{"cells": [{"cell_type": "markdown", "id": "3a4603bd", "metadata": {}, "source": ["# Le pendule\n", "\n", "On consid\u00e8re l'\u00e9quation :\n", "$$ \\theta^{\\prime\\prime} = -\\sin{\\theta}$$\n", "\n", "Pour r\u00e9soudre cette \u00e9quation, on d\u00e9finit le tableau $y(t) = (\\theta(t), \\theta^\\prime(t))$. \n", "\n", "1. \u00c9crire la fonction Python ``f(t, y)`` qui renvoie la d\u00e9riv\u00e9e de $y$\n", "\n", "2. R\u00e9soudre et tracer le resultat de l'\u00e9quation diff\u00e9rentielle pour les conditions initiales : $\\theta(0) = 2\\pi/4$ et $\\theta^\\prime(0) = 0$\n", "\n", "3. V\u00e9rifier que l'\u00e9nergie totale est conserv\u00e9e"]}], "metadata": {"kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8"}, "varInspector": {"cols": {"lenName": 16, "lenType": 16, "lenVar": 40}, "kernels_config": {"python": {"delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())"}, "r": {"delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) "}}, "types_to_exclude": ["module", "function", "builtin_function_or_method", "instance", "_Feature"], "window_display": false}}, "nbformat": 4, "nbformat_minor": 5}