{ "cells": [ { "cell_type": "markdown", "id": "a01c0773", "metadata": {}, "source": [ "# Etude de l'équation différentielle du pendule non linéaire:\n", "$y'' = -\\sin{y}$ avec la condition initiale\n", "$y(0) = \\frac{17\\pi}{18},\\quad y'(0) = 0.$" ] }, { "cell_type": "code", "execution_count": 1, "id": "f30df373", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_ivp" ] }, { "cell_type": "markdown", "id": "3fccb7ec", "metadata": {}, "source": [ "#### Question 1. Résolution avec solveur intégré de Python" ] }, { "cell_type": "markdown", "id": "5176ad10", "metadata": {}, "source": [ "On réecrit l'équation sous forme d'un système du premier ordre en posant \n", " $y[0] = y$ et $y[1] = y'$" ] }, { "cell_type": "code", "execution_count": 2, "id": "2c65cd63", "metadata": {}, "outputs": [], "source": [ "#fonction definissant l'équation différentielle\n", "def pend(t, y):\n", " dydt = [y[1], - np.sin(y[0])]\n", " return dydt" ] }, { "cell_type": "code", "execution_count": 3, "id": "1ee07e1b", "metadata": {}, "outputs": [], "source": [ "# pendule initial quasiment vertical (170°) à vitesse nulle\n", "y0 = [np.pi*17/18, 0.0]\n", "#duree de simulation\n", "T=64\n", "# resolution avec schéma RK45\n", "sol = solve_ivp(pend, [0, T], y0, dense_output=True)\n", "# on veut suffisamment de points pour le graphe\n", "t = np.linspace(0, T, 100)\n", "y = sol.sol(t)" ] }, { "cell_type": "code", "execution_count": 4, "id": "8896e936", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#tracé des courbes solutions\n", "plt.plot(t, y[0], 'b', label='y')\n", "plt.plot(t, y[1], 'g', label=\" y' \")\n", "plt.legend(loc='best')\n", "plt.xlabel('t')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "2e3aac6e", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plan de phases\n", "plt.plot(y[0], y[1], 'b')\n", "plt.axis('equal')\n", "plt.xlabel('y')\n", "plt.ylabel(\"y'\")\n", "plt.title('schéma RK45 de Python')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2ac13f41", "metadata": {}, "source": [ "#### Question 2. Schéma implicite-explicite" ] }, { "cell_type": "code", "execution_count": 6, "id": "6b04ee47", "metadata": {}, "outputs": [], "source": [ "# duree de simulation\n", "T = 64\n", "# pas\n", "h = 1e-2\n", "# nombre de points de la subdivision\n", "N = int(T/h)\n", "#initialisation des variables\n", "q = np.zeros(N)\n", "p = np.zeros(N)\n", "# conditions initiales\n", "q[0], p[0] = y0\n", "# schéma Euler symplectique\n", "# p_{n+1} = p_n - h sin q_n\n", "# q_{n+1} = q_n + h p_{n+1}\n", "for k in range(N-1):\n", " p[k+1] = p[k] - h*np.sin(q[k])\n", " q[k+1] = q[k] + h*p[k+1]" ] }, { "cell_type": "code", "execution_count": 7, "id": "9505696b", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#trace des courbes solutions\n", "t=np.linspace(0,T,N)\n", "plt.plot(t, q, 'b', label=r'$y$')\n", "plt.plot(t, p, 'g', label=r\"$y'$\")\n", "plt.legend(loc='best')\n", "plt.xlabel('t')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "id": "b0ecc326", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plan de phases\n", "plt.plot(q, p, '-')\n", "plt.axis('equal')\n", "plt.xlabel('y')\n", "plt.ylabel(\"y'\")\n", "plt.title('schéma Euler implicite-explicite')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "117784ba", "metadata": {}, "source": [ "#### Question 3. Conservation de l'énergie." ] }, { "cell_type": "code", "execution_count": 9, "id": "21970e1b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pour le schéma implicite-explicite:\n", "max |E(t) - E(0)|= 0.0076617528911484545\n", "qmplitude de variation = 0.015308219870332818\n", "Pour le schéma RK45:\n", "max |E(t) - E(0)|= 0.04505415112335387\n", "amplitude de variation= 0.05104294341917559\n" ] } ], "source": [ "#test de conservation de l'énergie\n", "t=np.linspace(0,T,N)\n", "y = sol.sol(t)\n", "E= -np.cos(q[0])\n", "print('Pour le schéma implicite-explicite:')\n", "print('max |E(t) - E(0)|=',np.max(np.abs(0.5*p**2 - np.cos(q) - E)))\n", "print('qmplitude de variation =',np.max(0.5*p**2 - np.cos(q)) - np.min(0.5*p**2 - np.cos(q)))\n", "\n", "print('Pour le schéma RK45:')\n", "print('max |E(t) - E(0)|=',np.max(np.abs(0.5*y[1]**2 - np.cos(y[0])-E)))\n", "print('amplitude de variation=',np.max(0.5*y[1]**2 - np.cos(y[0]))-\\\n", " np.min(0.5*y[1]**2 - np.cos(y[0])))" ] }, { "cell_type": "code", "execution_count": 10, "id": "26207a5e", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t=np.linspace(0,T,N)\n", "y = sol.sol(t)\n", "plt.plot(t,0.5*p**2 - np.cos(q))\n", "plt.plot(t,0.5*y[1]**2 - np.cos(y[0]))\n", "plt.plot(t,-np.cos(y0[0])*np.ones(len(t)))\n", "plt.xlabel('t')\n", "plt.ylabel('energie')\n", "plt.legend(['E(t) implicite-explicite','E(t) RK45','E(0)'])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b80376e5", "metadata": {}, "source": [ "Le schéma implicite-explicite conserve mieux l'énergie que le schéma standard de Python. Pourtant le schéma standard de Python est d'ordre 5 alors que le schéma implicite-explicite est d'ordre 1. On voit aussi sur que la trajectoire dans le plan de phase se referme mieux avec le schéma implicite-explicite. Avec le schéma de Python, les oscillations du pendule semblent perdre peu à peu de l'amplitude. Le pendule semble perdre de l'énergie avec Python. " ] }, { "cell_type": "markdown", "id": "860861f5", "metadata": {}, "source": [ "#### Question 4. Calcul des périodes numériques." ] }, { "cell_type": "code", "execution_count": 11, "id": "af16e2e1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "la periode numérique est 15.33\n" ] } ], "source": [ "# Obtenir les temps où la vitesse angulaire change de signe (passage par un maximum)\n", "t_max = t[np.where(np.diff(np.sign(p)) < 0)]\n", "\n", "# Calculer la période comme la différence entre deux temps successifs de passage par un maximum\n", "periode = np.mean(np.diff(t_max))\n", "print('la periode numérique est',round(periode,2))" ] }, { "cell_type": "code", "execution_count": 12, "id": "d37bd5a1", "metadata": {}, "outputs": [], "source": [ "# detecte quand la vitesse y' change de signe positif\n", "# en devenant ensuite negative\n", "# cela correspond aux maximums de y\n", "def retour(t, y): return y[1]\n", "retour.terminal = False\n", "retour.direction = -1" ] }, { "cell_type": "code", "execution_count": 13, "id": "4040cee7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[array([ 0. , 14.433816 , 28.04291236, 41.20155337, 54.22983391])]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = solve_ivp(pend, [0, T], y0,\n", " dense_output=True, events=retour)\n", "sol.t_events" ] }, { "cell_type": "code", "execution_count": 14, "id": "3c36c72a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "la periode numérique est 13.56\n" ] } ], "source": [ "# Obtenir les temps où les événements se produisent (passage par un maximum)\n", "t_max = sol.t_events[0]\n", "# Calculer la période comme la différence entre deux temps successifs de passage par un maximum\n", "periode = np.mean(np.diff(t_max))\n", "print('la periode numérique est',round(periode,2))" ] }, { "cell_type": "markdown", "id": "baa7ac69", "metadata": {}, "source": [ "On trouve sur wikipedia\n", "https://fr.wikipedia.org/wiki/Pendule_simple#Cas_pleinement_non_lin%C3%A9aire\"\n", "que la période théorique du pendule est 2.44 x 2 $\\pi$" ] }, { "cell_type": "code", "execution_count": 15, "id": "e4bbe39e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "la periode théorique est 15.33\n" ] } ], "source": [ "print('la periode théorique est',np.round(2*np.pi*2.44,2))" ] }, { "cell_type": "markdown", "id": "17d1678e", "metadata": {}, "source": [ "Le schéma implicite-explicite donne un période correcte, ce n'est pas le cas de solve_ivp qui sous-estime la période." ] }, { "cell_type": "markdown", "id": "ff4a1c5b", "metadata": {}, "source": [ "#### Question 5. Changement de condition initiale." ] }, { "cell_type": "code", "execution_count": 16, "id": "17aa0e45", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# conditions initiales\n", "q[0], p[0] = 19*np.pi/20, 0\n", "# schéma Euler symplectique\n", "# p_{n+1} = p_n - h sin q_n\n", "# q_{n+1} = q_n + h p_{n+1}\n", "for k in range(N-1):\n", " p[k+1] = p[k] - h*np.sin(q[k])\n", " q[k+1] = q[k] + h*p[k+1]\n", " # plan de phases\n", "plt.plot(q, p, '-')\n", "plt.axis('equal')\n", "plt.xlabel('y')\n", "plt.ylabel(\"y'\")\n", "plt.title('schéma Euler implicite-explicite')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "id": "bf82b83f", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#trace des courbes solutions\n", "t=np.linspace(0,T,N)\n", "plt.plot(t, q, 'b', label=r'$y$')\n", "plt.plot(t, p, 'g', label=r\"$y'$\")\n", "plt.legend(loc='best')\n", "plt.xlabel('t')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "id": "60eb1610", "metadata": {}, "outputs": [], "source": [ "# pendule initial quasiment vertical (171°) à vitesse nulle\n", "y0 = [np.pi*19/20, 0.0]\n", "#duree de simulation\n", "T=64\n", "# resolution avec schéma RK45\n", "sol = solve_ivp(pend, [0, T], y0, dense_output=True)\n", "# on veut suffisamment de points pour le graphe\n", "t = np.linspace(0, T, 100)\n", "y = sol.sol(t)" ] }, { "cell_type": "code", "execution_count": 19, "id": "81698c4c", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#tracé des courbes solutions\n", "plt.plot(t, y[0], 'b', label='y')\n", "plt.plot(t, y[1], 'g', label=\" y' \")\n", "plt.legend(loc='best')\n", "plt.xlabel('t')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "id": "566bf98b", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plan de phases\n", "plt.plot(y[0], y[1], 'b')\n", "plt.axis('equal')\n", "plt.xlabel('y')\n", "plt.ylabel(\"y'\")\n", "plt.title('schéma RK45 de Python')\n", "#plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9cbb9723", "metadata": {}, "source": [ "Avec solve_ivp, on obtient un résultat non physique, après 3 périodes, le pendule fait un tour complet au lieu de revenir! Cela semble dû à un défaut de conservation de l'énergie. Le schéma implicite-explicite se comporte bien." ] }, { "cell_type": "code", "execution_count": 21, "id": "583d98c7", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t=np.linspace(0,T,N)\n", "y = sol.sol(t)\n", "plt.plot(t,0.5*p**2 - np.cos(q))\n", "plt.plot(t,0.5*y[1]**2 - np.cos(y[0]))\n", "plt.plot(t,-np.cos(y0[0])*np.ones(len(t)))\n", "plt.xlabel('t')\n", "plt.ylabel('energie')\n", "plt.legend(['E(t) implicite-explicite','E(t) RK45','E(0)'])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3b978066", "metadata": {}, "source": [ "On voit un excès d'energie non physique à t= 50 environ là où le pendule fait un tour complet." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }