Unequal Mass.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ellipsefns\n",
    "#getfocus, getsemiminor, theoreticalx, theoreticaly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import initdatuneq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "angle 0.0\n",
      "0.0\n",
      "(array([3.14159265, 0.        ]), 0.0, 25, 0.0, array([1., 1.]))\n"
     ]
    }
   ],
   "source": [
    "delta=0.005 #with dtmin=0.001, accuracy of 1e-6 appears to be too much to ask. try 0.05\n",
    "rad0=25\n",
    "ecc0=0.0 #set ecc = 0 for circle, ecc < 1 for ellepse, = 1 for parabola, >1 for hyperbola\n",
    "theta0= 0.0 #math.pi/6. #math.pi/6.\n",
    "mass0_1=1.0\n",
    "mass0_2=1.0\n",
    "initdatequneq=initdatuneq.InitialDataEqualMassConic(rad0,ecc0,theta0,mass0_1,mass0_2)\n",
    "print(initdatequneq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import getxyuvtwouneq_apper #unequal mass version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "useperihelion=True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initdat 25 [3.14159265 0.        ] 0.0 [-1.  1.] [1.2246468e-16 0.0000000e+00]\n",
      "coordsep 25\n",
      "pi\n",
      "zero\n",
      "[-25.  25.]\n",
      "[0. 0.]\n",
      "circle\n",
      "r0 50.0\n",
      "(array([1., 1.]), array([[-12.5       ,   0.        ,   0.        ,  -0.        ,\n",
      "         -0.14142136,   0.        ],\n",
      "       [ 12.5       ,   0.        ,   0.        ,  -0.        ,\n",
      "          0.14142136,   0.        ]]), array([[ 0.0016, -0.    ,  0.    ],\n",
      "       [-0.0016, -0.    ,  0.    ]]))\n"
     ]
    }
   ],
   "source": [
    "xyuvaequneq=getxyuvtwouneq_apper.getxyuvequneq(initdatequneq,useperihelion)\n",
    "print(xyuvaequneq)\n",
    "masses,xvec,avec=xyuvaequneq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import RK4implicit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RK4implicit(h,t,xvec,f): #not a finite difference so no step in y\n",
    "    k1= h*f(t,xvec)\n",
    "    k2=h*f(t+h/2, xvec+k1/2)\n",
    "    k3=h*f(t+h/2,xvec+k2/2)\n",
    "    k4=h*f(t+h,xvec+k3)\n",
    "    return t+h, xvec+1/6.*(k1+2.*k2+2.*k3+k4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import OrbitDiffEqAdaptive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 1.] [[-12.5          0.           0.          -0.          -0.14142136\n",
      "    0.        ]\n",
      " [ 12.5          0.           0.          -0.           0.14142136\n",
      "    0.        ]] 0.0\n",
      "[1. 1.] [[-12.5          0.           0.          -0.          -0.14142136\n",
      "    0.        ]\n",
      " [ 12.5          0.           0.          -0.           0.14142136\n",
      "    0.        ]] 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<OrbitDiffEqAdaptive.OrbitDiffEqAdaptive at 0x7f1e4c45b6a0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "masses, xvec,avec=xyuvaequneq\n",
    "ODEeq= OrbitDiffEqAdaptive.OrbitDiffEqAdaptive(masses,xvec,avec,0.0, delta)\n",
    "ODEeq.print2D()\n",
    "ODEeq.print2D()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([1., 1.]), array([[-12.5       ,   0.        ,   0.        ,  -0.        ,\n",
      "         -0.14142136,   0.        ],\n",
      "       [ 12.5       ,   0.        ,   0.        ,  -0.        ,\n",
      "          0.14142136,   0.        ]]), array([[ 0.0016, -0.    ,  0.    ],\n",
      "       [-0.0016, -0.    ,  0.    ]]))\n"
     ]
    }
   ],
   "source": [
    "print(xyuvaequneq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import timestepAdaptive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import parabfns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ellipsefns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import hyperbfns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "numsteps=10000 #50000\n",
    "\n",
    "#numsteps=6000*10\n",
    "\n",
    "dt=.01\n",
    "dtmax=1\n",
    "dtmin = 0.001\n",
    "outputevery=1\n",
    "nptimes, npstar1x, npstar2x, npstar1a, npstar2a,nperr,npdt= timestepAdaptive.timestepAdaptive(numsteps,dt,dtmax,dtmin,xyuvaequneq,outputevery,delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Orbit Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t= np.linspace(-math.pi,math.pi,100000)\n",
    "xax=-200+np.arange(0,400)\n",
    "plt.ylim(-200,200)\n",
    "plt.xlim(-100,100)\n",
    "#plt.axis('equal')\n",
    "mtot=masses[0]+masses[1]\n",
    "semimajor0=rad0*masses[1]/mtot\n",
    "semimajor1=rad0*masses[0]/mtot\n",
    "plt.title(\"Adaptive RK4, Rp=\"+str(rad0)+\", m1=\"+str(masses[0])+\", m2=\"+str(masses[1])+\" e=\"+str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi)))\n",
    "plt.plot(hyperbfns.getxtheory(theta0,ecc0,semimajor1,t,1),hyperbfns.getytheory(theta0,ecc0,semimajor1,t,1),'b')\n",
    "plt.plot(hyperbfns.getxtheory(theta0,ecc0,semimajor0,t,-1),hyperbfns.getytheory(theta0,ecc0,semimajor0,t,-1),'g')\n",
    "plt.plot(npstar1x[:,0],npstar1x[:,1],'k')\n",
    "plt.plot(npstar2x[:,0],npstar2x[:,1],'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t= np.linspace(-math.pi,math.pi,100000)\n",
    "xax=-200+np.arange(0,400)\n",
    "plt.ylim(-100,100)\n",
    "plt.xlim(-100,100)\n",
    "plt.axis('equal')\n",
    "mtot=masses[0]+masses[1]\n",
    "semimajor0=rad0*masses[1]/mtot\n",
    "semimajor1=rad0*masses[0]/mtot\n",
    "plt.title(\"Adaptive RK4, Rp=\"+str(rad0)+\", m1=\"+str(masses[0])+\", m2=\"+str(masses[1])+\" e=\"+str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi)))\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,semimajor0,t,1),ellipsefns.getytheory(theta0,ecc0,semimajor0,t,1),'b')\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,semimajor1,t,-1),ellipsefns.getytheory(theta0,ecc0,semimajor1,t,-1),'g')\n",
    "#plt.plot(npstar1x[:,0],npstar1x[:,1],'y')\n",
    "#plt.plot(npstar2x[:,0],npstar2x[:,1],'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t= np.linspace(0,2*math.pi,100)\n",
    "xax=-200+np.arange(0,400)\n",
    "plt.ylim(-200,200)\n",
    "plt.xlim(-200,200)\n",
    "semimajor0=rad0*masses[1]/mtot\n",
    "semimajor1=rad0*masses[0]/mtot\n",
    "plt.title(\"Adaptive RK4, Rp=\"+str(rad0)+\", m1=\"+str(masses[0])+\", m2=\"+str(masses[1])+\" e=\"+str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi)))\n",
    "#plt.title(\"Parabolic Orbit, Adaptive RK4, F=\"+str(rad0)+\", theta=\"+str(round(180*theta0/math.pi)))\n",
    "#plt.axis('equal')\n",
    "xth1=parabfns.getxtheory(theta0,ecc0,semimajor1,t,1)\n",
    "yth1=parabfns.getytheory(theta0,ecc0,semimajor1,t,1)\n",
    "xth0=parabfns.getxtheory(theta0,ecc0,semimajor0,t,-1)\n",
    "yth0=parabfns.getytheory(theta0,ecc0,semimajor0,t,-1)\n",
    "plt.plot(xth1,yth1,'b')\n",
    "plt.plot(xth0,yth0,'g')\n",
    "#plt.plot(xth1,yth1,'o')\n",
    "plt.plot(npstar1x[:,0],npstar1x[:,1],'y')\n",
    "plt.plot(npstar2x[:,0],npstar2x[:,1],'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# RK4 Quality Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "25 12.5\n",
      "[12.49999997 12.49999821  0.          0.14142135  0.14142136  0.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, 2*math.pi, 100)\n",
    "xax=np.arange(0,100*len(npstar2x[:,1]))\n",
    "xax=xax-len(xax)/2\n",
    "oneellipse=int(len(npdt))\n",
    "plt.ylim(-20,20)\n",
    "plt.xlim(-20,20)\n",
    "a=rad0/2\n",
    "print(ellipsefns.getfocus(a,ecc0))\n",
    "print(rad0,ellipsefns.getsemiminor(a,ecc0))\n",
    "print(np.max(npstar1x,axis=0))\n",
    "#plt.ylim(-1,1)\n",
    "#plt.xlim(74.999,75)\n",
    "plt.title(\"Elliptical Orbit, RK4, a=\"+str(rad0)+\", e=\"+ str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi))+ \" degrees\")\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,a,t,1),ellipsefns.getytheory(theta0,ecc0,a,t,1),'b')\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,a,t,-1),ellipsefns.getytheory(theta0,ecc0,a,t,-1),'g')\n",
    "plt.plot(npstar1x[:oneellipse,0],npstar1x[:oneellipse,1],'y')\n",
    "plt.plot(npstar2x[:oneellipse,0],npstar2x[:oneellipse,1],'r')\n",
    "plt.plot(xax, np.tan(theta0)*xax,'c')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, 2*math.pi, 100)\n",
    "xax=np.arange(0,100*len(npstar2x[:,1]))\n",
    "xax=xax-len(xax)/2\n",
    "\n",
    "#plt.ylim(-200,200)\n",
    "#plt.xlim(-200,200)\n",
    "plt.ylim(-1,1)\n",
    "plt.xlim(74.999,75)\n",
    "plt.title(\"Elliptical Orbit, RK4, a=\"+str(rad0)+\", e=\"+ str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi))+ \" degrees\")\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,1),ellipsefns.getytheory(theta0,ecc0,rad0,t,1),'b')\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,-1),ellipsefns.getytheory(theta0,ecc0,rad0,t,-1),'g')\n",
    "plt.plot(npstar1x[:oneellipse,0],npstar1x[:oneellipse,1],'*y')\n",
    "plt.plot(npstar2x[:oneellipse,0],npstar2x[:oneellipse,1],'*r')\n",
    "plt.plot(xax, np.tan(theta0)*xax,'c')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, 2*math.pi, 100)\n",
    "xax=np.arange(0,100*len(npstar2x[:,1]))\n",
    "xax=xax-len(xax)/2\n",
    "\n",
    "#plt.ylim(-200,200)\n",
    "#plt.xlim(-200,200)\n",
    "plt.ylim(-10,10)\n",
    "plt.xlim(-25,-20)\n",
    "plt.title(\"Elliptical Orbit, RK4, a=\"+str(rad0)+\", e=\"+ str(ecc0)+\", theta=\"+str(round(180*theta0/math.pi))+ \" degrees\")\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,1),ellipsefns.getytheory(theta0,ecc0,rad0,t,1),'b')\n",
    "plt.plot(ellipsefns.getxtheory(theta0,ecc0,rad0,t,-1),ellipsefns.getytheory(theta0,ecc0,rad0,t,-1),'g')\n",
    "plt.plot(npstar1x[:,0],npstar1x[:,1],'*y')\n",
    "plt.plot(npstar2x[:,0],npstar2x[:,1],'*r')\n",
    "plt.plot(xax, np.tan(theta0)*xax,'c')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00000000e+00, 4.71404521e-05, 1.36153972e-04, ...,\n",
       "       3.28050000e-03, 3.28050000e-03, 3.28050000e-03])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nperr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.xlabel(\"timestep\")\n",
    "plt.ylabel(\"Rel err: 1/30 *|x2-x1|*(h'/h)^5\")\n",
    "plt.title(\"Relative error, RK4\")\n",
    "relerrplt,=plt.plot(np.arange(2,oneellipse),nperr[2:oneellipse],'b',label=\" dtmin = \"+ str(dtmin)+\" delta = \"+str(delta))\n",
    "plt.legend(handles=[relerrplt])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This curve should be constant and about equal to delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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StFPb4ifrDWvguWvIzKxaXy2C1wNXA4dXLAvg+7VEVBN3DZmZVes1EUTEv+a/7xu8cOrnRGBmVtbJfQQnSXqpkm9IuknSmwYjuIHkriEzs2qdXD76/oh4HHgTsA3wbuALtUZVA3cNmZlV6yQRtL46DwO+GREL8Q1lZmajRieJYL6kn5ESwVxJWwDPd7JxSYdIWiypR9Kpfaz3dkkhqauzsNedu4bMzKp1ch/B8cCewJKIeErSNsBaTyBLGgPMAA4GlgPzJM2OiEVt620BnATcsI6xrxN3DZmZVVtriyAino+ImyLi0Tz/UH5K2drsC/RExJKIeBaYRfWNaJ8Bvgg83XnY/edEYGZWVufD68cDywrzy3PZCyTtBUyIiB/3tSFJJ0jqltS9cuXKfgXjriEzs2p1JoI+SdoA+DLwibWtGxEzI6IrIrrGjRvXr/25a8jMrFon5whav9z/lnRH8XUR0cnzCFYAEwrzO+Syli2AVwO/VPp2fgUwW9LUiOjuJK7+cCIwMyvr5IayM4CLSfcQbAv8t6RPd7DtecBkSZMkjQWmAbNbCyPisYjYNiImRsRE4HqgtiTgriEzs2qdtAiOAV4TEU8D5KeVLQA+29ebImK1pOnAXGAMcGFELJR0FtAdEbP7ev9Ac9eQmVm1ThLBvcAmrLmqZ2PKXTy9iog5wJy2sjN6WffATra5vpwIzMzKOkkEjwELJV1FOkdwMHCjpHMBIuLEGuMbMO4aMjOr1kki+EF+tfyynlDq5a4hM7Nqa00EEXGxpE2BHSNi8SDEVCsnAjOzsk6uGjqcdHL4p3l+T0mDeqJ3ILhryMysWic3lJ1JGi7iUYCIWADsXFtENXHXkJlZtU4SwaqIeKytrKPRR4cjJwIzs7JOThYvlPQuYIykycCJwG/rDWvguWvIzKxaJy2CjwF/CTwDXEK6nPSkOoOqg7uGzMyqddIieEtEnA6c3iqQdBTw3dqiqpETgZlZWSctgtM6LBvW3DVkZlat1xaBpENJj6cc37qLOHspsLruwAaau4bMzKr11TV0L9ANTAXmF8qfAD5eZ1B1ciIwMyvrNRFExM3AzZIuiYhVAJK2Ij1R7JHBCnCguGvIzKxaJ+cIrpL0UklbAzcB50s6p+a4auMWgZlZWSeJ4GUR8TjwNuCbEbEf8MZ6wxp4bhGYmVXrJBFsKGk74B3AlTXHUxufLDYzq9ZJIjiL9JSxuyJinqSdgTvrDas+TgRmZmWdDEP9XQo3j0XEEuDtdQZVB3cNmZlV62QY6l0l/ULSbXl+jw4fXj8suUVgZlbWSdfQ+aQ7iVcBRMQtwLQ6gzIzs8HTSSLYLCJubCvr6M5iSYdIWiypR9KpFcs/JOlWSQsk/UbSlE622x/uGjIzq9ZJInhQ0i6kB9cj6UjgvrW9SdIYYAZwKDAFOLrii/6SiPiriNgT+BLw5XWIvV/cNWRmVtbJ6KMfBWYCu0taASwFju3gffsCPfnkMpJmAUcAi1or5PsTWjYnJ5s6uEVgZlatk6uGlgAHSdoc2CAinuhw2+OBZYX55cB+7StJ+ihwMjAWeEOH2+43twjMzMrWmggkbQm8B5hIurkMgIg4cSACiIgZwIz8FLRPA++tiOEE4ASAHXfcsZ/7WY8gzcxGsU66huYA1wO3sm7PKl4BTCjM75DLejML+K+qBRExk9Q9RVdX13p9pbtFYGZW1kki2CQiTu7HtucBkyVNIiWAacC7iitImhwRrbuU30KNdyy7RWBmVq2TRPAtSR8kjTP0TKswIh7u600RsVrSdNLwFGOACyNioaSzgO6ImA1Ml3QQ6R6FR6joFhpobhGYmZV1kgieBc4mPbO49bs6gJ3X9saImEPqWiqWnVGYPqnjSM3MrBadJIJPAK+MiAfrDqZO7hoyM6vWyQ1lPcBTdQcyWNw1ZGZW1kmL4E/AAknXUD5HMCCXjw4WtwjMzKp1kgiuyK9RwS0CM7OyTu4svngwAqmbWwRmZtV6TQSSLouId0i6lYoxgCJij1ojq4lbBGZmZX21CFqXdr51MAIxM7Oh0etVQxHRGmr6IxFxT/EFfGRwwhs47hoyM6vWyeWjB1eUHTrQgQwWdw2ZmZX1dY7gw6Rf/jtLuqWwaAvguroDG2huEZiZVevrHMElwE+AzwPFx0w+sbZxhoYztwjMzMp6TQQR8RjwGHD04IVTH7cIzMyqdXKOYFRxi8DMrKwxicAtAjOzao1JBC1uEZiZlTUuEZiZWVljEoG7hszMqjUmEbS4a8jMrKwxicAtAjOzao1JBC1uEZiZlTUmEbhFYGZWrdZEIOkQSYsl9Ug6tWL5yZIWSbpF0i8k7VRnPGmfde/BzGxkqS0RSBoDzCCNVDoFOFrSlLbV/gfoyg+5uRz4Ul3xmJlZtTpbBPsCPRGxJCKeBWYBRxRXiIhrIuKpPHs9sENdwbhryMysWp2JYDywrDC/PJf15njSaKcvIukESd2SuleuXLleQblryMysbFicLJZ0LNAFnF21PCJmRkRXRHSNGzeuX/twi8DMrFpfzyNYXyuACYX5HXJZiaSDgNOB10fEMzXGk/dX9x7MzEaWOlsE84DJkiZJGgtMA2YXV5D0WuDrwNSIeKDGWNwiMDPrRW2JICJWA9OBucDtwGURsVDSWZKm5tXOBl4CfFfSAkmze9ncgHGLwMysrM6uISJiDjCnreyMwvRBde6/vN/B2pOZ2cgyLE4WDya3CMzMyhqXCMzMrKwxicBdQ2Zm1RqTCFrcNWRmVtaYROAWgZlZtcYkgha3CMzMyhqTCNwiMDOr1phE0OIWgZlZWeMSgZmZlTUmEbhryMysWmMSQYu7hszMyhqTCNwiMDOr1phE0OIWgZlZWWMSgVsEZmbVGpMIWtwiMDMra0wicIvAzKxaYxJBi1sEZmZljUsEZmZW1phE4K4hM7NqjUkELe4aMjMra0wicIvAzKxarYlA0iGSFkvqkXRqxfK/k3STpNWSjqwzljX7HIy9mJmNHLUlAkljgBnAocAU4GhJU9pW+wNwHHBJXXG0uEVgZlZtwxq3vS/QExFLACTNAo4AFrVWiIi787Lna4yjxC0CM7OyOruGxgPLCvPLc9k6k3SCpG5J3StXrhyQ4MzMLBkRJ4sjYmZEdEVE17hx4/q5jQEOysxslKgzEawAJhTmd8hlQ8pdQ2ZmZXUmgnnAZEmTJI0FpgGza9xfn9wiMDOrVlsiiIjVwHRgLnA7cFlELJR0lqSpAJL2kbQcOAr4uqSFdcXT4haBmVlZnVcNERFzgDltZWcUpueRuoxq5xaBmVm1EXGyeCC5RWBmVtaYROAWgZlZtcYkgha3CMzMyhqXCMzMrKwxicBdQ2Zm1RqTCFrcNWRmVtaYROAWgZlZtcYkgha3CMzMyhqTCNwiMDOr1phE0OIWgZlZWeMSgZmZlTUmEbhryMysWmMSQYu7hszMyhqTCNwiMDOr1phE0OIWgZlZWWMSwW67wVFHwZgxQx2JmdnwUuuDaYaTqVPTy8zMyhrTIjAzs2pOBGZmDedEYGbWcLUmAkmHSFosqUfSqRXLN5Z0aV5+g6SJdcZjZmYvVlsikDQGmAEcCkwBjpY0pW2144FHIuKVwDnAF+uKx8zMqtXZItgX6ImIJRHxLDALOKJtnSOAi/P05cAbJV/pb2Y2mOpMBOOBZYX55bmscp2IWA08BmzTviFJJ0jqltS9cuXKmsI1M2umEXGyOCJmRkRXRHSNGzduqMMxMxtV6ryhbAUwoTC/Qy6rWme5pA2BlwEP9bXR+fPnPyjpnn7GtC3wYD/fO1K5zs3gOjfD+tR5p94W1JkI5gGTJU0ifeFPA97Vts5s4L3A74Ajgasj+h4eLiL63SSQ1B0RXf19/0jkOjeD69wMddW5tkQQEaslTQfmAmOACyNioaSzgO6ImA1cAHxLUg/wMClZmJnZIKp1rKGImAPMaSs7ozD9NHBUnTGYmVnfRsTJ4gE0c6gDGAKuczO4zs1QS521li55MzMb5ZrWIjAzszZOBGZmDdeYRLC2AfBGCkkTJF0jaZGkhZJOyuVbS7pK0p3571a5XJLOzfW+RdJehW29N69/p6T3DlWdOiVpjKT/kXRlnp+UByvsyYMXjs3lvQ5mKOm0XL5Y0puHqCodkbSlpMsl3SHpdkkHjPbjLOnj+d/1bZK+I2mT0XacJV0o6QFJtxXKBuy4Stpb0q35Ped2NGxPRIz6F+ny1buAnYGxwM3AlKGOq5912Q7YK09vAfyeNKjfl4BTc/mpwBfz9GHATwAB+wM35PKtgSX571Z5equhrt9a6n4ycAlwZZ6/DJiWp78GfDhPfwT4Wp6eBlyap6fkY78xMCn/mxgz1PXqo74XAx/I02OBLUfzcSYNObMU2LRwfI8bbccZ+DtgL+C2QtmAHVfgxryu8nsPXWtMQ/2hDNIHfwAwtzB/GnDaUMc1QHX7IXAwsBjYLpdtByzO018Hji6svzgvPxr4eqG8tN5we5HuTP8F8AbgyvyP/EFgw/ZjTLp35YA8vWFeT+3HvbjecHuR7rJfSr6go/34jcbjzJqxx7bOx+1K4M2j8TgDE9sSwYAc17zsjkJ5ab3eXk3pGupkALwRJzeFXwvcALw8Iu7Li/4IvDxP91b3kfaZfAU4BXg+z28DPBppsEIox9/bYIYjqc6TgJXAf+fusG9I2pxRfJwjYgXwH8AfgPtIx20+o/s4twzUcR2fp9vL+9SURDDqSHoJ8D3gnyLi8eKySD8FRs11wZLeCjwQEfOHOpZBtCGp++C/IuK1wJ9IXQYvGIXHeSvS0PSTgO2BzYFDhjSoITAUx7UpiaCTAfBGDEkbkZLAtyPi+7n4fknb5eXbAQ/k8t7qPpI+k78Bpkq6m/RcizcAXwW2VBqsEMrxv1A3lQczHEl1Xg4sj4gb8vzlpMQwmo/zQcDSiFgZEauA75OO/Wg+zi0DdVxX5On28j41JRG8MABevuJgGmnAuxEnXwFwAXB7RHy5sKg1gB/57w8L5e/JVx/sDzyWm6BzgTdJ2ir/EntTLht2IuK0iNghIiaSjt3VEXEMcA1psEJ4cZ1bn0VxMMPZwLR8tckkYDLpxNqwExF/BJZJ2i0XvRFYxCg+zqQuof0lbZb/nbfqPGqPc8GAHNe87HFJ++fP8D2FbfVuqE+aDOLJmcNIV9jcBZw+1PGsRz3+ltRsvAVYkF+HkfpGfwHcCfwc2DqvL9IjQ+8CbgW6Ctt6P9CTX+8b6rp1WP8DWXPV0M6k/+A9wHeBjXP5Jnm+Jy/fufD+0/NnsZgOrqYY4rruCXTnY30F6eqQUX2cgX8D7gBuA75FuvJnVB1n4DukcyCrSC2/4wfyuAJd+fO7CziPtgsOql4eYsLMrOGa0jVkZma9cCIwM2s4JwIzs4ZzIjAzazgnAjOzhnMisGEtj8D5kcL89pIur3F/e0o6rK7tDxRJF0k6cu1rmq2dE4ENd1uSRpkEICLujYg6vwD3JN2XMWoV7tI1A5wIbPj7ArCLpAWSzpY0sTWOu6TjJF2Rx2+/W9J0SSfnQdqul7R1Xm8XST+VNF/SryXtnsuPUhr3/mZJv8p3nZ8FvDPv752SNs/jx9+Yt3tEYd8/lPTLPB78v1YFL+lJSZ/L+7he0stzeekXvaQn898DJV2bt71E0hckHZP3f6ukXQqbP0hSt6Tf5/GYWs9sOFvSPKXx6/9PYbu/ljSbdLeu2RpDfZedX3719eLFw/W+ME8aq76H9FyGcaTRJz+Ul51DGpAP0h2bk/P0fqShCCDdqTk+T29Z2OZ5hf39O3Bsax3S3emb5/XuI90RuinpTs6uivgDODxPfwn4dJ6+CDiysN6T+e+BwKOk4YQ3Jo0T82952UnAVwrv/ynpx9xk0h2qmwAnFPaxMenO5El5u38CJg31MfVr+L3cRLSR7pqIeAJ4QtJjwI9y+a3AHkqjtP418F2teVDTxvnvdcBFki4jDXBW5U2kAe/+Oc9vAuyYp6+KiIcAJH2fNPxHd9v7nyWNqw9pSOWDO6jTvMhDEku6C/hZoU5/X1jvsoh4HrhT0hJg9xzvHoXWxstIieJZ4MaIWNrB/q1hnAhspHumMP18Yf550r/vDUjj2e/Z/saI+JCk/YC3APMl7V2xfQFvj4jFpcL0vvbxWarGa1kVEa3y51jzf251jg1JG5CeQNZpnXrbX+R4PxYRpYHlJB1IahGYvYjPEdhw9wSp66dfIj2rYamko+CFZ8C+Jk/vEhE3RMQZpIfATKjY31zgY3kkRyS9trDsYKVnzW4K/AOphdGpu4FW4pkKbLSudQOOkrRBPm+wM2mAtbnAh5WGKkfSrkoPtDHrlROBDWu56+W6fFL37H5u5hjgeEk3AwtJDz8BODufgL0N+C3pObfXAFNaJ4uBz5C+pG+RtDDPt9xIei7ELcD3IqK9W6gv5wOvzzEdQP9+rf8hx/AT0rmRp4FvkE4G35Tr9XXc8re18OijZv0g6TjSyeHpQx2L2fpyi8DMrOHcIjAzazi3CMzMGs6JwMys4ZwIzMwazonAzKzhnAjMzBrufwG94VoB1VIurQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.xlabel(\"timestep number\")\n",
    "plt.ylabel(\"timestep size\")\n",
    "plt.title(\"Evolution of timestep with step\")\n",
    "relerrplt,=plt.plot(np.arange(2,oneellipse),npdt[2:oneellipse],'b',label=\" dtmin = \"+ str(dtmin)+\" delta = \"+str(delta))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For appropriately set tolerances, adaptive timestep no longer has feedback issues. Tol=delta=0.0005 or less. The important thing is that this curve is smooth and has no constant regions where the value is pinned to either the maximum or minimum. We also seek reasonable starting values for the timestep. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.title(\"horizontal position vs relative error\")\n",
    "plt.plot(npstar1x[2:oneellipse,0], nperr[2:oneellipse],'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"y\")\n",
    "plt.ylabel(\"rel error\")\n",
    "plt.title(\"y vs rel error\")\n",
    "plt.plot(npstar1x[2:oneellipse,1],nperr[2:oneellipse])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"rel error\")\n",
    "plt.title(\"r vs rel error\")\n",
    "rstar1x=np.sqrt(npstar1x[:,0]**2+npstar1x[:,1]**2)\n",
    "plt.plot(rstar1x[2:oneellipse],nperr[2:oneellipse],'*b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"r\")\n",
    "plt.title(\"r vs t\")\n",
    "plt.plot(nptimes[2:oneellipse], rstar1x[2:oneellipse], '*b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "thetaellipse = np.arctan2(npstar1x[2:oneellipse,1],npstar1x[2:oneellipse,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"theta\")\n",
    "plt.title(\"theta vs t\")\n",
    "plt.plot(nptimes[2:oneellipse],thetaellipse,'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"theta\")\n",
    "plt.ylabel(\"rel error\")\n",
    "plt.title(\"rel error vs theta\")\n",
    "plt.plot(thetaellipse, nperr[2:oneellipse],'*b')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conservation of angular momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Lstability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.3032610005507655e-11, -1.1785113019581408)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaL, Lavg, Lavg2, Ltot,npcm, npvcm =Lstability.Lstability(npstar1x,npstar2x,masses)\n",
    "deltaL, Lavg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.892930422466633e-11"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaL*Lavg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nptimes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Ltot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391],\n",
       "       [ 0.        ,  0.        , -3.53553391]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ltot[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1e4704a190>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(nptimes,Ltot[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit conserves angular momentum to a tolerance of deltaL. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conservation of Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Estability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.909724817079113e-11, -0.020000000000659757)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaE, Eavg,Etot,Ekinetic,Egrav = Estability.Estability(npstar1x, npstar2x, masses)\n",
    "deltaE, Eavg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.8194496342842216e-13"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltaE*Eavg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1e471726a0>]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimes,Etot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1e47235dc0>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimes,Ekinetic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1e4968e850>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimes,Egrav)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1e47111fd0>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nptimes,(Ekinetic+1/2*Egrav)/Ekinetic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit conserves energy to a relative error of deltaE. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symmetry of the two stars orbits with respect to eachother "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import orbitSymmetricTol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcancelsx, allcancelsa=orbitSymmetricTol.howSymmetric(npstar1x,npstar2x,npstar1a,npstar2a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcancelsx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit is symmetric with respect to x and v up to a tolerance of allcancelsx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "allcancelsa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "npstar1x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbit is symmetric with respect to a to up to or better than a tolerance of allcancelsa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing for precision in perihelion and aphelion recovery from knowledge of the initial angle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import aeTest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.plot( np.abs(npstar1x[:,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findPerapHelionThetaIsZero(npstar1x,ecc0,rad0,useperihelion):\n",
    "    maxindex=len(npstar1x[:,1])\n",
    "    apindex=np.argmin(np.abs(npstar1x[10:int(maxindex/2),1]))+1\n",
    "    print(apindex)\n",
    "    delta=math.floor(.2*apindex)\n",
    "    print(delta)\n",
    "    perindex=np.argmin(np.abs(npstar1x[delta:apindex-delta,1]))+delta\n",
    "    print(perindex)\n",
    "    print(apindex/perindex)\n",
    "    if np.abs(apindex/perindex-2.)>0.05: \n",
    "        perindex=np.argmin(np.abs(npstar1x[apindex+delta:2*apindex+delta,1]))+delta+apindex\n",
    "        print(perindex)\n",
    "        apindex,perindex=perindex,apindex\n",
    "        print(apindex,perindex)\n",
    "        print(apindex/perindex)\n",
    "    #apindex3=np.argmin(np.abs(npstar1x[100:apindex2-100,1]))+100\n",
    "    #apindex4=np.argmin(np.abs(npstar1x[100:apindex3-100,1]))+100\n",
    "    #perindex=np.argmin(np.abs(npstar1x[100:apindex2-100,1]))+100\n",
    "    if useperihelion:\n",
    "        apindex,perindex=perindex,apindex\n",
    "    coordap=[npstar1x[apindex,0],npstar1x[apindex,1]]\n",
    "    coordper=[npstar1x[perindex,0],npstar1x[perindex,1]]\n",
    "    ra=np.sqrt(np.sum(np.array(coordap)**2))\n",
    "    rp=np.sqrt(np.sum(np.array(coordper)**2))\n",
    "    e=(ra-rp)/(ra+rp)\n",
    "    a=1./2.*(ra+rp)\n",
    "    deltae=np.abs(e-ecc0)/ecc0\n",
    "    deltaa=np.abs(a-rad0)/rad0\n",
    "    return apindex,perindex,coordap,coordper,ra,rp,e,a,deltae,deltaa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if theta0==0:\n",
    "    apindex,perindex,coordap,coordper,ra,rp,e,a,deltae,deltaa=findPerapHelionThetaIsZero(npstar1x,ecc0,rad0,useperihelion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if theta0!=0:\n",
    "    perindex,apindex,coordper,coordap,rp,ra,e,a,deltae,deltaa=aeTest.findPerApHelion(npstar1x,theta0,ecc0,rad0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recovered perihelion radius given by r_per, recovered aphelion radius given by r_ap, a is semimajor axis computed from the orbit, e is eccentricty computed from the orbit, delta a is relative error on the semimajor axis, and delta e is eccenticity relative error. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "apindex,perindex,coordap,coordper,ra,rp,e,a,deltae,deltaa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimes[:perindex],npstar1x[:perindex,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit t as a function of the eccentric anomoly (angle from the center of the elipse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findEccentricAnomoly(coordap, coordper):\n",
    "    Ecenter=np.array(coordap)+np.array(coordper)\n",
    "    Ecenter/=2.\n",
    "    return Ecenter\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ellipsecenter=findEccentricAnomoly(coordap,coordper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ellipsecenter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getEllipsecenter(ecc,rad,theta, useperihelion):\n",
    "    #ind of use perihelion\n",
    "    rp=rad*(1-ecc)\n",
    "    ra=-rad*(1+ecc)\n",
    "    rcent=(rp+ra)/2\n",
    "    #print(rp,ra,rcent)\n",
    "    rcentx=rcent*np.cos(theta)\n",
    "    rcenty=rcent* np.sin(theta)\n",
    "    return [rcentx,rcenty]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(np.array(coordap)+np.array(coordper))/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "getEllipsecenter(ecc0,rad0,theta0, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.arctan2(-1.,0)/math.pi*180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getEang(npstar2x,ecc,rad,theta, useperihelion):\n",
    "    ellipsecenter=getEllipsecenter(ecc,rad,theta, useperihelion)\n",
    "    #print(ellipsecenter)\n",
    "    #print(npstar1x)\n",
    "    #print(npstar1x[:,0])\n",
    "    xfortan=npstar2x[:,0]-ellipsecenter[0]\n",
    "    yfortan=npstar2x[:,1]-ellipsecenter[1]\n",
    "    #print(\"xy\",xfortan,yfortan)\n",
    "    Eang=np.arctan2(yfortan,xfortan)\n",
    "    Eangtheta=2*np.arctan2(np.sqrt(1-ecc)*np.sin(theta/2.),np.sqrt(1+ecc)*np.cos(theta/2.))\n",
    "    Eang-=Eangtheta\n",
    "    #if useperihelion:\n",
    "    #    Eang-=math.pi\n",
    "    print(len(Eang))\n",
    "    for i in np.arange(len(Eang)):\n",
    "        #if xfortan[i]<0:\n",
    "        #    Eang[i]+=math.pi\n",
    "        if Eang[i]<0:\n",
    "            Eang[i]+=2*math.pi\n",
    "    print(xfortan,yfortan,Eang/math.pi*180)\n",
    "    print(\"Eang\",Eang)\n",
    "    return xfortan, yfortan,Eang"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.arctan2(-6.69327422*10**-6, -0.02240526)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def xofeccanom(rad,Eang,ecc):\n",
    "    return rad*(np.cos(Eang)+ecc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def yofeccanom(rad, Eang, ecc):\n",
    "    b=getsemiminor(rad,ecc)\n",
    "    return b*np.sin(Eang) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tofEccAnom(npstar2x, rad,ecc,theta,mass, useperihelion):\n",
    "    xE0,yE0,Eang=getEang(npstar2x,ecc,rad,theta, useperihelion)\n",
    "    b=getsemiminor(rad,ecc)\n",
    "    #fitval=rad*b*(Eang-ecc*np.sin(Eang))\n",
    "    sgn=-1\n",
    "    if useperihelion:\n",
    "        sgn*=-1\n",
    "    # added a factor of 2 in front of fitval\n",
    "    fitval=rad**(1.5)*mass**(-.5)*(Eang-sgn*ecc*np.sin(Eang))\n",
    "    fitval*=2\n",
    "    print(Eang, ecc,rad,mass,fitval)\n",
    "    return fitval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def residualtEang(pars,nptimes,npstar2x):\n",
    "    residual=np.abs(nptimes-tofEccAnom(npstar2x,pars['rad'],pars['ecc'],pars['theta'],pars['mass'],pars['useperihelion']))\n",
    "    #print(nptimes, residual)\n",
    "    return residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "endindex=apindex\n",
    "if useperihelion:\n",
    "    endindex=perindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "endindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xE0,yE0,Eang0=getEang(npstar2x[0:endindex-1,:],ecc0,rad0,theta0, useperihelion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nptimesoneorbit=nptimes[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(Eang0, xE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(Eang0, yE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(xE0,yE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,xE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,yE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,yE0/xE0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.arctan(0./1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "yE0[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xE0[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,np.arctan2(yE0,xE0)*180/math.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Eangtest=tofEccAnom(npstar2x[0:endindex-1,:],rad0,ecc0,theta0,masses[0], useperihelion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.max(Eangtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nptimes[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nptimesoneorbit=nptimes[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tpredoneorbit=Eangtest[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Eangoneorbit=Eang0[0:endindex-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,npstar2x[0:endindex-1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,Eangoneorbit/math.pi*180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,tpredoneorbit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(nptimesoneorbit,tpredoneorbit, label='times')\n",
    "plt.xlabel(\"T timesteps\")\n",
    "plt.ylabel(\"T computed from angle\")\n",
    "plt.title(\"Times using start parameters\")\n",
    "plt.show()\n",
    "plt.plot(nptimesoneorbit,tpredoneorbit-nptimesoneorbit, label='residual')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(nptimesoneorbit,tpredoneorbit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lmfit import Minimizer,Parameters\n",
    "pfittEang = Parameters()\n",
    "pfittEang.add(name='theta', value=theta0, min=theta0-math.pi, max=theta0+math.pi, vary=True)\n",
    "pfittEang.add(name='rad', value=rad0, min=0, vary=True)\n",
    "pfittEang.add(name='ecc', value=ecc0, min=0, max=1.0, vary=True)\n",
    "pfittEang.add(name='mass', value=masses[0], vary=False)\n",
    "pfittEang.add(name='useperihelion', value=True, vary=False)\n",
    "\n",
    "minit = Minimizer(residualtEang, pfittEang, fcn_args=(nptimesoneorbit,npstar2x[:endindex-1,:]))\n",
    "\n",
    "outt = minit.leastsq()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "outt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Semimajor axis fit is good to about .1 percent at an eccentricity of 0.5. rad=49.886512 for delta=0.0001. rad=49.8863857 for delta = 0.0005. ecc = 0.51764747 for delta = 0.0001. ecc = 0.51765166 for delta = 0.0005. so both ecc and rad improve with a smaller delta, but not quickly. The program runs very slowly for large delta and requires 500000 timesteps for delta=0.0001. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tfinal=nptimesoneorbit[endindex-2]\n",
    "tfinal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fft import fft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import blackman\n",
    "wndow=blackman(len(nptimesoneorbit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ftresiduals=fft(nptimesoneorbit-tpredoneorbit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xf = np.linspace(0.0, 1.0/(2.0*dt), len(nptimesoneorbit)//2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.semilogy(xf[1:len(nptimesoneorbit)//2], 2.0/len(nptimesoneorbit) * np.abs(ftresiduals[1:len(nptimesoneorbit)//2]), '-b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ftr=fft(np.sqrt(npstar1x[:endindex-1,0]**2+npstar1x[:endindex-1,1]**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.xlabel(\"frequency\")\n",
    "plt.ylabel(\"Fourier transform of t(E)\")\n",
    "plt.title(\"Fourier transform of time computed from eccentric anomaly\")\n",
    "plt.semilogy(xf[1:len(nptimesoneorbit)//2], 2.0/len(nptimesoneorbit) * np.abs(ftr[1:len(nptimesoneorbit)//2]), '-b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the fourier transform of the triangle wave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.title(\"Fourier transform of residuals of times\")\n",
    "plt.xlabel(\"frequency\")\n",
    "plt.ylabel(\"FT(t(E))\")\n",
    "plt.semilogy(xf[1:50], 2.0/len(nptimesoneorbit) * np.abs(ftresiduals[1:50]), '-b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.xlabel(\"bin number\")\n",
    "plt.ylabel(\"FT(t(E))\")\n",
    "plt.title(\"Fourier transform of residuals of times\")\n",
    "plt.semilogy(np.arange(1,30), 2.0/len(nptimesoneorbit[:29]) * np.abs(ftresiduals[1:30]), '*b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Peak at the second harmonic and the sixth harmonic. The second harmonic seems natural due to the symmetry of the orbit but the sixth harmonic is harder to explain. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementing the Adaptive RK4 hasn't changed the fit, residuals, or harmonics, sadly. There is still a 2% error in the fit for an eccentricity of 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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