax [ 4.44444444e-05 -4.44444444e-05]\n",
      "ay [-0. -0.]\n",
      "az [-0. -0.]\n",
      "a [1.97530864e-09 1.97530864e-09]\n",
      "150.0 0.11547005383792516 0.0 22500.013333333332 3375003.0000004442\n",
      "-150.0 -0.11547005383792516 0.0 22500.013333333332 3375003.0000004442\n",
      "ax [ 4.44444049e-05 -4.44444049e-05]\n",
      "ay [ 3.42133189e-08 -3.42133189e-08]\n",
      "az [-0. -0.]\n",
      "a [1.9753063e-09 1.9753063e-09]\n",
      "149.99991111111112 0.23094010767585033 0.0 22500.02666667457 3375006.0000035563\n",
      "-149.99991111111112 -0.23094010767585033 0.0 22500.02666667457 3375006.0000035563\n",
      "ax [ 4.44443391e-05 -4.44443391e-05]\n",
      "ay [ 6.84265769e-08 -6.84265769e-08]\n",
      "az [-0. -0.]\n",
      "a [1.97530396e-09 1.97530396e-09]\n",
      "149.99973333333335 0.34641016151377546 0.0 22500.040000071116 3375009.000020001\n",
      "-149.99973333333335 -0.34641016151377546 0.0 22500.040000071116 3375009.000020001\n",
      "ax [ 4.44442469e-05 -4.44442469e-05]\n",
      "ay [ 1.02639774e-07 -1.02639774e-07]\n",
      "az [-0. -0.]\n",
      "a [1.97530162e-09 1.97530162e-09]\n",
      "149.9994666667457 0.46188014692506285 0.0 22500.053333578275 3375012.000062223\n",
      "-149.9994666667457 -0.46188014692506285 0.0 22500.053333578275 3375012.000062223\n",
      "ax [ 4.44441284e-05 -4.44441284e-05]\n",
      "ay [ 1.3685289e-07 -1.3685289e-07]\n",
      "az [-0. -0.]\n",
      "a [1.97529928e-09 1.97529928e-09]\n",
      "149.99911111147983 0.5773499954831964 0.0 22500.066667251354 3375015.000142666\n",
      "-149.99911111147983 -0.5773499954831964 0.0 22500.066667251354 3375015.000142666\n",
      "ax [ 4.44439835e-05 -4.44439835e-05]\n",
      "ay [ 1.71065905e-07 -1.71065905e-07]\n",
      "az [-0. -0.]\n",
      "a [1.97529694e-09 1.97529694e-09]\n",
      "149.99866666772016 0.6928196387617817 0.0 22500.080001145678 3375018.000273778\n",
      "-149.99866666772016 -0.6928196387617817 0.0 22500.080001145678 3375018.000273778\n",
      "ax [ 4.44438123e-05 -4.44438123e-05]\n",
      "ay [ 2.05278798e-07 -2.05278798e-07]\n",
      "az [-0. -0.]\n",
      "a [1.9752946e-09 1.9752946e-09]\n",
      "149.9981333357037 0.8082890083345864 0.0 22500.09333531654 3375021.000468\n",
      "-149.9981333357037 -0.8082890083345864 0.0 22500.09333531654 3375021.000468\n",
      "ax [ 4.44436148e-05 -4.44436148e-05]\n",
      "ay [ 2.39491549e-07 -2.39491549e-07]\n",
      "az [-0. -0.]\n",
      "a [1.97529225e-09 1.97529225e-09]\n",
      "149.99751111572016 0.923758035775581 0.0 22500.10666981925 3375024.000737778\n",
      "-149.99751111572016 -0.923758035775581 0.0 22500.10666981925 3375024.000737778\n",
      "ax [ 4.44433909e-05 -4.44433909e-05]\n",
      "ay [ 2.73704138e-07 -2.73704138e-07]\n",
      "az [-0. -0.]\n",
      "a [1.97528991e-09 1.97528991e-09]\n"
     ]
    }
   ],
   "source": [
    "dt=1 #*31556926 #seconds per year\n",
    "numsteps=100000\n",
    "savestep=100\n",
    "mass0,x,y,z0,vx,vy,vz0,ax,ay,az0=xyuvaeqtwoellipses\n",
    "print(x)\n",
    "xcoord1=[]\n",
    "xcoord2=[]\n",
    "ycoord1=[]\n",
    "ycoord2=[]\n",
    "vxarr1=[]\n",
    "vxarr2=[]\n",
    "vyarr1=[]\n",
    "vyarr2=[]\n",
    "axarr1=[]\n",
    "ayarr1=[]\n",
    "axarr2=[]\n",
    "ayarr2=[]\n",
    "Earr=[]\n",
    "Larr=[]\n",
    "t=0.0\n",
    "tarr=[]\n",
    "masstotal=1.\n",
    "L=np.zeros(len(mass0))\n",
    "for i in np.arange(1,numsteps):\n",
    "    mass, x,y,z,vx,vy,vz,ax,ay,az=timestep(i,t,dt,masstotal,mass0,x,y,z0,vx,vy,vz0,ax,ay,az0)\n",
    "    PE=getPotentialEnergy(x[0],y[0],x[1],y[1], mass[0],mass[1])\n",
    "    KE=0.\n",
    "    for j in np.arange(len(mass)):\n",
    "        KE+=getKineticEnergy(vx[j],vy[j], mass[j])\n",
    "    L[0]=getAngularMomentum(x[0],y[0],vx[0],vy[0],mass[0])\n",
    "    E=PE+KE\n",
    "    #print(x,y,vx,vy,ax,ay,E,L)\n",
    "    #print(ay) #forces should be equal and opposite, but in reduced mass framework accelerations are also equal and opposite\n",
    "    #accelerations should evolve from y to x with time in a sinusoidal manner even in reduced mass framework\n",
    "    #print(ax)\n",
    "    t+=dt\n",
    "    if i%savestep==0:\n",
    "        xcoord1.append(x[0])\n",
    "        xcoord2.append(x[1])\n",
    "        ycoord1.append(y[0])\n",
    "        ycoord2.append(y[1])\n",
    "        vxarr1.append(vx[0])\n",
    "        vxarr2.append(vx[1])\n",
    "        vyarr1.append(vy[0])\n",
    "        vyarr2.append(vy[1])\n",
    "        axarr1.append(vx[0])\n",
    "        axarr2.append(vx[1])\n",
    "        ayarr1.append(vy[0])\n",
    "        ayarr2.append(vy[0])\n",
    "        Earr.append(E)\n",
    "        Larr.append(L[0])\n",
    "        tarr.append(t)\n",
    "#mass, x,y,z,vx,vy,vz,ax,ay,az=timestep(2,0,dt,mass,x,y,z,vx,vy,vz,ax,ay,az)\n",
    "#print(x,y,vx,vy,ax,ay) \n",
    "#mass, x,y,z,vx,vy,vz,ax,ay,az=timestep(3,0,dt,mass,x,y,z,vx,vy,vz,ax,ay,az)\n",
    "#print(x,y,vx,vy,ax,ay) \n",
    "#mass, x,y,z,vx,vy,vz,ax,ay,az=timestep(4,0,dt,mass,x,y,z,vx,vy,vz,ax,ay,az)\n",
    "#print(x,y,vx,vy,ax,ay) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "print(yi[star2],yi[star1],yvec,rvec,yhat,NewtonF,ayii[star2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1163\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1163\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1163\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1163' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1163\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1163\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1163\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1163' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1163\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.30127018922193\n",
      "5.0\n",
      "0.0\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"494523a4-86a1-4913-8524-4617eb285428\" data-root-id=\"1164\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
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ellipse 1\"},\"renderers\":[{\"id\":\"1228\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1240\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1176\",\"type\":\"BasicTicker\"},{\"attributes\":{\"click_policy\":\"hide\",\"items\":[{\"id\":\"1210\",\"type\":\"LegendItem\"},{\"id\":\"1224\",\"type\":\"LegendItem\"},{\"id\":\"1240\",\"type\":\"LegendItem\"},{\"id\":\"1258\",\"type\":\"LegendItem\"}],\"location\":\"bottom_left\"},\"id\":\"1209\",\"type\":\"Legend\"},{\"attributes\":{\"ticker\":{\"id\":\"1176\",\"type\":\"BasicTicker\"}},\"id\":\"1179\",\"type\":\"Grid\"}],\"root_ids\":[\"1164\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"9dcba3e1-11a9-4bc6-999b-233728a21609\",\"roots\":{\"1164\":\"494523a4-86a1-4913-8524-4617eb285428\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1164"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"dt=1, Euler Method, e=0.5\", plot_width=400, plot_height=400, y_range=[-350,350],x_range=[-350,350])\n",
    "t = np.linspace(0, 2*math.pi, 100)\n",
    "focus=getfocus(rad0,ecc0)\n",
    "b=rad0*np.sqrt(1-ecc**2)\n",
    "print(b)\n",
    "print(focusx)\n",
    "p.line(xcoord1,ycoord1, line_color=\"purple\",legend=\"Ellipse 1\")\n",
    "p.line(xcoord2,ycoord2, line_color=\"blue\",legend=\"Ellipse 2\")\n",
    "\n",
    "#p.line(focusx+rad0*np.cos(t),b*np.sin(t), line_color=\"green\", legend=\"Ideal ellipse 1\")\n",
    "#p.line(-focusx+rad0*np.cos(t),b*np.sin(t), line_color=\"orange\", legend=\"Ideal ellipse 2\")\n",
    "p.line(focus*np.cos(theta0)+rad0*np.cos(t)*np.cos(theta0)-b*np.sin(t)*np.sin(theta0),focus*np.sin(theta0)+rad0*np.cos(theta0)*np.sin(t)+b*np.sin(theta0)*np.cos(t), line_color=\"cyan\", legend=\"Ideal ellipse 1\")\n",
    "p.line(-focus*np.cos(theta0)+rad0*np.cos(t)*np.cos(theta0)-b*np.sin(t)*np.sin(theta0),-focus*np.sin(theta0)+rad0*np.cos(theta0)*np.sin(t)+b*np.sin(theta0)*np.cos(t), line_color=\"black\", legend=\"Ideal ellipse 2\")\n",
    "\n",
    "print(theta0)\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "\n",
    "show(p) # show the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1369\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1369\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1369\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1369' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1369\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1369\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1369\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1369' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1369\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "999\n",
      "999\n",
      "999\n",
      "-4.330637660316054\n",
      "0.0032938185187060425\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"9777bc12-684f-445e-95a6-eb176d8630ba\" data-root-id=\"1370\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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\",\"dtype\":\"float64\",\"shape\":[999]}},\"selected\":{\"id\":\"1428\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1427\",\"type\":\"UnionRenderers\"}},\"id\":\"1404\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"formatter\":{\"id\":\"1412\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1387\",\"type\":\"BasicTicker\"}},\"id\":\"1386\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1412\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1414\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1406\",\"type\":\"Line\"},{\"attributes\":{\"label\":{\"value\":\"Angular Momentum\"},\"renderers\":[{\"id\":\"1420\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1430\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1387\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1428\",\"type\":\"Selection\"},{\"attributes\":{\"callback\":null},\"id\":\"1373\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1377\",\"type\":\"LinearScale\"}],\"root_ids\":[\"1370\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"24512150-426e-48e4-9d6e-03aaf5096ac6\",\"roots\":{\"1370\":\"9777bc12-684f-445e-95a6-eb176d8630ba\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1370"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "print(len(Larr))\n",
    "print(len(tarr))\n",
    "print(len(Earr))\n",
    "print(max(Larr))\n",
    "print(max(Earr))\n",
    "\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"Energy\", plot_width=400, plot_height=400)\n",
    "p.line(tarr,np.array(Earr), line_color=\"purple\",legend=\"Energy\")\n",
    "p.line(tarr,np.array(Larr)-max(Larr),line_color=\"blue\", legend=\"Angular Momentum\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "\n",
    "show(p) # show the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1527\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1527\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1527\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1527' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1527\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1527\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1527\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1527' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1527\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "999\n",
      "999\n",
      "999\n",
      "-4.330637660316054\n",
      "0.0032938185187060425\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"107cc9f7-2804-45f9-a7bb-8f00e0de75cb\" data-root-id=\"1528\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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AyomW74TwhA5I1x8RvoBUDjbH0eQWsDQN2+W68r5gBAD4UyUJLL/D+VPKpT3O33P/NHBIsoTPM/XAhkp2b87T+teOT4DzTmP7s5LV09zt4/+9Os7KVw0z95itJmphLFP1CiL/pBFrE/wE4lZbaiiD+9P74NHmlZP/7fnGxaLKI/Oc+2+7n3vD9Owuckc9HNP63LcuZUHtk/s5Bu9x7V4j81lFJ1DibqP/8Haq9FLvE/gs/X71Sn9T+M+GDQbGf6P4z+/axoVv8/cN8b1KEtAkAvmf5oTK4EQN7PkkySIAdAuavhdCJ4CUCWdNSzOqkLQCDsmKfiqA1AqojYViJtD0DOW3K1mXYQQA0cRwzWEBFANnCrdVGCEUBVsJ1m5cgRQH0DTGdD4xFABzlhrvrQEUDbD/lgeZIRQA+CinoJKRFAAp+qdcmWEEBehI7GQb0PQB97+WJiCA5AAZ436oUXDECdHRAyYPQJQKU+EMmWqQdAd490qotCBUCcFPGkJMsCQDKX5IyQTwBAeYE+tBa4+z80l0CnRPn2PzRuNtHyefI/FZhqN0ug7D+z08qlZyDlP/ZpsSeUMd0/jwNVQ2lS0j9eG3ZnFrDDP4GD6U+xW68/qXS0iM8khT+zGg4q30pgP+1Ulsq0n6I/KlXnt8HgvD/AHMpHNWrNP/MetWL2pdg/yD78KBJt4j+75lN0CYvpP3YzMzQYxfA/elABfcsh9T+RkoA7Zcb5P5nwpHlRnP4/myAQZwfGAUCdNgb6zz4EQKaH6Np/rAZA2yNMgkoDCUAj0MCJ0jcLQKBHxqpgPw1AA7hypxcQD0Ah22gRklAQQGHzrsBz9RBAfvJagI5zEUA+pDkofMgRQBaKNIqe8hFAnQ0BbSfxEUBkiTWXHMQRQG9XgdRXbBFAg4RB8oLrEECiv1/ED0QQQF+h561Y8g5AMFE+CGcdDUAD51hvNBILQPxXh3Wz2ghA6B9I4q6BBkBz/fr8lBIEQOpT0Ko/mQFAocxz53RD/j956/4aD3D5P/r+iiPKz/Q/cnVGByd58D/QjTENewLpP25ipgmq9uE/lxmy0Rni1z96b0fbSDvMP5fjeda8PLs/HAhyJn/PoD/QlgLZg25UP1bY2eWDA4k/2UNO8ajEsD9ZCMFZR33EP481IhHG0tI/4JhNFJrD3T9WqBuY423lP70KcE7P7ew/lTPL/5We8j/GXNJd3hn3PwI31PcY0/s/Tik7bL9ZAEB1giCCzNECQP6mdzrZRQVAN8EhWyWqB0Derxt5Q/MJQA4rqqNPFgxATPvNLSMJDkAEMf+fhMIPQCVoxHgpnRBA7ZoiodU0EUC5uSw1hKURQFDzn+ot7RFAHKuln48KEkCodgyIL/0RQB/HOZhexRFAto0hLzZkEUB9XEwSktsQQLJIDOAGLhBAjJJQWKq9DkD4DW4Us+MMQCcVvqzz1gpAMzYLMiChCECutebXpkwGQB2e9p5+5ANAQX1LyPNzAUC+wtQE5gz+P0YqLYioTvk/5wgEkEzD9D/Xtfcu93/wP6ZDjyToMOk/UQ83L7Y94j/MFBIr+IzYPxpKdp//ms0/q1y7HnOnvT94m31RbR+kPzASDJBKAGk/2DqCmqucfz+6CWnrMTyrP6ACudjfvsE/xoLkzprM0D8Vr3PbIQrbP9TDbk0+tOM/+ccz+S3X6j/64YrGbGbxP2+BGQQ6uPU/qBI3iwlN+j+DvjM4sw//P/sWToYe9QFAiacWBCBjBEAQM+l6p8YGQJ4Cf66uFAlA0pzwYpJCC0CP3JNCQ0YNQPpi9yh0Fg9AWDigf2JVEECsvGyy9P0QQPLwyTjlgRFAD9XsedHeEUCN5/vSChMSQPtJQnieHRJA4S5+9ln+EUCefTM9zLURQNYX0ypDRRFAq4Syo8WuEED1BeiZFOoPQMBAnyjWNg5Ay6O8eatLDEAu+JluczEKQK9W3THn8QdAGrF+IW2XBUAV/ZuG6CwDQDs0//yGvQBAOBEA8Bip/D+KlHqzPfr3PxuLsCgkhPM//Jw9K9e27j9wNjqBlSbnP4fIlGVteuA/D2gFFkei1T/TsXHRIxPJP76IFMgWUrc/BIJIRF4dmj/+mq30cU8yP/XZVSOpPZA/sBT9Bspqsj8gwlVjXHDFP7dNCqK+P9M/lb295r0J3j/3Cz6VFnLlP4Uq9jHRyew/U8xrSRh18j8uX4FK5tb2P6yapCMxdvs/JKH25OMeAEAPB/H85YsCQNgBj6EL9wRAs9judFBVB0Bu5Eth8ZsJQNR8bZqdwAtACSwyUqW5DUCZYaBMJX4PQJEtS0gXgxBAVKogw3QlEUAPdb/1WaMRQLT72o+c+hFA1lgEMsIpEkCMlrpkBjASQHYz/1FdDRJAeYPgO3PCEUDqEi25qFARQOxt388LuhBA2CuKEk4BEEDAn87lb1MOQN858A4zbgxAxr1bGXJbCkBmhnTmfiQIQEFijqlG0wVAHym1XCVyA0CnPQOItwsBQFFt/U9WVf0/7BCIAiGz+D9MW1hcV0X0Py9OZFyPH/A/iDkM2y6o6D+RuSvoTefhP2RselNYNNg/4+P/D+9ozT8R4g1QH+K9P8F2xIWKAKU/lz6EBVUEcD9LT9OR/qh4P3ezzb/nNqg/Uov8b6BBwD+nQOb9kzPPPw6/v4m1UNk/0UVGLViN4j/+TjLX42HpPwbgpzn3g/A/ay3KQ+uu9D9jqwvGfR/5P6iwPPYuwv0/naGMUFJBAUCucBV8AaYDQN+0RMqjBAZAXbBClNJSCEDRFTUrb4YKQA7YgxLPlQxAnSLLSeZ3DkDa4253NxIQQPm3c8UGyhBAELGstThgEUAlPNQ7ONIRQLKR4QMPHhJAtNAhKm5CEkDKDTUYtD4SQE64P2vvEhJAQhx/1N6/EUD3davy7UYRQOeG8S8vqhBA9/Aqe6XYD0AvlommNSEOQLPtAcmaNQxArghLFEceCkCSFUXRbeQHQMNxxsnakQVA8oWfA8cwA0CTW4KNq8sAQKBaxU8m2vw/pWBeM9c++D9UfqEFr9nzPwE/WPIFfO8/8LhvSsX75z91EL1VkFPhP7V4+9k9Qdc/qWJ0K6/vyz+dwL8YN867P2Ns3wjLl6I/iU04YgQUZT/Jr6sB3kiAP8Aj8Gjzy6o/ui1BhP1FwT+rE5zAPUfQP0teZgtkJNo/BdC+8HMH4z+NCbFGKenpP6TGKzWLzPA/cGCQhcP69D+ueVVL8mz5P6GUGGysD/4/2gqld15nAUD6VEYHv8oDQGPSNOmZJwZAEZZOU7NzCEAEoGsqHqUKQPYVxu9msgxAGaj/Y7ySDkAvk6mYCh8QQHv6sv6o1hBAOBtVqi1tEUDroX16HeARQPOxVgmYLRJAHmciJV9UEkAIOoCE21MSQL+EdaceLBJAG7Hk4uHdEUAgHEqggmoRQC+vZuf70xBAWfjFUt0cEEBoxDY1f5AOQJGDP9ZtswxAZMuEiIaqCkCyGBJQfn4IQBVCkMaZOAZA7fG6goXiA0Btu3z+LIYBQKcWulEhW/4/c8ZapTfF+T++ZclH9l31P4jx0YfoN/E/iPkKY/3I6j8Dhvnhi+fjP08j+eeY0Ns/oECM65zI0T+MQlgZ6sHDPwoVZVDu6bA/UHTolvqRjT+NuId0ZOYyPyuL1FNVZ5g/CdMlO6estT/rIZeTjkTHPzwJNKKPEdQ/hSwtGYaV3j8PNxGAAoHlP0F16Gp7kew/fO9g90sv8j+/8/Qt2WP2PxlGL4TO1Po/k76TRJpv/z/+w+V+fhACQC+Wu7qsagRAjNfLEYO8BkBOfwV1T/wIQAUx4dyqIAtABFlVbaAgDUDzetvJ0vMOQEUBg39PSRBASlEyOB77EEDrfoeibIwRQNjCfW3Z+hFA1JKN7JREEkCILejEaGgSQIILQB29ZRJAY1uxOJs8EkA8kglwre0RQIHOpYc8ehFAofs3ayrkEEB1Z8tj6i0QQJxBVs7ttA5A179OVIraDEDHYulRbdQKQBx+pcMRqwhANmpODIdnBkASnznaShMEQOXn+TAhuAFAjb8Zg9a//j+WEHyB+yj6P+dQW9zuvvU/LWUM/DCU8T9+TrNPbnTrP3pjrtxDguQ/Cn139OTd3D/m3+swvafSPw9hbR5bGcU/LHzn/NW5sj8ifpDdq1aSP+BMrsV7j9U+KrdtQm0vlD/Vg51k46GzP1xb+h8WwsU/ENLDFWgT0z/LM0G9BF3dP/mZrw1TyeQ/U2ay9o3A6z8pWzEFh7vxPySqI9ZO5vU/5PGwyD9P+j801ZbiAOT+P8dXVhXGyAFAv60KQj8iBEBuTTRctHQGQIJnDiyQtghAvFIHjofeCkDsfzC+v+MMQDDr6J/yvQ5A7rurNsgyEEBhuVcj7+kQQP023ZOIgRFAhBs7bTL3EUBe9LVHF0kSQDfFtGv1dRJAZHYRZyN9EkCg88sskl4SQFnMTrvMGhJAHNKbT/WyEUASYZ01wCgRQAKYVk9sfhBA2yw763JtD0A5AZy6uakNQP7TtGbnuAtARotvUeiiCUDnenNZOnAHQBGnEjLKKQVAccm4K8/YAkBlr+n+pYYAQFN0uFxWefw/CMP/KSsI+D87XItlo8vzP+IpsRt5qe8/en6kAatm6D+03dMT4OvhPy4FLSvgpdg/zNgQqIjIzj8cunWIWW/AP+CUf2Du46k/dBf0K2/KgD/r1azI6bdfPy1CqwbrT6A/pYEKa/L0uD/0X4+W7lDJP1vxIC/eMdU/u6YRkTm33z8kLbJQOQfmP8aJr8EdA+0/isMV4LRZ8j/KfGgZuXz2P/lPwmwd2vo/auH9enxg/z+TRPFC5/4BQP4BgmjYTwRAQbVEN9eZBkD/pmeuxNMIQHe77mvB9ApAQpzt4VD0DEAjRAgOe8oOQJuKIhf2NxBApVzC+gjvEEAgiZblmocRQIttUNZJ/xFAO5nsqTZUEkCv7FqqDIUSQGk3FfkGkRJAtgKNvvN3EkD+jRwQNToSQJq8Noe/2BFAhXHKjRZVEUASvQptRrEQQLw00Wm43w9A14q9NrcnDkCwnS32ZUEMQNPbhkFbNApAbqVYO8kICECd52W4XMcFQM5R4XAaeQNA9Ve2xjonAUBNyR9oCbb9P4pcgPJQO/k/UIxJRTXw9D9JySX83+XwP8auB0/sWOo/wixiwq6l4z9eD1g6iJnbPzxpCRj3ytE/AsDtlmUNxD+4DPVzS66xP+BG/zg6/JA/CI0o1kbk+z6LudLY0hiUP4rofPBJN7M/+I9g0pstxT+HLZlBJIXSP9EPxJnyeNw/GrLFOikl5D+VbFH6/uTqP9HNG1GEMPE/PdJ7iLk99T+sVahzAYr5Pw7Q82BLBP4/L8Y2JWxNAUCk6JL8wJ0DQNBrMb0B6gVAnkMI4CApCEAPcLKjSVIKQOrhktMCXQxAF+wB+U9BDkCeq2t00PcPQLG4+ALuvBBAHpVMLM5gEUAVyBGYEeURQJFdA3S+RxJA4zjCgF+HEkBSw45HCaMSQAGkOy5dmhJAOnZvYYptEkC/p9WVTB0SQA/SRanoqhFArsQMNScYEUAn0UQqTWcQQDzZ3zAlNg9ALI1pii9tDUAu5EOEsXoLQD6OOWU/ZglA+0gq8es3B0ADI18EKfgEQHpql+qmrwJAk8Mw7zJnAEBTSxpLK0/8P3bii9Hi8vc/ESS5H0PK8z+aWPY/a8rvPzQ3mgQ1peg/GWqoyiFA4j8ZqCumD2fZPy0RBJf1KNA/i+ue9PbRwT9AD9RcKRSuPz+ODQgLHok/JNoAHVw7PT8d2nt9AwSYPzNnTA2st7Q/0wzjXisExj/SwRPcXubSPwSe/vmTvNw/BcPAiJIv5D/ONbv62dDqP9SaLDNvFPE/aX0qYNUN9T/rAUtTgEX5P+Au8lhlq/0/gf7WamUXAUBq0Xi5Q18DQIdvFnqhpAVAj90C4tveB0DoARwjegUKQMcOX31NEAxAAIU5QZD3DUDfJilOA7QPQKpIMs+EnxBAn6KGu2BJEUBqul9uDdURQJVuDXt1QBJAUbp9CP6JEkDPNrIFjbASQCY0OXeNsxJAGCzqy/GSEkAog40uNE8SQPF9t9FU6RFAVG7ZOtZiEUCIyUSZt70QQImh53ra+A9A0bqImK5DDkDYWpqhbWIMQNov76tCXApAojnmbeY4CEDa76e1gQAGQO+0RCiOuwNADVdxwbVyAUAaLewjY13+P79+j3xQ8Pk/V0U8gBmv9T94IEva+6nxP2D1ggid4Os/Bpb3s40g5T/FELFMCFvePymxGeFPPNQ/MjATodwWyD8J6im76J23P9SrHp7qep4/f8n0plUUWz960VmWOwmBPzlaIg9ra6k/3WyJtE0AwD/KxsJFptvNP4MgWBPP29c/Ht1Kp/BT4T+mwNyMYJTnPx9Lmwdcl+4/oP7+Bhch8z9bB9S11zv3P0t7Zb1bjPs/ULJyCiUBAEAPp4LcYUYCQLiVpxRSjQRAmwnaVWHNBkAWfrysGf4IQLnXwn1DFwtAySdpYQQRDUBnrAx6/OMOQO1E9eqwRBBAH0EovIz9EED6uoHX5pkRQLSoC7KAFxJASeBcFJB0EkAXjUdhxa8SQGn7fwlQyBJAjqr+HuG9EkBAPAwCrJASQESYDSllQRJAuXovCz/REUAH6OA85UERQGaKi9N1lRBAAhkjWPKcD0ApCWxqsN8NQAhuS8ii+QtAmkGV+9jxCUAMc8HG2s8HQIB8tyeMmwVAE6caLBBdA0BknTcCqxwBQHEC6mZHxf0/kefT6ktu+T+OqQn7SET1P7nICIF4VvE/eOPyC2Rm6z/DKStrbs/kPwT9V9YRAN4/EjfV05ga1D8Yot8nnCTIPx1SX67nELg/6QaCiVgxoD9uYKYohTVjPylt7dBq43o/o4A3/eGipj/jrgJQcl+9P6bqyW/nyss/3Uko8SNl1j/V0qR98lvgP1SKDqoKXOY/CttogAEd7T+Dw3F5IkPyP3lPUWBxPvY/AneA5fRx+j+w+tBFac7+P25rx077oQFA6D7tCDXhA0CdBwwjuBwGQO0DQSdoTAhASj1TJ1NoCkBBpIt5zmgMQHq3cnySRg5AQgTN/dT6D0AUIc7ysL8QQF7K1eVYZxFAaoiZEv/xEUD1cCpgqV0SQFZUQibOqBJApnaZ3FnSEkBT0pwfs9kSQAB3r/q8vhJA4AhUbteBEkBilv4u3iMSQJEhzJ8lphFA+6jcEnYKEUBC8HVfBVMQQK2toMjdBA9ATuLGJFQ3DUAxWDxE/0MLQO+rLjT7MQlADWC0pdQIB0C0TNdObdAEQNE+3QrfkAJAKlqzJF5SAEAJBMlzNjr8P87hwUxK8vc/kCMU05bc8z8L3NrmAgjwP8lefBcNBek/C3MGQe+x4j8XgoUya1vaPwikZVLlGNE/dIbymON7wz9apfj/65SxPwrNN6EFIZI/5VHkatmn4D6Fcg0ZSzWQP1A7ppjznrA/Nd9gTlLDwj8GX2Zw053QP2lFQ2Cqwdk/SAVW8NpV4j+ihmSECproP5YZSaWJlu8/f7oQqvSY8z8eaDwYQqj3P7fER1By6vs/hKilUQwoAEA/WyGKp2QCQIS3UDj4ogRA0OFeiunaBkDuSC3BgQQJQKsi/Pj+FwtAMAKSBvMNDUB2i0sEXt8OQMqDHJjjQhBAoKi/4an9EEArmrm5bZ0RQFx4Giv9HxJA8Gpi94+DEkC5kLuXzcYSQMb7k6bR6BJAN4W1pC7pEkDi3f8S78cSQM+M8t+UhRJAD5sqLhcjEkD3b8V+3qERQFUELFC/AxFAu6IMR/NKEEDGOVr4IfQOQEpfaRwFKA1AzFgNNfY3C0BAuHSH1ioJQE3tQN7pBwdA\",\"dtype\":\"float64\",\"shape\":[999]}},\"selected\":{\"id\":\"1602\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1601\",\"type\":\"UnionRenderers\"}},\"id\":\"1575\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1550\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"data_source\":{\"id\":\"1589\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1590\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1591\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1593\",\"type\":\"CDSView\"}},\"id\":\"1592\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"callback\":null},\"id\":\"1531\",\"type\":\"DataRange1d\"},{\"attributes\":{\"overlay\":{\"id\":\"1572\",\"type\":\"BoxAnnotation\"}},\"id\":\"1551\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1577\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1552\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1601\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1572\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"1570\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"click_policy\":\"hide\",\"items\":[{\"id\":\"1574\",\"type\":\"LegendItem\"},{\"id\":\"1588\",\"type\":\"LegendItem\"},{\"id\":\"1604\",\"type\":\"LegendItem\"}],\"location\":\"bottom_left\"},\"id\":\"1573\",\"type\":\"Legend\"},{\"attributes\":{\"callback\":null},\"id\":\"1533\",\"type\":\"DataRange1d\"},{\"attributes\":{\"line_color\":\"cyan\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1590\",\"type\":\"Line\"},{\"attributes\":{\"label\":{\"value\":\"L external\"},\"renderers\":[{\"id\":\"1592\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1604\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1553\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1602\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1535\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1554\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1537\",\"type\":\"LinearScale\"},{\"attributes\":{\"data_source\":{\"id\":\"1562\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1563\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1564\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1566\",\"type\":\"CDSView\"}},\"id\":\"1565\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1650\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"formatter\":{\"id\":\"1568\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1540\",\"type\":\"BasicTicker\"}},\"id\":\"1539\",\"type\":\"LinearAxis\"},{\"attributes\":{\"formatter\":{\"id\":\"1570\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1545\",\"type\":\"BasicTicker\"}},\"id\":\"1544\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1540\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1651\",\"type\":\"Selection\"},{\"attributes\":{\"ticker\":{\"id\":\"1540\",\"type\":\"BasicTicker\"}},\"id\":\"1543\",\"type\":\"Grid\"}],\"root_ids\":[\"1528\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"925a3723-11f9-41b9-b0d0-deb27d6bbcd1\",\"roots\":{\"1528\":\"107cc9f7-2804-45f9-a7bb-8f00e0de75cb\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1528"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "print(len(Larr))\n",
    "print(len(tarr))\n",
    "print(len(Earr))\n",
    "print(max(Larr))\n",
    "print(max(Earr))\n",
    "\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"Angular Momentum\", plot_width=400, plot_height=400)\n",
    "#p.line(tarr,1000*np.array(vxarr1), line_color=\"purple\",legend=\"External\")\n",
    "#p.line(tarr,np.array(ycoord1),line_color=\"green\")\n",
    "#p.line(tarr,1000*np.array(vyarr1), line_color=\"blue\")\n",
    "#p.line(tarr,np.array(xcoord1), line_color=\"yellow\")\n",
    "p.line(tarr,np.array(vxarr1)*np.array(ycoord1), line_color=\"orange\", legend=\"vx*y\")\n",
    "p.line(tarr,np.array(vyarr1)*np.array(xcoord1),line_color=\"black\", legend=\"vy*x\")\n",
    "p.line(tarr,(np.array(vxarr1)*np.array(ycoord1)-np.array(vyarr1)*np.array(xcoord1)), line_color=\"cyan\", legend=\"L external\")\n",
    "#p.line(tarr,np.array(Larr),line_color=\"blue\", legend=\"Internal\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1725\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1725\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1725\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1725' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1725\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1725\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1725\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1725' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1725\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "999\n",
      "999\n",
      "999\n",
      "-4.330637660316054\n",
      "0.0032938185187060425\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"116c6c18-22c0-4262-8d77-e68ed89a3fca\" data-root-id=\"1726\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
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\",\"dtype\":\"float64\",\"shape\":[999]}},\"selected\":{\"id\":\"1843\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1842\",\"type\":\"UnionRenderers\"}},\"id\":\"1773\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1747\",\"type\":\"PanTool\"},{\"attributes\":{\"line_color\":\"cyan\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1761\",\"type\":\"Line\"}],\"root_ids\":[\"1726\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"e5543e05-64a6-4c91-9d86-389d38f6d7df\",\"roots\":{\"1726\":\"116c6c18-22c0-4262-8d77-e68ed89a3fca\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1726"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "print(len(Larr))\n",
    "print(len(tarr))\n",
    "print(len(Earr))\n",
    "print(max(Larr))\n",
    "print(max(Earr))\n",
    "\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"Angular Momentum computed two ways\", plot_width=400, plot_height=400)\n",
    "#p.line(tarr,1000*np.array(vxarr1), line_color=\"purple\",legend=\"External\")\n",
    "#p.line(tarr,np.array(ycoord1),line_color=\"green\")\n",
    "#p.line(tarr,1000*np.array(vyarr1), line_color=\"blue\")\n",
    "#p.line(tarr,np.array(xcoord1), line_color=\"yellow\")\n",
    "#p.line(tarr,np.array(vxarr1)*np.array(ycoord1), line_color=\"orange\")\n",
    "#p.line(tarr,np.array(vyarr1)*np.array(xcoord1),line_color=\"black\")\n",
    "p.line(tarr,(np.array(vxarr1)*np.array(ycoord1)-np.array(vyarr1)*np.array(xcoord1)), line_color=\"cyan\", legend=\"L external\")\n",
    "p.line(tarr,np.array(Larr),line_color=\"blue\", legend=\"Internal\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1905\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1905\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1905\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1905' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1905\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1905\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1905\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1905' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1905\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"b41847a7-25a0-4fe3-8cc9-fa0a35911603\" data-root-id=\"1906\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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\",\"dtype\":\"float64\",\"shape\":[999]}},\"selected\":{\"id\":\"2033\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"2032\",\"type\":\"UnionRenderers\"}},\"id\":\"1953\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1932\",\"type\":\"HelpTool\"},{\"attributes\":{\"source\":{\"id\":\"1940\",\"type\":\"ColumnDataSource\"}},\"id\":\"1944\",\"type\":\"CDSView\"},{\"attributes\":{\"line_color\":\"purple\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1941\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1928\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1954\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1964\",\"type\":\"Selection\"},{\"attributes\":{\"data_source\":{\"id\":\"1953\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1954\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1955\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1957\",\"type\":\"CDSView\"}},\"id\":\"1956\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"formatter\":{\"id\":\"1946\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1918\",\"type\":\"BasicTicker\"}},\"id\":\"1917\",\"type\":\"LinearAxis\"},{\"attributes\":{\"source\":{\"id\":\"1953\",\"type\":\"ColumnDataSource\"}},\"id\":\"1957\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1915\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1955\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"2032\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1963\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"ticker\":{\"id\":\"1918\",\"type\":\"BasicTicker\"}},\"id\":\"1921\",\"type\":\"Grid\"},{\"attributes\":{\"label\":{\"value\":\"x\"},\"renderers\":[{\"id\":\"1943\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1952\",\"type\":\"LegendItem\"},{\"attributes\":{\"callback\":null},\"id\":\"1909\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1946\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"formatter\":{\"id\":\"1948\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1923\",\"type\":\"BasicTicker\"}},\"id\":\"1922\",\"type\":\"LinearAxis\"},{\"attributes\":{\"callback\":null},\"id\":\"1911\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"2033\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1913\",\"type\":\"LinearScale\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1950\",\"type\":\"BoxAnnotation\"}],\"root_ids\":[\"1906\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"9de775a3-cc0e-44c9-9881-fe9d2206f738\",\"roots\":{\"1906\":\"b41847a7-25a0-4fe3-8cc9-fa0a35911603\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1906"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "\n",
    "\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"coordinates vs time\", plot_width=400, plot_height=400)\n",
    "p.line(tarr,np.array(xcoord1), line_color=\"purple\",legend=\"x\")\n",
    "p.line(tarr,np.array(ycoord1), line_color=\"blue\", legend=\"y\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"2095\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"2095\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"2095\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2095' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"2095\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"2095\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"2095\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2095' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"2095\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "999\n",
      "999\n",
      "999\n",
      "-4.330637660316054\n",
      "0.0032938185187060425\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"e1bc04db-bb67-459f-8408-56db6d903f39\" data-root-id=\"2096\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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\",\"dtype\":\"float64\",\"shape\":[999]}},\"selected\":{\"id\":\"2233\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"2232\",\"type\":\"UnionRenderers\"}},\"id\":\"2143\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"label\":{\"value\":\"x 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\",\"dtype\":\"float64\",\"shape\":[999]}},\"selected\":{\"id\":\"2154\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"2153\",\"type\":\"UnionRenderers\"}},\"id\":\"2130\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"2118\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"callback\":null},\"id\":\"2099\",\"type\":\"DataRange1d\"},{\"attributes\":{\"data_source\":{\"id\":\"2143\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"2144\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"2145\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"2147\",\"type\":\"CDSView\"}},\"id\":\"2146\",\"type\":\"GlyphRenderer\"}],\"root_ids\":[\"2096\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"b003276b-2f9e-4df0-a996-8ea229f56000\",\"roots\":{\"2096\":\"e1bc04db-bb67-459f-8408-56db6d903f39\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2096"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "print(len(Larr))\n",
    "print(len(tarr))\n",
    "print(len(Earr))\n",
    "print(max(Larr))\n",
    "print(max(Earr))\n",
    "\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"velocity vs time\", plot_width=400, plot_height=400)\n",
    "p.line(tarr,np.array(vxarr1), line_color=\"purple\",legend=\"x velocity\")\n",
    "p.line(tarr,np.array(vyarr1),line_color=\"blue\", legend=\"y velocity\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"2295\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"2295\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"2295\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2295' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"2295\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"2295\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"2295\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2295' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"2295\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"229993dd-2def-4f52-a8bb-c8f2350ec146\" data-root-id=\"2296\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = {\"6cd689ff-37e3-4616-91dc-24c82d98dc79\":{\"roots\":{\"references\":[{\"attributes\":{\"below\":[{\"id\":\"2307\",\"type\":\"LinearAxis\"}],\"center\":[{\"id\":\"2311\",\"type\":\"Grid\"},{\"id\":\"2316\",\"type\":\"Grid\"},{\"id\":\"2341\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"2312\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"plot_width\":400,\"renderers\":[{\"id\":\"2333\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"2297\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"2323\",\"type\":\"Toolbar\"},\"x_range\":{\"id\":\"2299\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"2303\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"2301\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"2305\",\"type\":\"LinearScale\"}},\"id\":\"2296\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"2320\",\"type\":\"SaveTool\"},{\"attributes\":{\"callback\":null},\"id\":\"2299\",\"type\":\"DataRange1d\"},{\"attributes\":{\"text\":\"Angular 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Momentum\"},\"renderers\":[{\"id\":\"2333\",\"type\":\"GlyphRenderer\"}]},\"id\":\"2342\",\"type\":\"LegendItem\"},{\"attributes\":{\"ticker\":{\"id\":\"2308\",\"type\":\"BasicTicker\"}},\"id\":\"2311\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2318\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"2308\",\"type\":\"BasicTicker\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"2313\",\"type\":\"BasicTicker\"}},\"id\":\"2316\",\"type\":\"Grid\"},{\"attributes\":{\"formatter\":{\"id\":\"2338\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"2313\",\"type\":\"BasicTicker\"}},\"id\":\"2312\",\"type\":\"LinearAxis\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2332\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"2330\",\"type\":\"ColumnDataSource\"}},\"id\":\"2334\",\"type\":\"CDSView\"},{\"attributes\":{\"overlay\":{\"id\":\"2340\",\"type\":\"BoxAnnotation\"}},\"id\":\"2319\",\"type\":\"BoxZoomTool\"}],\"root_ids\":[\"2296\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"6cd689ff-37e3-4616-91dc-24c82d98dc79\",\"roots\":{\"2296\":\"229993dd-2def-4f52-a8bb-c8f2350ec146\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2296"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "# create a new plot with default tools, using figure\n",
    "p = figure(title=\"Angular Momentum\", plot_width=400, plot_height=400)\n",
    "p.line(tarr,Larr,line_color=\"purple\", legend=\"Angular Momentum\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "\n",
    "show(p) # show the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.pydata.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"2477\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"2477\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"2477\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2477' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n",
       "  var css_urls = [];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {} // ensure no trailing comma for IE\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"2477\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"2477\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"2477\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2477' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"2477\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"d1e9f437-dcc8-492e-9c5f-1e4de66408da\" data-root-id=\"2478\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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linear momentum\"},\"renderers\":[{\"id\":\"2515\",\"type\":\"GlyphRenderer\"}]},\"id\":\"2524\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"2616\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2617\",\"type\":\"Selection\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"2499\",\"type\":\"PanTool\"},{\"id\":\"2500\",\"type\":\"WheelZoomTool\"},{\"id\":\"2501\",\"type\":\"BoxZoomTool\"},{\"id\":\"2502\",\"type\":\"SaveTool\"},{\"id\":\"2503\",\"type\":\"ResetTool\"},{\"id\":\"2504\",\"type\":\"HelpTool\"}]},\"id\":\"2505\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"2499\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"2500\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"callback\":null},\"id\":\"2483\",\"type\":\"DataRange1d\"},{\"attributes\":{\"overlay\":{\"id\":\"2522\",\"type\":\"BoxAnnotation\"}},\"id\":\"2501\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"2502\",\"type\":\"SaveTool\"}],\"root_ids\":[\"2478\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"997fa2f9-164e-4a55-b0a2-ac43e0c7c018\",\"roots\":{\"2478\":\"d1e9f437-dcc8-492e-9c5f-1e4de66408da\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2478"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "# create a new plot with default tools, using figure\n",
    "xmomentum=np.array(vxarr1)+np.array(vxarr2)\n",
    "p = figure(title=\"X linear momentum\", plot_width=400, plot_height=400)\n",
    "p.triangle(tarr,xmomentum, size=1, line_color=\"purple\",fill_color=\"purple\", fill_alpha=0.5, legend=\"X linear momentum\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "p.legend.click_policy=\"hide\"\n",
    "\n",
    "show(p) # show the results "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}