5. Mouvement 2D et vecteurs vitesse.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MOUVEMENT 2D ET VECTEURS VITESSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On étudie le mouvement d’une balle de golf à partir d’une chronophotographie dans le but est de tracer les vecteurs vitesse au cours du temps. Les mêmes outils présentés dans les activités précédentes sont réexploités. Les positions relevées toutes les 0,066 s sont rassemblées dans un tableau.\n",
    "\n",
    "**Capacité numérique** : représenter des vecteurs vitesse d’un système modélisé par un point lors d’un mouvement à l’aide d’un langage de programmation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Représentation de la trajectoire\n",
    "Le tableau des temps successifs, puis ceux des abscisses et des ordonnées sont créés. Pour représenter la trajectoire, il faut faire tracer l’ordonnée en fonction de l’abscisse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# le début du script est identique à ce qui précède. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11105df28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=0.066*np.arange(11) # Ici le nombre de mesures est N=11\n",
    "x=np.array([0.01,0.25,0.57,0.91,1.22,1.54,1.87,2.16,2.49,2.81,3.15])\n",
    "y=np.array([0.01549,0.3404,0.6812,1.010,1.297,1.559,1.768,1.95,2.08,2.158,2.193])\n",
    "plt.plot(x,y,'ro',label=\"y=f(x)\")\n",
    "plt.xlabel(\"xreelle\")\n",
    "plt.ylabel(\"yreelle\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.title(\"Trajectoire de la balle\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Représentation des vecteurs déplacement\n",
    "Comme précédemment, la boucle `for` permet de faire défiler les positions successives (termes de yreelle) et le tracé des vecteurs s’effectue avec la fonction `plt.arrow`. Comme précédemment, il faut prendre garde à redimensionner la liste, pour qu’elle contienne un élément de moins (car on ne peut pas calculer x[i+1] et y[i+1] pour la dernière valeur). La commande `len(t)` indique le nombre de valeurs dans la liste t."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119325828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=np.arange(len(t)-1)\n",
    "for i in n :\n",
    "    plt.arrow(x[i],y[i],x[i+1]-x[i],y[i+1]-y[i],head_width=0.05) #on fait tracer une série de vecteurs\n",
    "# de position initiale x[i],y[i], de coordonnées x[i+1]-x[i] et y[i+1]-y[i]\n",
    "# head_width est la largeur de la tête\n",
    "plt.xlim(0,4)\n",
    "plt.ylim(0,3)\n",
    "plt.grid()\n",
    "\n",
    "plt.title(\"Vecteurs déplacement\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion** : le résultat est plus lisible. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Représentation des vecteurs vitesse\n",
    "Pour les vecteurs vitesse, plusieurs définitions sont envisageables. La plus classique consiste à calculer le déplacement entre les points i et i+2, à diviser par l’intervalle de temps qui sépare ces deux positions et à affecter cette vitesse au point i+1. Ainsi, il faut à nouveau redimensionner la liste des i comme cela est proposé dans le script suivant : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1193baf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m=np.arange(len(t)-2) # comme on travaille dans la suite sur des intervalles i à i+2, il faut couper la boucle à N-2\n",
    "for i in m :\n",
    "    plt.arrow(x[i+1],y[i+1],0.1*(x[i+2]-x[i])/(t[i+2]-t[i]),0.1*(y[i+2]-y[i])/(t[i+2]-t[i]),head_width=0.05) #on fait \n",
    "# tracer une série de vecteurs de position initiale x[i+1],y[i+1], de coordonnées 0.1(x[i+2]-x[i])/(t[i+2]-t[i]) \n",
    "# et idem selon uy. \n",
    "# Ces longueurs correspondent au déplacement de i à i+2 rapporté à l'intervalle de temps correspondant.\n",
    "# on multiplie par 0.1 pour que la figure soit lisible.\n",
    "plt.xlim(0,4)\n",
    "plt.ylim(0,3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion** : On notera que si le résultat est plus lisible, il faut tout de même réfléchir à l’échelle de représentation du vecteur vitesse sur le graphe – c’est la raison du facteur 0.1 qui a été placé devant les vecteurs."
   ]
  }
 ],
 "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}