{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Description du système\n", "\n", "Le système se compose des éléments suivants:\n", "\n", "* une bobine $L$ d'état $\\phi_L(t)$ et de fonction de stockage $\\mathtt{H}_\\phi(\\phi_L)=\\frac{\\phi_L^2}{2L}$,\n", "* un condensateur $C$ d'état $q_C(t)$ et de fonction de stockage $\\mathtt{H}_q(q_C)=\\frac{q_C^2}{2C}$,\n", "* une résistance $R$ de variable associée $i_r$ et de puissance dissipée $D_r(i_r)=R\\, i_r^2$.\n", "\n", "On définit:\n", "\n", "* l'état $\\mathbf{x}=\\left(\\phi_L(t), q_C(t)\\right)^\\intercal$,\n", "* le Hamiltonien $\\mathtt{H}(\\mathbf{x}) = \\mathtt{H}_\\phi(x_1) + \\mathtt{H}_q(x_2)$,\n", "* la variable de dissipation $\\mathbf{w}=\\left(i_r\\right)^\\intercal$\n", "* la fonction de dissipation $\\mathbf{z}(\\mathbf{w})=\\left(R\\,w_1\\right)^\\intercal$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[phi_L, q_C]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sp\n", "\n", "x = sp.symbols(['phi_L','q_C'])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "le hamiltonien du système \n", "Python ne propose pas directement de fonctionnalités pour le calcul numériqe. Elles sont chargées depuis des modules externes. Les plus utilisés sont ```numpy``` pour les structures de données numériques (```numpy.array```, ```numpy.matrix```).\n", "Python itself does not provide usefool ttools for numerical computations. So we have to import them. Ther is several ways to import modules:\n", "* You can import all the methods and functions with \n", "```python\n", "from module import *\n", "```\n", "* You can import selected functions `f1` and `f2` from a given `module` with\n", "```python\n", "from module import f1, f2\n", "```\n", "* You can import the module with a specified label with\n", "```python\n", "import module as label\n", "```" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load Plot module\n", "import matplotlib.pyplot as plt\n", "# This line configures matplotlib to show figures embedded in the notebook, \n", "# instead of poping up a new window.\n", "%matplotlib inline\n", "# Load numerical module\n", "import numpy as np\n", "eps = np.spacing(1) # numerical precision\n", "\n", "from IPython.display import Latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Array definition\n", "On souhaite afficher la courbe $A\\sin(2\\pi f_0t)$ pour $t\\in [0,1]$. Tout d'abord on définit un signal \n", "\n", "$$\\begin{eqnarray}\n", "\\nabla \\times \\vec{\\mathbf{B}} -\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} & = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\\n", "\\nabla \\cdot \\vec{\\mathbf{E}} & = 4 \\pi \\rho \\\\\n", "\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n", "\\nabla \\cdot \\vec{\\mathbf{B}} & = 0 \n", "\\end{eqnarray}$$\n", "\n", "$s(f_0)=A\\sin(2\\pi f_0t)$, puis on l'utilise récursivement." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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o9Lyxnbx/EoXsCqF5FcMOh9RUHl0zb56C0u/4+vLIp1fCO78+fOPDfJErPyvT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\nYPCBHOednMRg5esLvPUWULmyPvLpTteuwj9m2TLV/84pKSI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Time Vector\n", "t = np.linspace(0,1,300)\n", "# Signal function\n", "A = 10 # Amplitude (V)\n", "s = lambda f0: A*np.sin(2*np.pi*f0*t)\n", "\n", "\n", "axis = plt.axes()\n", "# Plot for a list of f0\n", "for f0 in np.linspace(1,2,3):\n", " label = '$f_0=$'+str(f0)\n", " axis.plot(t, s(f0), label=label)\n", "\n", "# Plot axis\n", "axis.set_xlabel('Temps (s)')\n", "axis.set_ylabel('Amplitude (V)')\n", "\n", "# Plot label and legend\n", "axis.set_title('$\\sin(2\\pi f_0 t)$')\n", "axis.legend(loc=0) # option loc=0 set location with minimal overlap\n", "\n", "# activate a grid\n", "axis.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Somme\n", "Ici on somme les trois signaux pour visualiser une forme d'onde complexe *i.e.* nonpure." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YwBHaRYDzgLtVNSbfJ0SkMdBHVa/xXj8MZKubwTZnHy0obhO6/v3dugtTpsAJ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\n6piMMXF32WVQujR8+im0bRv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, [np.sum(e) for e in zip(*[s(f0) for f0 in [1,2,3]])], label='$\\sum_{i=1}^3 S_i(t)$')\n", "\n", "# Plot axis\n", "plt.xlabel('Temps (s)')\n", "plt.ylabel('Amplitude (V)')\n", "\n", "# Plot label and legend\n", "plt.title('$\\sin(2\\pi f_0 t)$')\n", "plt.legend(loc=1) # option loc=0 set location with minimal overlap\n", "\n", "# Show the plot\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }