From 3de0d69af7fe1b3c2691c0ee7a3f4dfa56c72e00 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Juan=20Luis=20Cano=20Rodr=C3=ADguez?= Date: Sat, 22 Mar 2014 15:17:57 +0100 Subject: [PATCH] Completada clase 6b --- Notebooks/Clase6b_Finale.ipynb | 365 +++++++++++++++++++++++++++------ 1 file changed, 303 insertions(+), 62 deletions(-) diff --git a/Notebooks/Clase6b_Finale.ipynb b/Notebooks/Clase6b_Finale.ipynb index 3de5f47..6bd0067 100644 --- a/Notebooks/Clase6b_Finale.ipynb +++ b/Notebooks/Clase6b_Finale.ipynb @@ -47,6 +47,13 @@ "" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Inspiraci\u00f3n: http://pybonacci.wordpress.com/2012/10/15/el-salto-de-felix-baumgartner-en-python/" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -106,7 +113,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "$$T(h) = \\begin{cases} T_0 - \\lambda h & 0 < h <= 11000 \\\\ T(11000) & 11000 < h <= 20000 \\end{cases}\n", + "$$T(h) = \\begin{cases} T_0 + \\lambda h & 0 <= h <= 11000 \\\\ T(11000) & 11000 < h \\end{cases}\n", "\\\\ ~\\\\ T_0 = 288.16 K \\\\\n", "\\lambda = -6.5 \\cdot 10^{-3}~\\text{K/m}$$" ] @@ -127,12 +134,50 @@ " T : Temperatura en Kelvin.\n", "\n", " \"\"\"\n", - " pass" + " T0 = 288.16 # K\n", + " ll = -6.5e-3 # K / m\n", + " if 0 <= h <= 11000:\n", + " T = T0 + ll * h\n", + " elif 11000 < h:\n", + " T = T0 + ll * 11000\n", + " # Es preferible que la funci\u00f3n tenga solo un `return`\n", + " return T" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 16 + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "help(T_ISA)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Help on function T_ISA in module __main__:\n", + "\n", + "T_ISA(h)\n", + " Temperatura en funci\u00f3n de la altitud seg\u00fan modelo ISA.\n", + " \n", + " Argumentos\n", + " ----------\n", + " h : Altura en metros.\n", + " \n", + " Devuelve\n", + " --------\n", + " T : Temperatura en Kelvin.\n", + "\n" + ] + } + ], + "prompt_number": 4 }, { "cell_type": "markdown", @@ -152,69 +197,237 @@ ], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "$$ \\rho(h) = \\begin{cases} \\rho_0 \\left( \\frac{T}{T_0} \\right)^{-\\frac{g}{\\lambda R}} & 0 <= h <= 11000 \\\\ \\rho(11000)~e^{\\frac{-g(z - 11000)}{R T}} & 11000 < h <= 20000 \\end{cases} $$" + "
**\u00a1Importante!** Si utilizas condicionales para comprobar las capas de la atm\u00f3sfera, seguramente tus funciones fallar\u00e1n si las quieres representar utilizando un `linspace`. Para estos casos es mejor utilizar la funci\u00f3n `np.select`:
" ] }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def T_ISA(h):\n", + " \"\"\"Temperatura en funci\u00f3n de la altitud seg\u00fan modelo ISA.\n", + "\n", + " Argumentos\n", + " ----------\n", + " h : Altura en metros.\n", + "\n", + " Devuelve\n", + " --------\n", + " T : Temperatura en Kelvin.\n", + "\n", + " \"\"\"\n", + " # Con esta l\u00ednea convertimos la entrada a un array\n", + " h = np.asarray(h)\n", + "\n", + " T0 = 288.16 # K\n", + " ll = -6.5e-3 # K / m\n", + "\n", + " T1 = T0 + ll * h\n", + " T2 = T0 + ll * 11000\n", + "\n", + " # 0 <= h <= 110000 no funciona para arrays\n", + " T = np.select([(0 <= h) & (h <= 11000), 11000 < h], [T1, T2])\n", + " return T" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 29 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "T_ISA(0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 30, + "text": [ + "288.16000000000003" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "T_ISA(np.array([0, 11000, 20000]))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 31, + "text": [ + "array([ 288.16, 216.66, 216.66])" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Como hemos puesto `h = np.asarray(h)`, podemos hacer esto\n", + "T_ISA([0, 11000, 20000])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 32, + "text": [ + "array([ 288.16, 216.66, 216.66])" + ] + } + ], + "prompt_number": 32 + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "$$\\rho_0 = 1.225~\\text{[SI]} \\\\\n", - "R = 287~\\text{[SI]}$$" + "Otra forma alternativa (idea de Alfredo y Laura):" ] }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def T_ISA(h):\n", + " \"\"\"Temperatura en funci\u00f3n de la altitud seg\u00fan modelo ISA.\n", + "\n", + " Argumentos\n", + " ----------\n", + " h : Altura en metros.\n", + "\n", + " Devuelve\n", + " --------\n", + " T : Temperatura en Kelvin.\n", + "\n", + " \"\"\"\n", + " # Con esta l\u00ednea convertimos la entrada a un array\n", + " h = np.atleast_1d(h)\n", + "\n", + " T0 = 288.16 # K\n", + " ll = -6.5e-3 # K / m\n", + "\n", + " T = np.zeros_like(h, dtype=float)\n", + "\n", + " T[(0 <= h) & (h <= 11000)] = T0 + ll * h[(0 <= h) & (h <= 11000)]\n", + " T[11000 < h] = T0 + ll * 11000\n", + "\n", + " return T" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 33 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "T_ISA(0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 35, + "text": [ + "array([ 288.16])" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "T_ISA([0, 11000, 20000])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 36, + "text": [ + "array([ 288.16, 216.66, 216.66])" + ] + } + ], + "prompt_number": 36 + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "
**\u00a1Importante!** Si utilizas condicionales para comprobar las capas de la atm\u00f3sfera, seguramente tus funciones fallar\u00e1n si las quieres representar utilizando un `linspace`. Para estos casos es mejor utilizar la funci\u00f3n `np.select`:
" + "$$ \\rho(h) = \\begin{cases} \\rho_0 \\left( \\frac{T}{T_0} \\right)^{-\\frac{g}{\\lambda R} - 1} & 0 <= h <= 11000 \\\\ \\rho(11000)~e^{\\frac{-g(z - 11000)}{R T}} & 11000 < h <= 20000 \\end{cases} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Ejemplo**:\n", - "\n", - "$$ f(x) = \\begin{cases} -x & x < 0 \\\\ x & x > 0 \\end{cases}$$" + "$$\\rho_0 = 1.225~\\text{[SI]} \\\\\n", + "R = 287~\\text{[SI]}$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ - "import numpy as np\n", + "def rho_ISA(h):\n", + " h = np.asarray(h)\n", "\n", - "def f(x):\n", - " cond_1 = x < 0\n", - " cond_2 = x > 0\n", + " T0 = 288.16 # K\n", + " ll = -6.5e-3 # K / m\n", + " g = 9.8 # m / s2\n", + " rho0 = 1.225 # kg / m3\n", + " R = 287.0 # [SI]\n", "\n", - " f_1 = -x\n", - " f_2 = x\n", - " \n", - " fx = np.select([cond_1, cond_2], [f_1, f_2])\n", - " return fx\n", + " rho1 = rho0 * (T_ISA(h) / T0) ** (-g / (ll * R) - 1)\n", + " # \u00bfHabr\u00e1 otra manera de hacerlo sin este copia-pega?\n", + " rho2 = rho0 * (T_ISA(11000) / T0) ** (-g / (ll * R) - 1) * np.exp(-g * (h - 11000) / (R * T_ISA(h)))\n", "\n", - "# Lo mismo, m\u00e1s breve\n", - "def f(x):\n", - " return np.select([x < 0, x > 0], [-x, x])" + " rho = np.select([(0 <= h) & (h <= 11000), 11000 < h], [rho1, rho2])\n", + " return rho" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 10 + "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [ - "f(np.array([-1, 0, 1]))" + "rho_ISA([0, 11000, 20000])" ], "language": "python", "metadata": {}, @@ -222,13 +435,13 @@ { "metadata": {}, "output_type": "pyout", - "prompt_number": 12, + "prompt_number": 38, "text": [ - "array([1, 0, 1])" + "array([ 1.225 , 0.36420497, 0.08817176])" ] } ], - "prompt_number": 12 + "prompt_number": 38 }, { "cell_type": "heading", @@ -254,21 +467,6 @@ "con condiciones iniciales $\\mathbf{y}(\\mathbf{0}) = \\mathbf{y_0}$. Por tanto, y al tratarse esta de una ecuaci\u00f3n en derivada segunda, hay que hacer una reducci\u00f3n de orden." ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**Ejemplo**:\n", - "\n", - "$$y'' + y = 0$$\n", - "\n", - "\n", - "$$ \\Rightarrow \\mathbf{y} = \\begin{pmatrix} y \\\\ y' \\end{pmatrix}$$\n", - "\n", - "$$\\frac{d\\mathbf{y}}{dt} = \\frac{d}{dt} \\begin{pmatrix} y \\\\ y' \\end{pmatrix} = \\begin{pmatrix} y' \\\\ y'' \\end{pmatrix} = \n", - "\\begin{pmatrix} y' \\\\ -y \\end{pmatrix} = \\mathbf{f}\\left(\\mathbf{y}\\right)$$" - ] - }, { "cell_type": "code", "collapsed": false, @@ -279,13 +477,20 @@ "\n", "# Funci\u00f3n del sistema\n", "def f(y, t):\n", - " return np.array([y[1], -y[0]])\n", + " g = 9.8 # m / s2\n", + " C_D = 0.4\n", + " A = 1.0 # m^2\n", + " m = 80 # kg\n", + " return np.array([\n", + " y[1],\n", + " -g + rho_ISA(y[0]) * y[1] ** 2 * C_D * A / (2 * m)\n", + " ])\n", "\n", "# Condiciones iniciales\n", - "y0 = np.array([1, 0])\n", + "y0 = np.array([39000, 0])\n", "\n", "# Vector de tiempos\n", - "t = np.linspace(0, 10)\n", + "t = np.linspace(0, 250)\n", "\n", "# Integramos la ecuaci\u00f3n\n", "sol = integrate.odeint(f, y0, t)\n", @@ -294,31 +499,30 @@ "vel = sol[:, 1] # Segunda columna: velocidad\n", "\n", "# Representamos la soluci\u00f3n\n", - "line, = plt.plot(t, pos, label=\"Position $y$\")\n", - "plt.plot(t, vel, '--', color=line.get_color(), label=\"Velocity $\\dot{y}$\")\n", - "plt.legend()" + "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(6, 6))\n", + "line, = axes[0].plot(t, pos / 1e3, label=\"Position $y$\")\n", + "axes[0].set_ylabel(\"Position (km)\")\n", + "axes[1].plot(t, vel, '--', color=line.get_color(), label=\"Velocity $\\dot{y}$\")\n", + "axes[1].set_ylabel(\"Velocity (m / s)\")\n", + "axes[1].set_xlabel(\"Time (s)\")\n", + "axes[0].legend()\n", + "axes[1].legend()\n", + "axes[0].set_title(\"Felix Baumgartner free fall\")\n", + "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 18, - "text": [ - "" - ] - }, { "metadata": {}, "output_type": "display_data", - "png": 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neEwe2jt7FTommcz1I871wyEbnPGXknBfW1xJK1PIWEz3Z15OLUWghzU0CIhJ\nposuYtNKEe6jeJdPYmYFEjOHUiPQRRfyEDHLDlfSyzAwKJKrHzbogio44y8lod62iE8vh0gkc/VL\npeHyjVJEynGwi240tHSivKaNkIpd0hLma4s4BU06FIHFVF1YGusiLb+aalFoT0NLJylnPTjjLyVC\nsynQ01HHzZJ60sdisj+zo6sXOUV1CCDoYBcddBGXXo5AT2tKUlSEetkg+WYVevsGaKELIoj0s0eM\nnAe+2KKLifj4SArOJBYS3i9n/GUgzIddszAySMqqhNc0c2hpyJbCmY7EppZSFuVjoKcJRytD3Mhj\nz0w5ws8OsamlGBTJ5/phM/0Dg7iaVYlQb+KrCXLGXwbCfGwRqwDjz2R/poOVIZ571GvyhhJCtS46\nunqRXViHOe7EnK6UhXBfW8SmlVKuC6IQmk2BgZ4mbhbJvopmiy7GI/1WDYRmU2BsQFyI5zCc8ZcB\nVztj3O3qQ3lNK9Wi0BZHa0N4OiuutCHZJGVVwmu6ObQJyKYoKwvnOGJFmAtl45NBmLctrqSXUS0G\nbYlNK0M4SQcKOeMvA3w+D6HeNqRH/SiDP1NSqNYFmQ+hpBgbaMPNwYRyXRBJqLcN4uSo7csmXTyI\nWCzGldQyhHLGn16E+Sgu5JODWvr6B5GUXYlQb1uqRWEdLnbG6OzmVtFjcbe7D2G+trCz0Celf874\ny4ifqyWK77QQUlFnPNjuz5QGKnVxI+8OHK0MYThFkzIZRsOm+4LP5yHES/bZP5t08SC6WurY9nQQ\naYckOeMvI2qqAsxxs0JCBleTdDRiMfvOP8SmliHc15ZqMVgLt4qmBs74y0HYn9EXZMFEf+aBqHT8\nfD6b8H6p0oVIJEZcehmtXD5BQUGE5cOnA74uFiiqbEZL+8P1iieDic8IXeCMvxwEeQqRnl+D7h72\nVFqSl9jUUrjYUpf0jGhyiupgoKsJodkUqkUZIaugFhv+9wfVYhCGupoKZrtZIiGTW0UrEs74y4Gu\ntjpmOJggOYecHP9M82dWN3agrrkTns6mhPdNlS5i0+jn8mmpKUB5TRsaWjqpFoUwQr1lOzjJtGeE\nTnDGX07CfGwRx8UpAwDi08sRPFMIAZ8dt5VYLKa8cMtYqAj4CPCwlitEkm4EzRTieu4d9LDInSUr\nzW3d+PdXsaSPw46nlEJCvW2QkFEhd3bCsWCaP/NKGnm+cSp0UVrdiv4BEabbTlX42BMRFBTEukmH\nvq4GptmuKl8HAAAgAElEQVROlTpdOtOeEUmIzyhHTy/5P4Kc8ZcT86m6MDPSQVZBLdWiUEr/wCCa\n27opTX9ANJf/nPXTsR5BgIc1Mm/X4m5XH9WiEEaYN7t+0GTlSloZwhTgauSMPwGE+pBz2pdJ/kxV\nFQF+fXc1NElK5EaFLq6kltHO5QMM6UJHSw3z5zjgTkM71eIQRoi3DRLSK6RKl86kZ0QSunr6kZZf\njSBPIeljccafAMJ97HAlrYyVMe7KSkNLJ6rq2+E1jb75id58LhTTbOjlkpKH4XTpuQpIl05XknMq\n4eZoAl1tddLH4ow/ATgJDSESi1FU1Uxov2z0Z8qKonWRkFmBAA9qcvdPBpvvC2lzZrFNFwkZFQo7\nU8IZfwLg8XhD/so09kRfKDtx6WUI8SI+hzrHxIT62CI+Q3mfo23PBOHRkGkKGYsz/gRBxmlftvkz\n5UGRuuju7Ud6fg0CPImpQkY0bL4v3OxN0NrRg8q6Nonas00XGmoqpO2bPQhn/AnCa5o5qhs6UNd0\nl2pRFIpYLMYvF2+SEupKFddz78DFzhh6CvC7ctyPvIneOCSHM/4EMXzwhsgj6kzwZ+aXNuLoxZtQ\nEZB7KylSF/EZ5bR2+TyoixOX81BRK9lMmQmESlEmlQnPCF3hjD+BhHjZKJ2/8koaecUmqEAkEiMh\nowIhJNRMJYvCymbEXC+hWgzCmDXDErfLm9Da0UO1KKyGM/4EEuBhjYxbNejuJSbRGxP8mQmZipkl\nK0oX+aUN0NFSo1Uitwd5UBdsm3RoqKnAz9UCiVmTr6KZ8IxIQnlNKzq6ehU6Jmf8CURXWx0u9sa4\nflO6I+pMpbbpLuqaOuHhRHwiN6qgu8tnLHxdLFB8pwXNbdKnRKYrId42iFciv//b3yUgPb9GoWNy\nxp9giJyF0d2fmZBRjgBPa9L9/YDidMEE4/+gLtRUBZg9w1KimTJTCPGyQUpOFfr6BydsR/dnRBI6\nOnuRX9KAWW6WCh2XM/4EE+I1lOhNmiPqTMXHxQJPL/WkWgzCYPJKhm2uHwM9TdhbGSDtVjXVopBO\nUnYlvKabQ1NdMSGew3DGn2CEZlOgo62G/NIGufuiuz/T3tIATtZGChlLEbqITy9H4EzFrGTkYSxd\nhPnaYsMKHwqkIY8Qr8ldP3R/RiSBqtUmve9yhsK2WZiywASXz3joaqnDWaiYH2JFMfwcsTln1sCg\nCEnZlZzxZwtEGX82+DOJgmxddPX0I6ugFnPc6XmqdzTKcl84WBmAx+NNmDOL6bro7O7D43NnwMRQ\nW+Fjc8afBDycTFHX1IlaJTvty2RScqrg5mgCHS01qkXh+BMejyeR64fJTNHRwMZVfpSMzRl/ElAR\n8BHgaY0EOWf/dPVnDooUn8qBbF3EpZNXhYxo6HpfkMFkq2hl0gXRyG38MzMzsXnzZrz88suIiooa\ns823336Ll19+Ga+99hpKS4lNfkZX2Oz3338iFd+fzqRaDMIYFImQmFXBWH//g7CpupePizlKq1tZ\ndYaBLshl/EUiEQ4ePIg33ngDH374Ia5evYqqqqr72qSnp6Ourg779u3Dhg0b8M0338glMFOY42GF\nzNu16O6R/bQvXf2Z8RnlCg+HJFMXN4vrYaSnBQtjXdLGIJKJdJF2qxqb3jujQGnIRVVFAH83KyRk\njj2RouszwgTkMv5FRUUwMzODiYkJVFRUEBgYiNTU1PvapKamIjQ0FADg5OSEzs5OtLa2yjMsI9DV\nUscMBxOk3KyavDGDqG7sQENLFyNj4ccjPr0cwV7kl81TBB6OpiirbkVTWxfVohAGm1fRVCKX8W9u\nboaR0b3wMkNDQzQ3N0/YxsjI6KE2bEXem5aO/syEjHIEeQoh4Ct2u4hMXTAtkdtEurg3U2bPad/A\nmda4kVuN3r6Bhz6j4zMiCW13e/D6vmhKw1gV8gRL+wVH/0ETExMZ+zrE2waXrxcjPiGBFvIQ8fr3\ny1kw1uyS+Xq6vf797GXUNbXBzcGEFvJI8jonJ2fCz011epHwZ4QMHeSV93VuVhocrQ2Rml/90Oc5\nOTmUyyfL66tZlegfGMTVq1cJ7V8aeGI5fnoKCgpw7Ngx7NixAwBw8uRJ8Hg8LF++fKTN119/jRkz\nZiAwMBAAsHnzZuzatQv6+vpj9hkTEwNvb29ZRaIdq7b+in//XyjcHZnvJhkUifD0v6Owf/tS1oRE\nHrmQg9vlTdi1IYxqUQijtaMHj/zjCKI/Xw91NRWqxSGE705loLb5LrY/E0y1KISw7bNLmD3DEivC\nXQjrMz09HZGRkRK3l2vm7+DggNraWtTX12NgYABJSUnw9fW9r42vry/i4+MBDP1YaGtrj2v4h6Ei\nlJAs2OSvFPD5+Omtx1hj+AFmn+odD31dDcydZY+65k6qRSGMEO+hnFlsOO3bPzCI5OxKBM2kdp9J\nLuMvEAjw7LPP4u2338aWLVsQEBAAKysrREdHIzo6GgDg7e0NExMTvPTSSzhw4ACee+65SfvNLqyT\nRyxaEeItu/GXdTnHRsjQRUdXL24W1cPf3YrwvslEEl3s/L9QWtckkBZ7SwMI+DwUVt6/X8jEZyTj\ndi2EZlNgbKD4U72jkXtN6OXlBS8vr/vemzdv3n2vJTH4o4nPKIfXNHN5RaMF7o4maGjpQnVjByym\nMiOUUFlIzq7CzGlm0FJQwWwO2Rk57ZtRzvgcRlTl8nkQWp7wzbxdS7UIhCHg8xHkKZTptC8Xw3wP\nMnTBpFO9o1HW+2KsAi9M1MWm1X74yyIPqsWgp/H/5s1HqBaBUJStKhETGM6mGEyx35VDcrynm6O8\nhvlnGFRVBLRYbdLS+Cs6hpxs5rhbIbuwDp3d0h27p5M/85eLN+U6rSwvROsiq6AW5lN1YWqkQ2i/\nioBO94UiGesMg7LqggjYZWVpiramGjycTJGSw8zTvtWNHTgQlQY1NQHVohAGG6N8xuLQ6UzUsyjq\nJ9jbZuQMA4d8cMZfQYR42yBOypuWLv7M+HRqTvWOhmhdxKWXI5RBp3pHI40uCiuaWBNqDABBnkLc\nyLt32pcuzwgT4Yy/ggjxskFiZgUGBpl3hoGpG6PjUVbdip7eAUy3nUq1KKTDtv0mfV2NkdO+TKO8\nhl7ZSWlr/Du6ehnrJhmLIf+ytlRnGOjgz6RLLDyRuohLL0OwlxA8Ho+wPhWJNLoI8LBGxu0adFG4\nX0M0o3/Q6PCMSMq+X64hKaeSajFGoK3x7+kdwLbPLqF/YJBqUQhjyPVTRrUYUpGUXQmvaea0iE4g\niviMclatZCZCV0sdbo4mrJpIhXozr7Zvb98AbuRVI8iTPtFltDX+xgbasDLRQ2YBe2L+Q71tpVqC\n08Gf6e5gihdXU1NmbjRE6aK1owcF5U3wc7UgpD8qkFYXbEoxAgC25vpQV1NBflkjLZ4RSbiRVw0n\noSH0dTWoFmUE2hp/gH3+Shfbqejq7UdZNXPqGVgY67LKN56YVYFZMyxZk/BMEhYFOOHZR7wmb8gQ\neDweQhm2iqbjvhmtjX/onxEyTFreTcTQTWsr8U3LJH8m2RCli/j0cgQzNMpnGGl1oa+rwao8P8DQ\nKjourZwRz4hYLP7T1Uiv+47Wxt9ZaISBQRFKGTRTnoxQGUI+OYihr38QKTeruFO9LMDT2RT1LZ1o\n7qB/veLu3gEsD5sOG/OJsxkrGlobfx6Ph3/+ZQ40WLRE93WxQFFlM1raJw/5Yoo/UxEQoYu0W9Ww\ns9CH0RQtAiSiDu6+GMoCEDxTiC6BCdWiTIqWhio2rqR+3+xBaG38ASBylj1jCmtLgrqaCma5WSKR\n5mX2+gcGWeNuGyY+XXmifJSBUG9bXEkro1oMxkJ7489GQr1sECdB9AWV/szvz2Rh/4lUysZ/EHl1\nIRaLEZfOjpQOsupCLBaj7W4PwdJQxxx3K2QV1KCjs5dqURgJZ/wpIGimENdv3hmzIDVdiEsrg/d0\ndtRUAIDCymYI+Dw4WBlQLQplJGVX4rVPoqkWgzA0NVThaKGFq1n0OTjFJDjjTwEGepoSHVGnyrfb\n0NKJyrp2Whl/eXUR/+esn6mnekcjqy68p5sjv7QB7SyaKa+Y640rDAr5pBOc8acIOkf9xGeUI8DD\nGqoqLMviSbNQO0Wjqa4KX1cLXM2i936TNIR42SA5u5KWmQA6u/uwac8ZiET03DtjjPF/57sEVt20\nw/H+E22qUuXzp2PGS3l00dDSifKaVlqtZORBHl2EeNF30iELt26mw8ZcH2n5NVSL8hApOVUQA+Dz\n6bnaZIzxtzLVw+XUUqrFIAxbC31oqasiv6yRalHuQyQSo7unHwEe1lSLQhiJmRXwd7di1UpGVoJp\nPFOWlTAfW1q6fug4iRoNY4x/uK8d4tLKMShiXkrk8Zgs0RsVPn8+n4cD/3oEutrqCh97IuTRRWxq\nGcJ97AiUhlrk0cVUfS3MnW2PxlZml0IcJigoCGE+Qzmz6BSaPCgSITGrAsE0ji5jjPG3MtGDkb6m\nVCmR6Y60id44pOduVx8ybtcgcCZ7VjLy8uZzoTCfyp6zM3YW+lAR8HG7vIlqUUbILqyDsYEWLGis\nZ8YYf+DP5R2LDnV4OJmirqkTNY0dY37OhLwlikJWXVzNroCnsxl0tei1kpEH7r64R2JiIng8HsJ8\nJM+ZpQiSs6tov9pklPGP8LVDbkkD1WIQhoqAj6CZQlal26UbsallCPe1pVoMDpIJ9bFBXBp9nqMX\nVvrimWUzqRZjQhhl/J2FRjiwYxnVYhBKqLfNuKsZLofLPWTRRW/fAJKyKxHmY0u8QBTC3Rf3GNaF\np5MZapvujruKVjR8Po/2OckYZfx5PB4rDumMZo6HNW4W1dPi2P23pzLQzaJyf9dz78DRypDxidw4\nJodbRUsPo4w/G9HSUIXfDMsxN34V6dstq27FLxdv0rbIiSy6iE0tQ4Qvvf2uskDUfXHw93RU1LYR\n0hdVjNZFqDe9XD90hzP+NCDCz47yMwwxN0oQ7mtL2wMp0jIoEiEug/P3T0RDaxcuXS+hWgzCmONh\njZyiOnR0sSd9BZlwxp8GhHjZIDWvGl0PuFwU6duNuVGKSD97hY0nLdLqIrOgFsb62rA00SNJIuog\n6r6I8LXD5RvMPjg5WhdaGqrwmmaOpGzqEr3lFtcz5gwFI41/Z3cfzl4tpFoMwtDTVoeHkyllOf6r\nGzpQ13yXNekPgD9dPn7sc/kQifd0c1Q3dNBmk5QIwnxtKf1B2/PDVRRXNVM2vjQw0virCPh491Ci\nRNWwmMJYrh9F+fwv3yhFmLctVAT0vR2k0YVYLEZsailrXT5E3RcqAj5CvG0Qm1pGSH9U8KAuwn1s\nkZxThR4K0qXXNd1FZV0bYyZR9H3aJ0BdTQX+7lYSFURhCuE+dkjKrqQkx//c2fZ49hEvhY9LFrfK\nGiHg8+FoZUi1KLSHDvtNRGKgp4nptlORTIHrJzatDMEzbRiTQ4qRxh8Awn1tEcuim9ZwiiachUZI\nuVk18p6ifP5mRjq0941Lo4vhg11sCwsehsj7wt/NCm9vjCCsP0Uzli7m+tlTspF9ObWUUa5Gxhr/\nIE8h0vNr0NndR7UohBHpx/wNODoQm1bKyhBPMlBTFcDUSIdqMQgl3NcWiZkV6OtXXObSlo5u3Cpt\nhL+7lcLGlBfGGn9dbXW4O5kiOadq8sYMIdzXDvEZ5SPpdrkcLveQVBcVtW1o6+iFu6MpyRJRB3df\n3GMsXRgbaMPR2vC+VTTZiERivP5UIO1P9Y6GscYfADau9IWTNXv8umZGOrA2nULLwhRM4XJqKcJY\ndF6BQzbmzrJHjAJdP0ZTtLA02Flh4xEBo42/u6MpbMz1qRaDUCJ8723Ake3zb+nopm2JuQeRVBds\njvIZhsvtc4/xdBHha4e49HJWFa0hGkYbfzYS4WeHK6llCila868vLrNq03yoXGMbfF0sqBaFcQyK\nRCi500K1GIRhaqQDWwt9XM+9Q7UotIUz/jRDaDYF+noayC6sI9W3297Zi+zCOsxhSLlGSXQRm1qG\nQE92FZ4fCzLui/bOXjyzKwrdvcxK7DeRLub62SPmOnsmN0TDGX8aooion/j0cvjNsISWhiqp4ygS\nLspHdgx0NeFiNxUpLAqgiJhlhyvpZRgYJG8VTafSkdLCGuPPJt/e8MGbwMBA0saIuVHCqJjkyfzc\n7Z29uFlUz6rC8+NBls8/ws+Ocad9J9KFxVRdWBrrIi2/mrTxEzMr8NY3caT1TyasMP4nY/Ox5/ur\nVItBGI5WhlBVESC/rJGU/ju7+5CaV41QGheXlpa4tDL4zbCEJotWMoom3McOCZns2iSNnGWPGBJX\n0ZdTS2FvZUBa/2TCCuM/280Kl2+Usuam5fF4iPC1w/e/xZPSf1NbN1bNdYWuNnPq2k7m5z6fXIQF\n/g4KkoZayNoLMjHUhtCMWaHGk+ki0s8OsamlpARQDAyKEJdeTvtavePBCuNvYawLofkUVu3sR/rZ\nIauknRSfotBsCl55wp/wfqmiua0bOcX1CGHRSoYqnlzkQesEf9JibToFxvrayLxdS3jfafnVMJ+q\nAwtjXcL7VgSs+SsvnOOI88lFVItBGK72xuCrqLEq/E4eJvLtRl8vRvBModK4fMiM85832wG+rswJ\nlZVEFxGz7EjJ9XMuqQiL5jgR3q+iYI3xnzvLHvHp5ZSkciUDHo+HcF9bUv2VbOFCcjEWzHGkWgwO\nmjLXb8jvT+SBRrFYjOKqZsxnsKuRNcZ/qr4WIv3sUd3AnsIUZlqdOJ9UxOhwMqIYz7db09iBsupW\nzGFQQi154XL73EMSXdha6ENfRwPZRXWEjcvj8fDD7hUwMdQmrE9FI3MWort37+Kjjz5CY2MjjI2N\nsWXLFmhrP6yITZs2QVNTE3w+HwKBAO+8845cAk/Ezv8LJa1vKrA10cTAYBPyyxrhamdMtTi05EJK\nMcL9bFl/sItDPiL/dP3MdDYjrE+mpwyXeeYfFRUFDw8PfPLJJ3Bzc0NUVNS4bXft2oX33nuPVMPP\nRoKDg7Eo0JGwkpUJGeX4NTqXkL4UzXi+3QvJRVioZC4fLrfPPSTVxXCiN6bkslIEMhv/1NRUhIYO\nzbTDwsJw48aNcdtybgvZWRzghIvJxYScUvwtNh8a6sxJOTsZpdUtaGrrZkzZPCZxs7geO/fHUi0G\nYdhbGkBTQxU3S+qpFoU2yGz829raoK8/lFFzypQpaGtrG7Mdj8fDW2+9hW3btuHSpUuyDqeUJCYm\nwsZcH6ZG2riRJ18Ya0tHN9Lyaxib/mAs3+755CLM93eAgM+arSuJUITP397SAFfSy9DSQe862ZLq\ngsfjYYG/Ay4ksSciUF4mnAa+9dZbaG1tfej9tWvX3vd6It/XW2+9BQMDA7S3t+Ott96CpaUlXFxc\nJhQqMTFxZDk3/MdV5tfTzAQ4d7UIc9ytZe6vutsAgZ7WyEy/Tvn3keX1MMOvAwMDcSG5GKvnGCrd\n/ZKTk6OQ8QI9rLH/cDSCZxjS6vuPfp2TkyNx+yVBzlj3xq/wsxlEWGiITOOdvRiLtMI2vLlpOS2+\n/4OvpYEnltEns3nzZuzatQv6+vpoaWnB7t278fHHH094zbFjx6ChoYFly5aN2yYmJgbe3t6yiDTC\npeslEPB5CGfoLPdBmtq68NhrR3H+0yehqS5bLPszu6Pwt0e9ETRTSLB01JBX2oBtn17C73ufYPzG\nG12JzyjHoT8y8e3OR6kWhTCe/c/veHqJJ0J9bGW6/vD5HNwub8Tu58OJFYwA0tPTERkZKXF7mdfL\nvr6+uHLlCgAgLi4Ofn5+D7Xp7e1Fd/fQsrGnpwfZ2dkQChVjfH69xMyNzbEwmqIFNwcTxKeXy3R9\nQ0snaho7GFVfdDKGN3o5w08ec9ytUFbTiupG9oRPLw12xunEApmvP59chIUB7AgwkNn4L1++HDk5\nOXjllVdw8+ZNLF8+tAxqbm4eieppbW3Fzp078dprr2HHjh3w9vaGp6cnMZJPQNBMIfJKGtDU1kX6\nWGQy2uWxONAJZ2SM+jE20EbUB08w+tj+aF2IRGJcTClmzUMoLYqK81dVEWC+vwOyC4iLjycaaXUx\nb5Y9rt28g7a7PVKPVVHbhuqGDvi5Wkp9LR2ROfRDR0cHb7755kPvGxoaYvv27QAAU1NTvP/++7JL\nJyMaaioI9rLBpeslWDPPTeHjk0G4rx32/HAVLe3dMNDTlPp6Wd1FdCSjoAZ6Ouqwt2RmNkUmsfWp\nQFatrnS11THHwwoXU4qxeu4Mqa69kFyEebPtGT2JGg07vsUYLPB3wIXkYqrFkIvRmzhaGqoIninE\nxWvM/k6yMloXF5KLsdBfOWf9gGLj/Olu+GXRxdIg6V0/YrEY51jk8gFYbPz93a1QWt2ChpZOqkUh\njEUBTjin5KFq/QODuHS9hMvlwyEzczysUd3QgfKahyMZx4PH4+H9l+fBw9GURMkUC2uNv6qKAMf3\nPA5jA+bm3njQnznbzRJVde2oqm+nSCLqGNbFtZt3IDSbwtg0ukTA5fa5hyy6UBHwsXCOI84kSreH\n5mBlSPuVkDSw1vgDQ1EybEJVRYB5s+1xTsKN37zSBuQWs+tE43klTOfAQTxLg51x5mqBUqd7YLXx\nZzpj+TMXBw65fiQ5nvHdqQzcrmgiQzSFExQUhJ6+ASRklGPebHuqxaEUKnL7VNa14XSC7CGSZCGr\nLpyFRtDWVEP6LeZULSMazvgzDDcHEwwMipBfOnF9347OXly7eQdzZ7HHUF66VgIPJ1PWreiYgIDP\nx4eHk1lVKlWWjV82wRl/GjOWP5PH42FxoBPOJk3s+om+XoLZbpbQY1Cd3olITEzE8ct5WBXhSrUo\nlEOFz9/CWBe25vpIzqlS+NgTIY8uFgU4Ija1FN29/eO26e0bQFFls8xj0BmlMP5V9e3ILCC+hidV\nLA6cPNPn2auFWBLkrECpyOVOUw/qmu4ikCXpKZjI4kAn/B53i2oxCMPYQBvujqa4klY2bpvo6yX4\n6HCy4oRSIEph/Cvr2vDeD1epFkNqxvNnCs2mwGyqDq7dHHsWVt3YgZI7LQj0tCZTPIVS0qKO5WHT\nWXPARh6oyue/KMARafk1qG+mT/i0vLpYGuQ84V7G8Zg8qQ+DMQWleJJmz7BCe2cv8kobqBaFMB4N\nnYbfLueP+dkUbXXs3TyfNdWtunr6cSG5GMtDp1MtilKjramGhQGOOHll7PuOiYT62OBmcf2Y54Fu\nlzeivrmTNckQH0QpjD+fz8PysOnjGku6MpE/c3GAE9Jv14yZdEtbUw1e09hT4ORCchGExmowNdKh\nWhRaQGWc/4blPli30J2y8R9EXl1oqqsiws9uzGp5xy7l4bFwF9auNtn5rcbg0ZBpiL5WjM7uPqpF\nIQRNDVUsCXLGiZg8qkUhnROX8xHkyuXxoQOGUzShq8WOIIJhhjN9jg6f7ujqRfS1YiwPY+9qU2mM\nv7GBNnxdLHAhhTm5cSbzZz4+dwai4m6ht29AQRIpnrzSBrR0dOO5JxZQLQpt4Gr43oMIXXg5m6O7\ndwC5JaPcwmJgx7MhmKrP3rBipTH+APDSmtkI9GDPJqjQbApcbI0Rfa2EalFI48TloaW3spVq5FAc\nfD4PqyNdceRCzsh7utrqmO/vQKFU5KNUT5SthT6j/MaS+DPXzJuBo9E3AQD5pQ2sOYQDAHe7+nDp\nWgkeDZ3O5bMZBaeLexCli8fCXXA1q5JWkUxko1TGn40EeFqjtaMHN3LvYOO7Z9DcRu+C29JwLqkQ\ns92sWL30ZjKxqaXo6hn/gBST0NVWx6IAx5GJlDLAGX8aI4k/U8DnY/XcGfjk6DXMdrNk1MpmIsRi\nMU5czsfKCBcAnJ97NHTRxemEApyb5KQ52RCpi7UL3HHyyq0JT/yyCc74s4Blwc7IL23AkkD2nOjN\nKa5Hd28/a0rmsZHVc2fg10u5EiUZZAJCsymYJjSiZQI7MlBK4y8Wixlx4EtSf2ZeaQP0tNVRUDFx\nsjcmcSJmaKOXzx/Kn875ue9BF13MmmGJ3r5BZBdSV+OXSF0MikQorGzG92eylCLVs1Iaf5FYjH9+\ndAEF5exId3zkwk08Md8NJy7nT5jvhym0d/biSloZHgmZRrUoHBPA5/OwKtIVv17KpVoUQkjMrID5\nVB3oaKohOaeSanFIRymNv4DPx/Kw6Th6id6bO5L6M1eETcczS2fCzEgHcell5AqlAM4kFiDQU3hf\noXq6+LnpAJ10sSzYGQmZFZQFGhCpi+E8Pn9Z6I6fz+dMfgHDUUrjDwCPz5uByzdKUTNGegSmETnL\nHupqKlgzzw2/RjN7FiYSiXE8Jg8rI12oFoVDAqboaOCLrUugq61GtShycae+HbklDZjv74AFcxxR\nVNGM4ip2pnIeRmmNv4GuJlaEueDQH5lUizIu0vozI2fZofROK0rutJAkEfnEppVCXU0F3g/kJqKL\nn5sO0E0Xbg4mlCURJEoXJy7nY2mQMzTUVKCmKsCqua44fIHds3+lNf4AsH6xBy6kFKOu6S7VohCC\nqooAKyKmMzZWWSQS46sTadi40pdVhbI56I+9lQFWRd4rFLQqwhWXrpWgpYM952YeRKmNv4GeJvZu\nnk/baley+DNXRbjiQnIxOrp6SZCIXC5dL4GGusqYKXTp5OemGk4X9yBKF0uDnCE0mzLy2nCKJiL9\n7HGCYZmApUGpjT8A+LhYQFNDlWoxpOZOfTvudj2codTYQBtBM4X4+RyzlqyDIhG++i0VL3Czfg6a\nsHbh0B4am1KmjEbpjT+dGc+fKRaL8eb+WFwZJ7Jn40pfHI2+iaa2LhKlI5aLKcXQ01bHHHerMT+n\nm5+bSuiqC5FIjN9i8xVqLMnUhZO1ERysDBiVCVgaOOPPQGJTy3C3uw+LAhzH/NzSRA+LA51wICpd\nwZLJxsCgCF//lsbN+hkOjwecTy5i1QnZvyz0wOFzOaw5xTwazvjTmLH8mf0Dg/jklxRsWec/YZrj\nv8/CPCkAAA+JSURBVD3qjYvJxaiobSNTREI4n1QEI30tzJoxfioHzs99D7rqgsfj4e+Pz8LXJ9MU\nVmNCHl2k36qZdJUS4GENkViMmBulMo9DVzjjP4qY6yVobKW3q+TE5XxYmehhjvvEdQkM9DSxbpE7\nvjh+Q0GSyUb/wCC+PslF+LAFD0dTTLedimM0rzBXVd+OVz++iM7uiZO48fk8vPpkAD46nIwelhVN\n4oz/KFLzq/Hj2SyqxRjhQX9md08/volKx+Z1/hJd/5cF7ki/VYO8EvrmMTpztRDmU3Xg42IxYTu6\n+rmpgO66eHG1Hw79kamQkqmy6uKr31KxZv4M6OtqTNrW19UCrnbG+Olstkxj0RXO+I/imaUz8Xvc\nbdrmxNfUUMXBNx+Bk7WRxO03rPDBJ7+k0NJn2T8wiG+i0vHCSl+qReEgECdrI8x2s6TtRmnJnRYk\nZ1fhLws9JL5m81p//Hw+mzVnggDO+N+HqZEOFsxxwA80mf2P5c+0MdeXqo9HQ6ehvrkTKTeriBKL\nME7F34bQdAq8HjjNOxZ09XNTARN08a/nQrBCAcXPZdHFl8dvYP1iD+hoSZ6SwtJED6siXbHv6DWp\nxyObvv5B7Pr6itTXccb/AZ5ZOhNRV26hpZ2es39pUVUR4O9rZmHfL9dolaa2r38QB3/PwPMrfagW\nhYMENNVVabmHU1DRhOyiOjw+b4bU1/51mRfS8muQVVhLgmSy8/XJNJkOdXLG/wHMp+piUYAjLdLU\nEuXbjfC1g6qKAOeTiwjpjwiirtyCg5UBPJ3MJGpPdz+3IuF0cQ9pdeFoZYiDbz4KTXXpD3Zqaaji\npTWz8MGPSbSZSOWVNiDqyi1sfyZY6ms54z8GLz8xG88+4kW1GITB4/HwyhOz8cXxG+jrp/60YmNr\nF76JSsfGlX5Ui8KhZPD5PFiZ6Ml8/aIAJ/D5PJxJpP4sQ//AkLtn8zp/mepcc8Z/DDTVVSnLUjia\noKAgxKWX4adz8kcZ+LhYwN7SAMcpDsETicTY+VUsHg2bBld7Y4mvY4KfW1EwUReDInKKDClaF3w+\nD6+tD8Rnx64rJJppIg7+ngEzIx0sCXSS6XrO+NOY/oFBfHQ4BfaWBoT099KaWfj2VAalZxkOn89B\nZ3cfNqzgfP3KQkVtG5588zd09bCjMLqbgwlmz7DCt6cyKJOhoLwJx2Jy8a9nQ2TeW+GMP43575en\nYDFVFwEeEx/okhQnayOsinTF6/uiKUlWdausEd/+kYH/vRgp9cqK83Pfg2m6EJpNgYutMf57MJ7w\nkGNJdEHG4ayX1szCydhbqKxT/An6YXfPS2tmw8RQW+Z+OOMvAe2dvQqP743PKEdcTjPe/FsIof1u\nWOEDXW01fPhzMqH9TkZ3Tz/e+DwGr60PgKUcPlcOZvL604EoudOicLdjeU0rVm39lXAXjbGBNp5c\n7IH3Kdj8/f5MFgz0NPConDWuOeMvAeeSCrH98xjS/JYPUlzVjN0HruCT15bAfKouoX3z+Tz8d2ME\nUnKqcCr+NqF9T8QHPyXBzcEEiwJk808y0c9NFkzUhYaaCt57eR72/5ZK6InziXTR0zeArZ9ewjNL\nZ0Jbk/gyk08u8kBHZy8+/VVxsf/FVc04fC4H/3pOdnfPMJzxl4DVkTOgIuDjxzOKOd5tYqCN/70Y\nKXEYpLToaqlj75YF+PhICnKL60kZYzSXrpfgRl41tj4dSPpYHPRFaDYFbzwTjF0HrihktvzBj0mw\ntdDHyghy6kGrqQrw8T8XIi69HEcUUPJxYFCE3Qfi8OJqP0ImhZzxlwA+n4ddz4fhh7NZuF3eSPp4\nutrqmO1mRapv197SADueDcZr+6JJTWdR09iBdw4l4J1NkXLNvpjm5yYTJusicpY9vtq+FHw+MQfA\nxtPFuaRCpOZXy7UhKglTdDTw2euL8f3pLFwkOZ3FT+eyoaGugsfCifkx44y/hFhM1cU/1s3Bm1/G\noruXHVELkX72WBLkhK2fkrMBPCgS4V9fXsb6RZ6Y4WBCeP8czMRAT5PU/rt7+/Hp0evY89JcqVI4\nyIrFVF3se3UR9vyQiNS8alLG+OXiTRy5kIN//y2UsB9OzvhLwZIgJ7g5mODStRKFjKcI3+4LK32h\noa6Cj4+kENrvoEiEjw+nQEXAx1NLPOXuj4l+brLgdHGPsXShqa6KX99ZjWk2UxUmh7ONEd7ZNBdb\nP4tGYWUTYf2KRGJ8fCQFv0bn4rudywkNluCMvxTweDy8+bcQLA12JrTfvJIGyk7eCvh8vP1iJBIy\nKgirwNTY2oUX3z2D2xVNeGfTXMJmKhwckqKIGf+DzJphidfXB+KVD86jloDowL7+Qfzry8vILqzD\ntzsfhYUxwcEfsl6YnJyMf/zjH1izZg1KSsafCWd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MGRQUFFBYWEjLli0ZNmwYa9euZdu2bdjb2wPFz55q1qyZnqNV1rKRF2vmDOST1fsZ9t7P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\nlpbyEZbNjRkz5oYrRrZc9Nai6/Tp0zaP2ZZ6yw/Q+8P2zpYfb29vjBg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"text": [ - "" + "" ] } ], - "prompt_number": 18 + "prompt_number": 57 }, { "cell_type": "heading", @@ -361,10 +565,47 @@ { "cell_type": "code", "collapsed": false, - "input": [], + "input": [ + "gamma = 1.4\n", + "R = 287.0 # [SI]\n", + "c = np.sqrt(gamma * R * T_ISA(pos))\n", + "\n", + "M = np.abs(vel) / c\n", + "\n", + "plt.plot(t, M)\n", + "plt.plot(t, np.ones_like(t), 'k--')\n", + "plt.ylabel('Mach number')\n", + "plt.xlabel('Time (s)')\n", + "plt.title(\"Mach number\")" + ], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 58, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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0ndoriV27dsHd3R2zZ8/GvHnzMG/ePMyfP18TsQniyvUsDOwl/iKhS/3W5/7R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\nB5NH+qChsQnX7xTgyvUs/Pd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+ "text": [ + "" + ] + } + ], + "prompt_number": 58 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Barrera del sonido superada** ;)" + ] } ], "metadata": {}