{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color= 'red'>Représentation graphique en langage Python</font>\n",
    "\n",
    "L’objectif de ce complément est d’aborder, à travers des cas concrets rencontrés aux cours des activités expérimentales et numériques du programme, la majeure partie des instructions du langage de programmation Python présentes dans le point numérique du manuel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color= 'red'>Introduction</font>\n",
    "Dans de très nombreuses situations en Physique-Chimie, comme en mécanique pour représenter les positions successives d'un mobile assimilé à un point lors de son mouvement ou en électricité pour tracer la caractéristique tension-courant d'un dipôle, il est utile de tracer la représentation graphique $y = f(x)$ d'une grandeur $y$ en fonction d'une grandeur $x$.\n",
    "\n",
    "En langage de programmation Python, une représentation graphique se fait grâce aux fonctions et instructions du module ```pyplot``` de la bibliothèque `matplotlib` habituellement importé sous le préfixe `plt`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!/usr/bin/python                                                                       \n",
    "# -*- coding: utf-8 -*-\n",
    "import matplotlib.pyplot as plt       # Importe le module pyplot en plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La représentation graphique de la courbe d'équation $y=f(x)$, se fait grâce à l'instruction `plt.plot(x,y,paramètres)` où  `x` et `y` sont des objets contenant les abscisses et les ordonnées des points à représenter et `paramètres` précise l'aspect des points et/ou de la courbe. \n",
    "\n",
    "Les objets `x` et `y` peuvent être :    \n",
    "$\\quad$ -  soit des listes de nombres de type «liste» ;           \n",
    "$\\quad$ -  soit des tableaux de nombres comportant une seule ligne, de type «tableau» («array» en anglais) de la bibliothèque `NumPy`.  \n",
    "\n",
    "Quel que soit le type des objets `x` et `y`, la seule contrainte de l'instruction `plt.plot(x,y)` est qu'ils aient le même nombre de valeurs, c'est à dire qu'il y ait *autant de valeurs pour les abscisses que de valeurs pour les ordonnées*.\n",
    "\n",
    "La suite d'instructions pour tracer la courbe d'équation $y=f(x)$ est la suivante :   \n",
    "$\\qquad$**a.** $\\,$ Définir le domaine des abscisses, c'est à dire la liste ou le tableau `x` des abscisses ;                \n",
    "$\\qquad$**b.** $\\,$ Définir le domaine des ordonnées, c'est à dire la liste ou le tableau `y` des ordonnées ;             \n",
    "$\\qquad$**c.** $\\,$ Définir la figure et l'habillage de la courbe à l'aide des instructions du module `pyplot` ;            \n",
    "$\\qquad$**d.** $\\,$ Tracer les points et préciser leur aspect avec l'instruction `plt.plot(x,y,paramètres)` ;             \n",
    "$\\qquad$**e.** $\\,$ Afficher la figure à l'aide de l'instruction `plt.show()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color= 'red'>Exemple 1 : Lancer franc au Basket</font>  \n",
    "\n",
    "Les coordonnées ($\\,x\\,$,$\\,y\\,$) des positions successives du ballon lors d'un lancer franc au basket ont été obtenues par pointage de la position du centre du ballon sur 12 images  de la vidéo du lancer, grâce à un logiciel dédié :  \n",
    "$\\qquad$ - l'intervalle de temps entre chaque image vaut $\\Delta t$ = 66,62 ms ;          \n",
    "$\\qquad$ - l'origine des dates est choisie à l'image immédiatement après que le ballon a quitté les mains du joueur ;          \n",
    "$\\qquad$ - l'origine des axes est choisie à la position du ballon à l'origine des dates.  \n",
    "\n",
    "### 1. Représentation des positions successives du ballon\n",
    "\n",
    "#### 1.1. Définition des listes `x` et `y` des coordonnées des points\n",
    "Les dates des positions et les coordonnées des points sont définies dans 3 objets `t`, `x` et `y` de type «liste» :  \n",
    "$\\qquad$ - les valeurs sont rangées dans l'ordre entre crochets `[ ]` ;         \n",
    "$\\qquad$ - le point `.` est le séparateur décimal ;        \n",
    "$\\qquad$ - la virgule `,` permet de séparer les valeurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = [0.00,0.066,0.133,0.199,0.266,0.333,0.399,0.466,0.533,0.599,0.666,0.733]\n",
    "x = [0.00,0.28,0.55,0.80,1.05,1.31,1.56,1.85,2.11,2.35,2.61,2.87]\n",
    "y = [0.00,0.36,0.69,0.98,1.21,1.40,1.55,1.67,1.75,1.79,1.77,1.71]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2. Définition et affichage de la figure représentant les points\n",
    "La figure est initialisée par l'instruction `plt.figure()` qui permet également de définir sa taille (largeur,hauteur).   \n",
    "Si la taille de l'image et les échelles sur les axes ne sont pas précisées, l'affichage s'adapte automatiquement.\n",
    "\n",
    "Les `paramètres` de l'habillage des points les plus courants sont :   \n",
    "$\\qquad$ - couleurs : `'r'` rouge, `'b'`  bleu, `'c'` cyan, `'g'` vert, `'k'` noir ;      \n",
    "$\\qquad$ - formes : `'o'` point, `'+'` plus, `'x'` croix ;        \n",
    "$\\qquad$ - ligne entre les points :  `'-'`  ligne continue, `'--'` pointillés, `':'` petits points.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ZDjoo1wP40IfgzW/uOs+sWc6OXUGR6pgFR8Rw4LcppR2XUmd1YDawdWfPW0Q8DPwTSMCFKaWLlnL8icCJAEOHDt3tyiuvrFn8fWHevHmsWXk9hFaYbVk7tmVt2I61s6Jt2fbqq+x68smsOXMmUfF9l9rauPmPf4SODmLJEtIqq9Qy3IZW1udyg/Z2Br7yCk++850AjP7Qh3h1ww35+9e/DsA699/P/M0357V11617bCuq1m05duzYyVWNMKaU6vYAhgNTllHnfcCkbts2KX5uCNwH7F3N6+22226p0f3pT38qO4SWYVvWjm1ZG7Zj7SxXW55+ekqf/3xX+YQTUho2LKW2tpQg/9x++5rH2Cwa5nM5cWJKN96Yny9alNLgwSmdckoud3Sk9JOfpPToo+XFV4VatyVwV6oiv2nEpUKOpNuQaUppTvHzGeDXwO4lxCVJakR/+AOceWZX+Zln8qPTj34Et9zS81CfyjN+POy3X37e1gY33AAf+UguP/IIHHNMnkAB+Xq5c87J29VYyVtErAPsA/ymYtsaEbFW53PgQKDHGauSpH5gzhy44IKu2Yy33ZaXvOicVHDxxTlhq9S5FMfixfnnVlvVN2Yt3YABsNdeObGGfI3h9Onw3vfm8j335PXtOtecmzYNPvvZPPO1H6rnUiFXAH8FtouI2RFxfER8JCI+UlHtXcAfUkqvVGwbCtwaEfcBdwC/Syn9vl5xS5JKlhJrPvhg7n2BfJeBj360a0bo5z6Xv8QHDy4tRNVYRJ40MmRILo8Zk3tT3/a2XL7/fvjf/+2avXrttflWYy+8UEq49Va3RXpTSkdVUWcCeUmRym2zgF36JipJUkNatCj3pK2zDtx9N6M//GFYbbW8VMf48fl+nttum+t2rlum1rbBBl3P3/c+OOywvDwJ5CVfbr4Z1lorl7/znTxU/q1v5YWRZ8zIyeCkSS3R69pQw6aSpH6ssxdlwYK80v83v5nLu+7KtM9/Hv7jP3J5rbW6Ejf1X52JG+Rr5WbN6lqWBPLzQw/tWiJm+vSc+LcAkzdJUvmOPrrrhu2DB+frmw44IJfb2nj6gAO6htCkZfnUp/LdIGbM6Lo2sqMjl1uAyZskqf5++lM4quJqmm237VoYF/LF6J0L6Uorqre7QTQ5kzdJUt+bMgU+8Yl8LRvA88/nm5vPn5/LZ5yRH1It9XY3iCZn8iZJqr158/IN2jtv4P7ww3DRRfnWVACnnAK33upkA/WtFl0ixuRNkrRiut/s/dZb86w/gCeegPe/HyZOzOVx4+C55/KN3CEvBSFphZi8SZJWTOXN3qdPh733zkszQL626I474IQTcnmVVVyHTaqRuq3zJklqMdOmdS3v0dGRLwj/+Me79r/5zeXEJbU4e94kSdV5+mn44Q+7ErahQ7uGP9va8gXhW29dXnxSP2HyJknqXUpd62T99rdw0kn51kQAf/kLjBzZcjP5pEZn8iZJ6tmcObDLLnDVVbl81FF5qHSX4o6FLTqTT2p0Jm+SpC5TpsANN+TnG20E22wDa6+dy6uvnnvYJJXKCQuS1N+l1HXt2sc+Bs88k3vS2tryLYYkNRR73iSpP/vVr/J1a/Pm5fL558Mtt7gOm9TATN4kqT/p6IA//CFfzwawySZ5aPS553J55EhvAC81OJM3SepPZs/Odzu4+OJc3nPPPEt0iy3KjUtS1bzmTZJa3SmnwGuv5TXaNt8c/vhHeOtby45K0gqy502SWs2CBXDddV3lVVeFQYO6ymPH5m2SmpI9b5LUan7wAzj1VHjwwXw92ze+UXZEkmrInjdJanaPP56vY7vpplw+7jj405+8VZXUokzeJKkZPf10122qNtgAnnqqa8boBhvAmDEu9yG1KIdNJakZjRuXr2P7299gtdXgnntM1qR+wp43SWoG116bE7bFi3P5+9+Hn/yka7+Jm9RvmLxJUqOaMgVeeik/f+21fNuqzsV1997b+4xK/ZTJmyQ1omnTYKedunrXDjkEJk/O67RJ6tdM3iSpLLNmwQ47wMCB+ecpp8A55+R9I0fCJZfAUUflcoRDo5IAJyxIUnnGj4fp0/P9RqdPz0t+vPvdXfuPO6682CQ1LHveJKksnYkb5J/z58OECaWGJKnxmbxJUj11dMDLL+fnb3xj11BoWxtst115cUlqGiZvklQvHR2w335w4om5/Pvf52vbBgzIM0cnTSo3PklNwWveJKmvLVgAgwfn3rXDDoP118/bt9oKpk4tNzZJTceeN0nqS3fcAVtsAX/9ay6fcgocfXS5MUlqanVL3iLikoh4JiKm9LJ/TES8GBH3Fo8vVewbFxEzImJmRJxWr5glaYW99lr+uf32MHYsrL12ufFIahn17HmbAIxbRp0/p5RGFY+zACJiAHAecBCwPXBURGzfp5FK0so444ycsHV0wJprwlVX5XXcJKkG6nbNW0rplogYvgKH7g7MTCnNAoiIK4FDgQdqF50kraSOjq6FdLfbDl5+mbbO+5BKUg012jVve0bEfRFxXUR0/jd1GPB4RZ3ZxTZJagxPPw1vfWvuYQP4wAfge9+jY9CgcuOS1JIaabbp3cAWKaV5EfEfwDXANkBP94NJvZ0kIk4ETgQYOnQo7e3tfRBq7cybN6/hY2wWtmXt2JZVSin3tC1Zwo5tbTz14IM8W9FutmPt2Ja1Y1vWTllt2TDJW0rppYrn10bEDyNiCLmnbbOKqpsCc5ZynouAiwBGjx6dxowZ0zcB10h7ezuNHmOzsC1rx7aswjXXwNlnw803w+qrw377MaRbFduxdmzL2rEta6estmyYYdOI2CgiLzUeEbuTY3sOuBPYJiK2jIhBwJHAxPIilSRgvfXy2m3PP192JJL6mbr1vEXEFcAYYEhEzAa+DKwCkFK6ADgc+GhELAYWAEemlBKwOCI+BlwPDAAuSSm5qqWk+lq8GE4+GYYPh1NPhX32yb1u0dOVHZLUd+o52/SoZew/Fzi3l33XAtf2RVySVJWBA+G552Dddbu2mbhJKkHDDJtKUsN54AE44AB48slcvvJK+J//KTcmSf2eyZsk9WbQIPjHP2DmzFxu80+mpPI1zGxTSWoIEybAtGlwzjmw9dY5cRvon0pJjcP/RkpSpSlT4PbbYdGiXDZxk9RgTN4k9W8vvAD/9V9w3325fPbZ0N6eh0wlqQGZvEnq31KCX/8abr01l1dd1Vmkkhqa4wGS+p/Jk+HnP4dvfzsvtvuPf8Caa5YdlSRVxZ43Sf3P7bfD5ZfD7Nm5bOImqYmYvElqfR0dcPHFcP31ufyRj8CMGbDZZks/TpIakMOmklrTrFkwfnxO0rbdNs8e3XNPeMc7YMAAWGedsiOUpBViz5uk1vTOd+b12pYsyQncgAHw05+WHZUkrTSTN0mt6cEH80xSyMOmDz3kLFJJLcHkTVLrSCknaQAjRnTdzqqtDbbbrry4JKmGTN4ktY6zzoJdd4XHH4dJk3ICN2BA/jlpUtnRSVJNOGFBUvNLKQ+JHnssrL02DBuWe9umTi07MkmqOXveJDW3r389L/0BsMUW8MlPdg2XSlIL8i+cpOY2bx689BK89lrZkUhSXThsKqn5/O53eWh01Kh8nVuEM0kl9Rv2vElqLgsWwIc/DF/7Wi63tZm4SepX7HmT1Bxmz869bYMHwx/+AFttVXZEklQKe94kNb5p02DkSLjgglzefntYbbVyY5Kkkpi8SWp8I0bAJz4BBx9cdiSSVDqTN0mN6d57Yd994bnn8jVtX/0qbLZZ2VFJUulM3iQ1po4OeOyxfLcESdK/mLxJahxz58KVV+bnb3oTTJ+elwORJP2LyZukxnH22XD88fDMM7k80AnxktSdyZukcr32Wr6uDfJ1bbffDhtuWG5MktTA/G+tpPKkBOPHw/z50N4Oa60FO+1UdlSS1NBM3iSVJwKOPTYncd5MXpKqYvImqb4WLsxrto0bB4cdBkceWXZEktRU/K+upPqKgMmTYerUsiORpKZkz5ukvpdSXgLkXe/Kt7W69VZYddWyo5KkplS3nreIuCQinomIKb3s/8+IuL943BYRu1TseyQi/h4R90bEXfWKWVKN3H03vP/9cPHFuWziJkkrrJ49bxOAc4Gf9rL/YWCflNI/I+Ig4CJgj4r9Y1NKz/ZtiJJq6vnnYf31Ybfd4KabYJ99yo5Ikppe3XreUkq3AM8vZf9tKaV/FsXbgU3rEpikvnHFFbDllvkuCQBjxzqjVJJqoFH/kh4PXFdRTsAfImJyRJxYUkySlsc++8BRR8Emm5QdiSS1lEgp1e/FIoYDv00p7biUOmOBHwJvSyk9V2zbJKU0JyI2BG4ATi568no6/kTgRIChQ4fudmXnfRIb1Lx581hzzTXLDqMl2Ja1s6Jtuf7tt/OGv/2Nf3z843lWaT/nZ7J2bMvasS1rp9ZtOXbs2MkppdHLqtdQs00jYmfgYuCgzsQNIKU0p/j5TET8Gtgd6DF5SyldRL5ejtGjR6cxY8b0ddgrpb29nUaPsVnYlrWzwm15223w8MMM23VXWHfdmsfVbPxM1o5tWTu2Ze2U1ZYNM2waEZsD/wccnVJ6sGL7GhGxVudz4ECgxxmrkkrw4INwzz35+amn5nuTmrhJUp+pW89bRFwBjAGGRMRs4MvAKgAppQuALwFvAH4YebhlcdF1OBT4dbFtIHB5Sun39Ypb0lJ0dMB73pPXbrvjDhgwID8kSX2mbslbSumoZew/ATihh+2zgF1ef4Sk0sybB6uvnmeP/vSnMGSI17hJUp00zLCppCYwaxZstx2stRZsvHEu77orbLZZ2ZFJUr9h8iapeuPHw8yZ+fncubksSaorkzdJ1fnFL2DGjHydG+T7lc6YUW5MktQPmbxJWrann4bjjoN11um6S0JbWx5ClSTVlcmbpGUbOhTa2+HWW2HEiDyjdMQImDSp7Mgkqd9pqEV6JTWQJUvgpJNg3Dg47DAYXSz6PXVquXFJUj9nz5uknr36Ktx7L9x3X9mRSJIq2PMm6d+9/DLx2mt5Hbf29rwArySpYZi8SeqyaBHsuy/brb8+HHCAiZskNSCTN0ldBg2CI4/kmUWL2KjsWCRJPfKaN0kwbVrXRIRPf5rn99yz3HgkSb2y503q7zo64H3vy71ud97pPUolqcGZvEn9XVsbXH45DB5s4iZJTcDkTeqvrr4anngCPvlJ2HHHsqORJFXJa96k/uqaa+DXv4bFi8uORJK0HOx5k/qTlGDBgryG24QJOXEb6J8BSWom9rxJ/cnnPgf7758TuEGDchInSWoq/pdb6k/e8pY8u3TVVcuORJK0gux5k1rd/Plwxx35+XveA9/+dp5hKklqSv4Fl1rdJz6Rh0qfe67sSCRJNeCwqdTqzjoLxo+HN7yh7EgkSTVgz5vUimbOhDPOyLNLN9ooJ2+SpJZg8ia1ol/+Es4/Hx5/vOxIJEk1ZvImtZLOBXdPPRXuvx8237zceCRJNWfyJrWK3/0Odt4Z5szJ9yjdZJOyI5Ik9QGTN6lVbLghbLxxXnxXktSylit5i4i2iHBJdqmR3H9//vnmN8ONN8KQIeXGI0nqU8tM3iLioIj4aUQ8CiwCXo6IVyLizxHxhYhwbEYqy89+BqNGwa235nJEufFIkvpcr+u8RcRhwDeAtYBrga8Bc4AFwPrAjsD+wBkRMQE4I6U0t68DllTh8MNh7lzYc8+yI5Ek1cnSFuk9HfgUcG1KqaOH/VcDRMQw4BTgg8C3ax6hpH+3cCF861vw2c/C4MHwqU+VHZEkqY56Td5SSntUc4KU0hPA52oWkaSla2+HL385D5cefHDZ0UiS6szbY0nNIqV8Tdu4cTB1KowYUXZEkqQSVJ28RcS7gLHAhnSb6JBSem+N45JU6bHH4Igj4MILc4+biZsk9VtVLRUSEd8GrgJ2KjYt6faoSkRcEhHPRMSUXvZHRPxvRMyMiPsj4k0V+46JiH8Uj2OqfU2pZSxYAPPmlR2FJKlk1fa8HQMckVL6zUq+3gTgXOCnvew/CNimeOwBnA/sERHrA18GRgMJmBwRE1NK/1zJeKTG9uij+RZXm28O994Lba6rLUn9XbXfBPOB6Sv7YimlW4Dnl1LlUOCnKbsdWDciNgbeAdxLAjvQAAAeOUlEQVSQUnq+SNhuAMatbDxSQ5s2DXbYAc47L5dN3CRJVN/z9nXgcxHx4ZTS4j6MZxjweEV5drGtt+2vExEnAicCDB06lPb29j4JtFbmzZvX8DE2i5Zry44Ohh9+OHM23phFdf69Wq4tS2I71o5tWTu2Ze2U1ZbVJm8/Ag4GnoiIB4HXKnemlPatUTw9LQ+flrL99RtTugi4CGD06NFpzJgxNQqtb7S3t9PoMTaLlmnLn/8cDjwQNtgA9t2X4SWE0DJtWTLbsXZsy9qxLWunrLasdhzmAuDtwC3AfcDUbo9amQ1sVlHelHxXh962S61h1qw8RDpwIBx9NHzxi2VHJElqUNX2vL0XeHdK6Ya+DAaYCHwsIq4kT1h4MaX0ZERcD3wtItYr6h1IvgOE1BrGj4fp06GjI6/l9uc/lx2RJKlBVZu8PQs8sbIvFhFXAGOAIRExmzyDdBWAlNIF5Huo/gcwkzxJ4rhi3/MR8VXgzuJUZ6WUljbxQWounYkb5MV4H3yw3HgkSQ2r2uTty8BZEXFsSmmFF5pKKR21jP0JOKmXfZcAl6zoa0sNq6MDVl01r+MGeVbpdtuVG5MkqWFVm7x9FhgOPB0Rj/H6CQs71zguqf9oa4M77oDDD4eZM3PiNmlS2VFJkhpUtcnbL/s0Cqk/evZZ+O53803md9wxD51KkrQMVSVvKaWv9HUgUr8zaRJ85zvw3vfCLruUHY0kqUm4ZLtUluOOgxkzTNwkScvF5E2qt+9+N9/6CvI9SyVJWg4mb1I9Pf88nHMOXHRR2ZFIkppUtRMWJNXC+uvD5Mmw4YZlRyJJalL2vEn1MHUqnHdefj5sGKyySrnxSJKaVtU9bxGxB7AfsCHdkr6U0sdrHJfUWs4/H371KzjqqNz7JknSCqoqeYuIzwDfIN+2ag6QKnanHg+S1OX734fPfMbETZK00qrteTsF+HhK6dy+DEZqKUuWwNlnw8knw3rrwfDhZUckSWoB1V7ztjb5pvGSqnXPPTl5u+aasiORJLWQanvergDGAT/sw1ik1jJ6dJ6osPXWZUciSWoh1SZvjwNfiYi9gPt5/Y3pv1PrwKSmdd11eTbp/vubuEmSaq7a5O0EYB7w1uJRKQEmbxJASvDVr0JHB+y7L7S5Go8kqbaqvTH9ln0diNQSIuD3v4f5803cJEl9Yrm/XSJiaET4rSRVevll+J//gcWLYe21YaONyo5IktSiqkrCImKViPhGRLwMPAEML7afExH/1YfxSc3h//4PzjgD7r677EgkSS2u2h60LwPjgQ8Ar1ZsvwM4tsYxSc3nmGNgyhTYffeyI5Ektbhqk7ejgI+klH4DdFRsnwJsW/OopGZx6aUwc2Z+PmJEubFIkvqFapO3TYBHe9g+kOW4P6rUUl54AU49Fb7xjbIjkST1I9UmXlOBvYFHum1/LzC5lgFJTWPddeH222HjjcuORJLUj1SbvH0FuCwiNgMGAEdExAjg/cA7+yo4qSE9/DC0t8Nxx8FWW5UdjSSpn6lq2DSlNIncy3Yg+Zq3LwPbAONTSjf2XXhSA/rud+HTn4a5c8uORJLUD1V9vVpK6Xrg+j6MRWoO3/kOfPSjsMEGZUciSeqHeu15i4hYnhMtb32pqaQE3/sevPQSDBwII0eWHZEkqZ9a2rDp9Ij4QESstrQTRMTIiPgRcFptQ5MayH33wWc/Cz/7WdmRSJL6uaUNm54IfAM4NyJuBO4CngQWAusB2wNvI6/z9r/AuX0bqlSiUaNg8mTYaaeyI5Ek9XO9Jm8ppZuBPSLireRFeo8EtgAGA88C9wCXAJellF6oQ6xS/d16K3R0wN57w847lx2NJEnLnrCQUroNuK0OsUiNJSU47bR80/m774YBA8qOSJIk744g9SoCJk2CF180cZMkNYxqb48l9R8LF8K55+bh0vXWg+HDy45IkqR/qWvyFhHjImJGRMyMiNfNTo2I70bEvcXjwYh4oWLfkop9E+sZt/qZq6+Gk0+Gv/yl7EgkSXqdug2bRsQA4DzgAGA2cGdETEwpPdBZJ6X0yYr6JwO7VpxiQUppVL3iVT/2wQ/CDjvAbruVHYkkSa9Tz5633YGZKaVZKaVFwJXAoUupfxRwRV0ikwB+9St49NH83MRNktSgqkreIuKaiDg4IlYm2RsGPF5Rnl1s6+n1tgC2BG6q2LxaRNwVEbdHxGErEYf0ei+/DB/5CHzhC2VHIknSUkVKadmVIn4OHAa8CEwALk0p/WO5XijiCOAdKaUTivLRwO4ppZN7qHsqsGnlvojYJKU0JyK2Iid1+6WUHurh2BPJCwwzdOjQ3a688srlCbPu5s2bx5prrll2GC1hZdty9cce49X112eJ74efyxqxHWvHtqwd27J2at2WY8eOnZxSGr2selVd85ZS+s+IWBv4T+A44LSIuBW4GPhFSmlBFaeZDWxWUd4UmNNL3SOBk7rFMKf4OSsi2snXw70ueUspXQRcBDB69Og0ZsyYKkIrT3t7O40eY7NYobZ86im4+WZ43/v6JKZm5eeyNmzH2rEta8e2rJ2y2rLqYdCU0ksppfNTSrsDOwGTgQuBpyLiwohY1p267wS2iYgtI2IQOUF73azRiNiOfPutv1ZsWy8iVi2eDwH2Ah7ofqy03M45B44/PidxkiQ1geW+hi0iNiFPNDgYWAz8ktyjdn9EfKa341JKi4GPAdcD04CrU0pTI+KsiDikoupRwJXp38dzRwJ3RcR9wJ+Ar1fOUpVW2Dnn5J63jTYqOxJJkqpS1bBpRKxCTtg+RF7q4x7yTeuvSCnNK+q8lzxc+a3ezpNSuha4ttu2L3Urn9nDcbeRe/uk2pgwAY44AtZYw5mlkqSmUu06b08CAVwOnJZSur+HOjcA/6xVYFKfmTIlD5U++yx8ptfOYkmSGlK1ydsnyRMTFvZWIaX0T/LyHlJj23HHfPeEN7+57EgkSVpu1c42/VlfByL1uXvvhVdfhT32gLe8pexoJElaId6YXq1v1qx8u6tdd4W994YHHyw7IkmSVpjJm1rf+PEwfXp+vngxvOtd5cYjSdJKMHlTa0spJ24dHbnc0QEzZpQbkyRJK8HkTa1t4sScsEXkclsbbLdduTFJkrQSTN7U2g45BH78Yxg5EgYMgBEjYNKksqOSJGmFVbtUiNRcpk+HtdeGTTaBD30oPyRJagEmb2o9HR35RvODBsEdd3QNmUqS1AJM3tR62trgsstg4UITN0lSyzF5U2u5914YNQp28la4kqTW5IQFtYwNbr45L8R7ww1lhyJJUp8xeVPLeG7PPeE734F99y07FEmS+ozJm5rfU0/BwoV0DBoEn/xkXhJEkqQWZfKm5rZkCbzznXDoofluCpIktTgnLKi5DRgAZ5wBq63mzFJJUr9gz5ua17PP5p+HHQbjxpUbiyRJdWLypuY0aRJsuSXcfnvZkUiSVFcmb2pOo0fDf/4n7LJL2ZFIklRXXvOm5jJ/PgweDBtvDBdcUHY0kiTVnT1vah6LF8PBB8OHP1x2JJIklcaeNzWPAQPyArxbbFF2JJIklcbkTc1h8WIYOBC++MWyI5EkqVQOm6rx3Xor7LADzJhRdiSSJJXO5E2Nb7XVYNNNYejQsiORJKl0DpuqcaWU75owejT88Y9lRyNJUkOw502NKSU46ij49rfLjkSSpIZi8qbGtGhRvum8N5uXJOnfOGyqxrTqqnD11WVHIUlSw7HnTY3l73/PC/HOnZuvd4soOyJJkhqKyZsay0MPwbRp8NprZUciSVJDMnlTYznssJy8bbJJ2ZFIktSQ6pq8RcS4iJgRETMj4rQe9h8bEXMj4t7icULFvmMi4h/F45h6xq06OP10uO66/HzQoHJjkSSpgdVtwkJEDADOAw4AZgN3RsTElNID3apelVL6WLdj1we+DIwGEjC5OPafdQhdfW3evJy4LV4MBx1UdjSSJDW0es423R2YmVKaBRARVwKHAt2Tt568A7ghpfR8cewNwDjgij6KVfW05ppw2215hqkkSVqqeiZvw4DHK8qzgT16qPeeiNgbeBD4ZErp8V6OHdbTi0TEicCJAEOHDqW9vX3lI+9D8+bNa/gY+8qqTz3FsGuu4eHjjyetsspKn68/t2Wt2Za1YTvWjm1ZO7Zl7ZTVlvVM3npa86H7CqyTgCtSSq9GxEeAnwD7Vnls3pjSRcBFAKNHj05jxoxZ4YDrob29nUaPsc+cdx78/vds/rWvwVZbrfTp+nVb1phtWRu2Y+3YlrVjW9ZOWW1ZzwkLs4HNKsqbAnMqK6SUnkspvVoUfwTsVu2xakInnQTTp9ckcZMkqb+oZ/J2J7BNRGwZEYOAI4GJlRUiYuOK4iHAtOL59cCBEbFeRKwHHFhsUzO64IKctAFstFG5sUiS1GTqlryllBYDHyMnXdOAq1NKUyPirIg4pKj28YiYGhH3AR8Hji2OfR74KjkBvBM4q3PygprMCy/AmWfC975XdiSSJDWlut7bNKV0LXBtt21fqnh+OnB6L8deAlzSpwGq7627Ltx5JwwZUnYkkiQ1Je+woPp49lmYMCE/32wzGDy41HAkSWpWJm+qjx/8AD7yEXj44bIjkSSpqZm8qT6+9CX4y19gyy3LjkSSpKZm8qa+dd11eZLCgAGw227Lri9JkpbK5E1959ln4Ygj8k3nJUlSTdR1tqn6mSFD4IYbYOTIsiORJKll2POm2nvllXyjeYA998zLg0iSpJoweVPtnXkm7LsvPPFE2ZFIktRyHDZV7X3xi7nHbdiwsiORJKnl2POm2rn/fliyBNZZB9797rKjkSSpJZm8qTaefBL22gtOO63sSCRJamkOm6o2Nt4Yzj0XDjig7EgkSWppJm9aOa+9Bk89le9XeswxZUcjSVLLc9hUK+cLX4A3vQmeeabsSCRJ6hfsedPK+X//DzbaCDbcsOxIJEnqF+x50/KZNQt22AEGDsw/BwyAT32q7KgkSeo3TN60fMaPh+nT85Ig06blsiRJqhuTNy2fGTOgoyM/TymXJUlS3Zi8aflsuy20FR+btjbYbrty45EkqZ8xeVP1Lr0097ptvXW+1m3ECJg0qeyoJEnqV5xtquoNGwa77AKXX56TN0mSVHcmb1q2lCACDjwwPyRJUmkcNtXSdXTA4YfDhAllRyJJkjB507K88gq8+CIsWFB2JJIkCYdNtSxrrQXXX981w1SSJJXKb2T17JFH4Pjj4aWX8uSEiLIjkiRJmLypN7fdBr/5DcydW3YkkiSpgsmbevb+98NDD8Eb31h2JJIkqYLJm/7dVVfB7bfn5+usU24skiTpdZywoC6LF8NXvwqbbw7XXlt2NJIkqQcmb+oycCD8+c+wZEnZkUiSpF44bKq8EO9ll+Wf660HQ4aUHZEkSepFXZO3iBgXETMiYmZEnNbD/k9FxAMRcX9E/DEitqjYtyQi7i0eE+sZd8ubOBGOPtqbzEuS1ATqNmwaEQOA84ADgNnAnRExMaX0QEW1e4DRKaX5EfFR4BvA+4p9C1JKo+oVb79y6KFwww2w335lRyJJkpahnj1vuwMzU0qzUkqLgCuBQysrpJT+lFKaXxRvBzatY3z9z2OPwRNP5AV499/fhXglSWoC9UzehgGPV5RnF9t6czxwXUV5tYi4KyJuj4jD+iLAfueYY2DfffMsU0mS1BQipVSfF4o4AnhHSumEonw0sHtK6eQe6n4A+BiwT0rp1WLbJimlORGxFXATsF9K6aEejj0ROBFg6NChu1155ZV99jvVwrx581hzzTVLee3VH32UVefO5Z+jR5fy+rVWZlu2GtuyNmzH2rEta8e2rJ1at+XYsWMnp5SW+aVcz6VCZgObVZQ3BeZ0rxQR+wNfoCJxA0gpzSl+zoqIdmBX4HXJW0rpIuAigNGjR6cxY8bU7jfoA+3t7dQ9xtmzYdPWG5EupS1blG1ZG7Zj7diWtWNb1k5ZbVnPYdM7gW0iYsuIGAQcCfzbrNGI2BW4EDgkpfRMxfb1ImLV4vkQYC+gcqKDqjVlCmy7LVx6admRSJKkFVC3nreU0uKI+BhwPTAAuCSlNDUizgLuSilNBL4JrAn8IvLF84+llA4BRgIXRkQHOeH8erdZqqrWNtvAJz4BBx9cdiSSJGkF1PUOCymla4Fru237UsXz/Xs57jZgp76NrsV1dMCiRbDaavC1r5UdjSRJWkHeYaG/OPts2GsveOmlsiORJEkrwXub9hejRsHTT8Naa5UdiSRJWgkmb60upbz47vjx+SFJkpqaw6atbOFCGDMGrrqq7EgkSVKNmLy1snnz8s/VVis3DkmSVDMOm7ayIUOgvd17lkqS1ELseWtFd98Nxx6be95M3CRJaikmb63ozjtzj9uCBWVHIkmSaszkrRV9+MMwdSpssEHZkUiSpBozeWsl550Hkyfn52usUW4skiSpT5i8tYpXXoFvfQvOP7/sSCRJUh9ytmmrWGONfK3b6quXHYkkSepD9rw1u4UL4ZJL8p0UhgwxeZMkqcWZvDW7yy6D44+Hv/2t7EgkSVIdOGza7I4/HkaOhLe8pexIJElSHdjz1qweeACeeiovwrvXXmVHI0mS6sSet2bU0QHvfS+suSb89a/eRUGSpH7E5K0ZtbXB5ZfDq6+auEmS1M+YvDWbhx6CN74Rdt657EgkSVIJvOatmbS3w3bbwa9/XXYkkiSpJCZvzWSPPeALX4B3vKPsSCRJUkkcNm0Gnde2DR4MX/lK2dFIkqQS2fPWDE4+GcaMgUWLyo5EkiSVzJ63ZnDggbDFFjBoUNmRSJKkkpm8NbKOjrwsyOGHlx2JJElqEA6bNqrnn4ddd4Xf/rbsSCRJUgMxeWtUCxfCuuvCBhuUHYkkSWogDps2qk02yeu6eQcFSZJUwZ63RnP99XD88bBggYmbJEl6HZO3RvP3v8Pdd0NKZUciSZIakMlbo/nMZ+D222H11cuORJIkNSCTt0Zx5plw//35+aqrlhqKJElqXE5YaATPPAM/+hEsWQI771x2NJIkqYHVtectIsZFxIyImBkRp/Wwf9WIuKrY/7eIGF6x7/Ri+4yIaK07s2+4Idx7b+59kyRJWoq6JW8RMQA4DzgI2B44KiK271bteOCfKaWtge8C5xTHbg8cCewAjAN+WJyvec2aBSNGsM+++8IOO8DLL8OA5v6VJElS36tnz9vuwMyU0qyU0iLgSuDQbnUOBX5SPP8lsF9ERLH9ypTSqymlh4GZxfma1/jx8OCDREowfXouS5IkLUM9r3kbBjxeUZ4N7NFbnZTS4oh4EXhDsf32bscO6+lFIuJE4ESAoUOH0t7eXovYa26f6dNz4gbQ0UGaPp2bGzTWZjFv3ryGfb+bjW1ZG7Zj7diWtWNb1k5ZbVnP5K2nFWe7L2bWW51qjs0bU7oIuAhg9OjRacyYMcsRYh2NGJF73Iqbz8eIETRsrE2ivb3dNqwR27I2bMfasS1rx7asnbLasp7DprOBzSrKmwJzeqsTEQOBdYDnqzy2uUyaBCNGkNraciI3aVLZEUmSpCZQz+TtTmCbiNgyIgaRJyBM7FZnInBM8fxw4KaUUiq2H1nMRt0S2Aa4o05x942ttoKpU7n5j3+EqVNzWZIkaRnqNmxaXMP2MeB6YABwSUppakScBdyVUpoI/Bj4WUTMJPe4HVkcOzUirgYeABYDJ6WUltQrdkmSpEZR10V6U0rXAtd22/aliucLgSN6OfZs4Ow+DVCSJKnBeXssSZKkJmLyJkmS1ERM3iRJkpqIyZskSVITMXmTJElqIiZvkiRJTcTkTZIkqYmYvEmSJDURkzdJkqQmEvnWoa0pIuYCj5YdxzIMAZ4tO4gWYVvWjm1ZG7Zj7diWtWNb1k6t23KLlNIGy6rU0slbM4iIu1JKo8uOoxXYlrVjW9aG7Vg7tmXt2Ja1U1ZbOmwqSZLUREzeJEmSmojJW/kuKjuAFmJb1o5tWRu2Y+3YlrVjW9ZOKW3pNW+SJElNxJ43SZKkJmLyVicRMS4iZkTEzIg4rYf9q0bEVcX+v0XE8PpH2fiqaMdjI2JuRNxbPE4oI85mEBGXRMQzETGll/0REf9btPX9EfGmesfYDKpoxzER8WLFZ/JL9Y6xWUTEZhHxp4iYFhFTI+KUHur4uaxClW3pZ7MKEbFaRNwREfcVbfmVHurU9Tvc5K0OImIAcB5wELA9cFREbN+t2vHAP1NKWwPfBc6pb5SNr8p2BLgqpTSqeFxc1yCbywRg3FL2HwRsUzxOBM6vQ0zNaAJLb0eAP1d8Js+qQ0zNajHw6ZTSSOAtwEk9/Bv3c1mdatoS/GxW41Vg35TSLsAoYFxEvKVbnbp+h5u81cfuwMyU0qyU0iLgSuDQbnUOBX5SPP8lsF9ERB1jbAbVtKOqlFK6BXh+KVUOBX6astuBdSNi4/pE1zyqaEdVKaX0ZErp7uL5y8A0YFi3an4uq1BlW6oKxWdtXlFcpXh0nzBQ1+9wk7f6GAY8XlGezev/Ef2rTkppMfAi8Ia6RNc8qmlHgPcUwym/jIjN6hNaS6q2vbVsexZDLtdFxA5lB9MMimGnXYG/ddvl53I5LaUtwc9mVSJiQETcCzwD3JBS6vVzWY/vcJO3+ugp++6etVdTp7+rpo0mAcNTSjsDN9L1PyEtPz+TtXE3+ZY3uwA/AK4pOZ6GFxFrAr8CPpFSeqn77h4O8XPZi2W0pZ/NKqWUlqSURgGbArtHxI7dqtT1c2nyVh+zgcoeoE2BOb3ViYiBwDo4FNPdMtsxpfRcSunVovgjYLc6xdaKqvncahlSSi91DrmklK4FVomIISWH1bAiYhVysvHzlNL/9VDFz2WVltWWfjaXX0rpBaCd11/nWtfvcJO3+rgT2CYitoyIQcCRwMRudSYCxxTPDwduSi7C190y27HbtS+HkK/z0IqZCHywmN33FuDFlNKTZQfVbCJio85rXyJid/Lf3efKjaoxFe30Y2BaSuk7vVTzc1mFatrSz2Z1ImKDiFi3eD4Y2B+Y3q1aXb/DB/bVidUlpbQ4Ij4GXA8MAC5JKU2NiLOAu1JKE8n/yH4WETPJ2fqR5UXcmKpsx49HxCHkmVbPA8eWFnCDi4grgDHAkIiYDXyZfCEuKaULgGuB/wBmAvOB48qJtLFV0Y6HAx+NiMXAAuBI/2PWq72Ao4G/F9cXAXwe2Bz8XC6natrSz2Z1NgZ+Uqx40AZcnVL6bZnf4d5hQZIkqYk4bCpJktRETN4kSZKaiMmbJElSEzF5kyRJaiImb5IkSU3E5E2SJKmJmLxJ6pciYp+IeLBYu6nhRMQdEfHusuOQ1HhM3iT1V98Ezk4pLSk7kF58FTgnIvw7Lenf+EdBUr8TEW8FRgC/KDuWpbgWWAs4qOxAJDUWkzdJTau45+CTEfGlim07R8TCiDh8KYe+H7gxpTS/2/nGR8Tk4viHI+Ls4j66nfsfiYgvRsSFEfFSRMyOiM8uI8YzI2JKRBxTHD8vIi6NiEER8V8R8XhEPBcR36nsZSt6BK8FjlredpHU2kzeJDWtlNJc8v1rvxgRexY3jb4CuCKl9MulHPp24K7KDRHxDuDnwLnADsCHyPd+/Fq3Yz8J/B14E3AO8I2I2HMZoQ4HDgUOBt4DHAH8BngzcCBwAnAy8K5ux90B7LOMc0vqZ7y3qaSmFxHfAw4BbiYnZqNSSvOWUv8F4JMppUsrtt0C3JBS+mrFtsOAy4C1UkopIh4B/ppSOqqizj+An6SU/ruX1zoTOBXYKKX0YrHtl+SkbFhKaVGxrR2YklL6WMWxhwDXAINSSourbxFJrWxg2QFIUg2cCowDPgi8dWmJW2EwsLDbtt2A3SPi1IptbUXdjYAni233dztuDrDhMl7vsc7ErfA08GBn4laxrft5FgABrAYs63eS1E+YvElqBcOBzYAEbAX8bRn1nwXW67atDfgKPU9imFvx/LVu+xLLvgSlp2N62tZ92ZL1gYVVJKOS+hGTN0lNLSJWIV+rNpGctJ0fEX9JKT22lMPuAbbvtu1uYERKaWbfRLpCdiTHJUn/YvImqdl9lTzcuD/wInn49GcRMTal1NHLMdcDx3fbdhbw24h4FLgaWExOnnZPKX2uTyJftrcDvy/ptSU1KGebSmpaEbEP8GnggymlF1KegXUsMJJ8HVxvLgO2jYgdOjeklK4H3gmMJc/yvAM4DVhaD16fiYhhwFuBS5dVV1L/4mxTSf1SRHwd2CCl1L0HriFExDeBdVJKJ5Ydi6TGYs+bpP7qa8CsRr23KfAMcEbZQUhqPPa8Sfr/7dgBCQAAAICg/6/bEeiKCIAR5w0AYES8AQCMiDcAgBHxBgAwIt4AAEbEGwDASBczBl+MZl1iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('Lancer franc',figsize=(10,6))   # Initialise et nomme la figure\n",
    "plt.title('Positions successives du ballon',fontsize = 14)# Titre du graphe\n",
    "plt.xlabel('x (en m)',fontsize = 14)        # Label de l’axe des abscisses\n",
    "plt.ylabel('y (en m)',fontsize = 14)        # Label de l’axe des ordonnées\n",
    "plt.axis('equal')                           # Repère orthonormé\n",
    "plt.grid()                                  # Affiche une grille\n",
    "\n",
    "plt.plot(x,y,'or:',ms=4)# Nuage de points de coordonnées dans x et dans y \n",
    "                        # 'o' points 'r' rouges de taille (ms=markersize) 4,\n",
    "                        # ':'reliés par des petits points\n",
    "                    \n",
    "plt.show()                                  # Affiche la figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Représentation des vecteurs vitesse\n",
    "#### 2.1. Définition des listes `Vx` et `Vy` des coordonnées des vecteurs vitesse  \n",
    "Le vecteur vitesse $\\overrightarrow{v_{\\mathrm{i}}}$ au point $\\mathrm{M_{i}}$ est assimilable au vecteur vitesse moyenne entre les deux positions successives $\\mathrm{M_{i}}$ et $\\mathrm{M_{i+1}}$ séparées de l'intervalle de temps $\\Delta t = t_{\\mathrm{i+1}}-t_{\\mathrm{i}}$ :    \n",
    "$ \\qquad \\qquad \\overrightarrow{v_{\\mathrm{i}}} = \\dfrac{\\overrightarrow{M_{\\mathrm{i}}M_{\\mathrm{i+1}}}}{t_{\\mathrm{i+1}}-t_{\\mathrm{i}}}$.    \n",
    "Les coordonnées ${v_{x\\,\\mathrm{i}}}$ et ${v_{y\\,\\mathrm{i}}}$ du vecteur vitesse $\\overrightarrow{v_{\\mathrm{i}}}$ s'écrivent donc :  $ \\qquad v_{x\\,\\mathrm{i}} = \\dfrac{x_{\\mathrm{i+1}}-x_{\\mathrm{i}}}{t_{\\mathrm{i+1}}-t_{\\mathrm{i}}}\\qquad$ et  $\\qquad v_{y\\,\\mathrm{i}} = \\dfrac{y_{\\mathrm{i+1}}-y_{\\mathrm{i}}}{t_{\\mathrm{i+1}}-t_{\\mathrm{i}}}$.  \n",
    "\n",
    "Ainsi, les listes `Vx` et `Vy` des coordonnées des vecteurs vitesse sont calculées à partir des valeurs contenues dans les  listes `t`, `x` et `y`.  \n",
    "\n",
    "Pour appeler les valeurs des listes `t`, `x` et `y` dans les calculs, on fait appel aux propriétés suivantes :          \n",
    "$\\qquad$ - les valeurs rangées dans une liste `L` sont indexées par leur position `i` dans la liste ;       \n",
    "$\\qquad$ - l'indice de la valeur occupant la première position dans la liste est `0` ;      \n",
    "$\\qquad$ - l'instruction `L[i]` permet d'appeler la valeur rangée à la position d'indice `i`.   \n",
    "\n",
    "*Remarque :    \n",
    "Les valeurs des listes* `t`, `x` *et* `y` *portent les indices allant de* `0` *pour la première position à* `11` *pour la douzième position.*\n",
    "\n",
    "Le caractère répétitif du calcul des coordonnées des vecteurs vitesse pour chaque position `i` de la première à l'avant dernière position impose d'utiliser la boucle `for` que l'on peut par exemple intégrer dans la création de liste \"en compréhension\". Cette méthode de création de liste permet de définir une liste sur une seule ligne entre crochets.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vx =[(x[i+1]-x[i])/(t[i+1]-t[i]) for i in range(len(t)-1)]\n",
    "Vy =[(y[i+1]-y[i])/(t[i+1]-t[i]) for i in range(len(t)-1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les formules du calcul des coordonnées du vecteur vitesse sont appliquées de la première position d'indice `0` à l'avant dernière position d'indice `10` grâce à la fonction `range(len(t)-1)`, en effet :     \n",
    "$\\qquad$ - `range(n)` génère la liste des premiers entiers de `0` à `n-1` ;            \n",
    "$\\qquad$ - `len(t)` renvoie le nombre d'éléments de la liste `t`.              \n",
    "Donc `range(len(t)-1)` renvoie les entiers de `0` à `(len(t)-1)-1 = (12-1)-1` soit `10`. \n",
    "\n",
    "*Remarque :       \n",
    "Il est possible d'utiliser une autre syntaxe de création des listes* `Vx` *et* `Vy` *à l'aide de l'instruction* `list.append(valeur)` *qui insère* `valeur` *en dernière position de la liste* `list`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vx_bis,Vy_bis = [],[] # Création de deux listes vides   \n",
    "for i in range(len(t)-1):   \n",
    "    Vx_bis.append((x[i+1]-x[i])/(t[i+1]-t[i]))     \n",
    "    Vy_bis.append((y[i+1]-y[i])/(t[i+1]-t[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2. Affichage du vecteur vitesse toutes les deux positions\n",
    "\n",
    "L'affichage d'une flèche se fait grâce à l'instruction `plt.arrow(x,y,dx,dy,paramètres)` où :   \n",
    "$\\qquad$ - `x,y` sont les coordonnées du point du pied de la flèche ;       \n",
    "$\\qquad$ - `dx,dy` sont les projections orientées de la flèche sur les axes des abscisses et des ordonnées;          \n",
    "$\\qquad$ - `paramètres` permet de préciser l'aspect et les caractéristiques de la flèche.\n",
    "\n",
    "Afficher le vecteur vitesse $\\overrightarrow{v_{\\mathrm{i}}}$ au point $\\mathrm{M_{i}}$ revient à tracer une flèche au point de coordonnées `x[i],y[i]` telle que `dx`= `Vx[i]` et `dy`=`Vy[i]`. Cependant, pour visualiser correctement ces vecteurs, il est nécessaire de multiplier leurs coordonnées par un facteur d'échelle `e` à fixer selon la situation : `dx`= `e*Vx[i]` et `dy`=`e*Vy[i]`.\n",
    "\n",
    "Pour représenter le vecteur vitesse toutes les `2` positions, on parcourt grâce à une boucle `for` la liste d'entiers définie par la fonction `range(n,m,p)` de `n` inclus à `m` exclu par pas de `p` en prenant pour `n` l'indice de la première position, pour `m` l'indice de la dernière position dont on a calculé les coordonnées du vecteur vitesse et en fixant la valeur de `p` à `2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('Lancer franc',figsize=(10,6))   # Initialise et nomme la figure\n",
    "plt.title('Positions et vecteurs vitesse',fontsize = 14)  # Titre du graphe\n",
    "plt.xlabel('x (en m)',fontsize = 14)        # Label de l’axe des abscisses\n",
    "plt.ylabel('y (en m)',fontsize = 14)        # Label de l’axe des ordonnées\n",
    "plt.axis('equal')                           # Repère orthonormé\n",
    "plt.grid()                                  # Affiche une grille\n",
    "\n",
    "plt.plot(x,y,'or',ms=4)   # Nuage de points de coordonnées dans x et dans y\n",
    "\n",
    "for i in range(0,len(t)-1,2):\n",
    "    plt.arrow(x[i],y[i],0.05*Vx[i],0.05*Vy[i],width=0.01,color='c',\n",
    "              length_includes_head=\"true\",head_length=0.05, head_width=0.04)\n",
    "\n",
    "plt.show()                                  # Affiche la figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color= 'red'>Exemple 2 : Caractéristique tension-courant d'un dipôle</font>  \n",
    "\n",
    "Les valeurs de la tension $U$ (en V) et de l'intensité $I$ (en mA) aux bornes d'un dipôle sont relevées expérimentalement et on souhaite représenter et modéliser la caractéristique tension-courant $U=f(I)$ du dipôle.\n",
    "\n",
    "### 1. Représentation de la caractéristique tension-courant $\\,U=f(I)$\n",
    "\n",
    "#### 1.1. Définition des tableaux `U` et `I` des données expérimentales\n",
    "\n",
    "Pour ranger une collection de nombres les uns à la suite des autres, on peut utiliser des tableaux à une dimension, c’est-à-dire à une seule ligne, de type «tableau» («array» en anglais) de la bibliothèque `NumPy`  habituellement importée sous le préfixe `np`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!/usr/bin/python                                                                        \n",
    "# -*- coding: utf-8 -*-\n",
    "import matplotlib.pyplot as plt     # Importe le module pyplot en plt\n",
    "import numpy as np                  # Importe la bibliothèque numpy en np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'instruction `np.array(liste)` convertit la liste de valeurs `liste` définie entre crochets avec la même syntaxe que dans l'exemple 1 en un tableau de nombres à une ligne.\n",
    "\n",
    "Les valeurs expérimentales de la tension $U$ (en V) et de l'intensité $I$ (en mA) sont rangées dans l'ordre dans deux tableaux `U` et `I`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "U = np.array([0.0,1.0,2.0,3.0,4.0,5.0])     # U (en V) expérimental\n",
    "I = np.array([0.0,1.1,2.0,2.9,4.1,5.3])     # I (en mA) expérimental"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2. Définition et affichage de la figure représentant les points expérimentaux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('Etude d\\'un dipôle',figsize=(10,6))# Initialise la figure\n",
    "plt.title('Caractéristique Tension-Courant',fontsize = 14)# Titre du graphe\n",
    "plt.xlabel('I (en mA)',fontsize = 14)       # Label de l’axe des abscisses\n",
    "plt.ylabel('U (en V)', fontsize = 14)       # Label de l’axe des ordonnées\n",
    "\n",
    "plt.plot(I,U,'r+',ms=14,label='Points expérimentaux') # Points expérimentaux\n",
    "                                  # d’abscisses dans I et d’ordonnées dans U\n",
    "                                  # sous forme de points rouges non reliés\n",
    "                                  # de taille 14, label = nom de la courbe\n",
    "\n",
    "plt.grid()                                  # Affiche une grille\n",
    "plt.legend(fontsize=14)                     # Affiche la légende\n",
    "plt.show()                                  # Affiche les courbes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Modélisation de la caractéristique   \n",
    "Modéliser le nuage de points consiste à déterminer l’équation mathématique de la courbe qui se rapproche le plus de celle qu’ils tracent.  \n",
    "\n",
    "Dans le cas de la caractéristique du dipôle étudié, les points sont alignés sur une droite passant par l'origine.\n",
    "\n",
    "En langage de programmation Python, pour déterminer l'équation de cette droite, deux méthodes distinctes sont envisageables :   \n",
    "$\\qquad$ - à l'aide de la fonction `np.polyfit(I,U,1)` de la bibliothèque `NumPy` ;       \n",
    "$\\qquad$ - à l'aide de la fonction `linregress(I,U)` du module `stats` de la bibliothèque `SciPy`.   \n",
    "\n",
    "#### 2.1. Modélisation à l'aide de la fonction `np.polyfit(I,U,1)`\n",
    "\n",
    "**a. Modélisation**\n",
    "\n",
    "La fonction `np.polyfit(x,y,1)` modélise le nuage de points d’abscisses dans `x` et d’ordonnées dans `y` par une droite d’équation $y=ax+b$ et renvoie le tableau : `[a b]`.\n",
    "\n",
    "Les coefficients de la droite modélisant le nuage de points sont calculés par `np.polyfit(I,U,1)` et sont affectés dans cet ordre aux variables `a` et `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b = np.polyfit(I,U,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Remarque :   \n",
    "Si* `I` *et* `U` *sont de type «liste» et non de type «tableau», la fonction* `np.polyfit(I,U,1)` *peut être utilisée de la même façon car les fonctions de la bibliothèque* `NumPy` *s’appliquent aussi aux objets ressemblant à des tableaux (de type «array_like») comme les listes de nombres.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b. Affichage de la modélisation**\n",
    "\n",
    "Il s'agit d'ajouter sur la figure la courbe d'équation $U_{modelisation}=f(I)$ où les valeurs de $U_{modelisation}$ sont définies par la modélisation précédente, soit : $U_{modelisation}=a\\times I +b$.   \n",
    "\n",
    "Pour calculer les valeurs des ordonnées $U_{modelisation}$ de la modélisation, on fait appel à la propriété suivante :    \n",
    "Les opérations mathématiques usuelles appliquées à un objet de type «tableau» s'appliquent séparément à chaque élément du tableau.\n",
    "\n",
    "Donc, comme `I` est de type «tableau», sachant que `a` et `b` sont des nombres, l'instruction `a*I+b` renvoie le tableau des résultats du calcul appliqué à chaque valeur du tableau `I`.   \n",
    "\n",
    "L'affichage de la modélisation se fait alors grâce à l'instruction `plt.plot(I,a*I+b)` qui trace les points d'abscisses dans `I` et d'ordonnées dans `a*I+b`.\n",
    "\n",
    "*__Attention__ : Si* `I` *est de type «liste», les opérations mathématiques usuelles ne s'appliquent pas à chaque valeur de la liste.*   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('Etude d\\'un dipôle',figsize=(10,6))# Initialise la figure\n",
    "plt.title('Caractéristique Tension-Courant',fontsize = 14)# Titre du graphe\n",
    "plt.xlabel('I (en mA)',fontsize = 14)       # Label de l’axe des abscisses\n",
    "plt.ylabel('U (en V)', fontsize = 14)       # Label de l’axe des ordonnées\n",
    "\n",
    "plt.plot(I,U,'r+',ms=14,label='Points expérimentaux') # Points expérimentaux \n",
    "\n",
    "plt.plot(I,a*I+b,'b--',label='Modélisation')# Points d’abscisses dans I et\n",
    "                                            # d’ordonnées dans a*I+b en bleu\n",
    "                                            # reliés par des pointillés\n",
    "    \n",
    "plt.grid()                                  # Affiche une grille\n",
    "plt.legend(fontsize=14)                     # Affiche la légende\n",
    "plt.show()                                  # Affiche les courbes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c. Equation de la caractéristique**    \n",
    "Les valeurs expérimentales de la tension $U$ et de l'intensité $I$ étant données avec 2 chiffres significatifs, le résultat de la modélisation est donné aussi avec 2 chiffres significatifs.   \n",
    "Les instructions habituelles d'affichage de texte et de formatage des nombres permettent d'afficher l'équation de la caractéristique et la valeur de la résistance.    \n",
    "\n",
    "*Remarque :   \n",
    "Les valeurs de la tension $U$ et de l'intensité $I$ n'étant pas données dans le jeu d'unités __SI__, il faut en tenir compte pour afficher l'équation de la caractéristique en précisant les unités et pour donner la valeur estimée de la résistance en $\\Omega$.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t Modélisation de la caractéristique de la résistance :\n",
      "\t U (en V) = 0.96 x I (en mA)\n",
      "\t La résistance estimée vaut R = 9.6e+02 Ω.\n"
     ]
    }
   ],
   "source": [
    "print('\\t Modélisation de la caractéristique de la résistance :')\n",
    "print('\\t U (en V) =','{:.2f}'.format(a), 'x I (en mA)') \n",
    "print('\\t La résistance estimée vaut R =','{:.1e}'.format(1000*a),'Ω.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t a = 0.9582309582309583 (en V/mA) \n",
      "\t b = 0.040540540540540876 (en V)\n"
     ]
    }
   ],
   "source": [
    "print('\\t a =',a,'(en V/mA) \\n\\t b =',b,'(en V)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Remarque :  \n",
    "Dans l'instruction* `print()`, `\\t` *insère une tabulation et* `\\n`*renvoie à la ligne.* "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2. Modélisation à l'aide de la fonction `linregress(I,U)`\n",
    "\n",
    "**a. Modélisation**\n",
    "\n",
    "La fonction `linregress(x,y)`, importée directement depuis le module `scipy.stats`, fait l'étude statistique du nuage de points d’abscisses dans `x` et d’ordonnées dans `y` en en calculant la régression linéaire et renvoie dans l'ordre cinq valeurs :   \n",
    "$\\qquad$ - la pente ;     \n",
    "$\\qquad$ - l'ordonnée à l'origine ;        \n",
    "$\\qquad$ - le coefficient de corrélation ;        \n",
    "$\\qquad$ - la pvalue ;       \n",
    "$\\qquad$ - l'erreur standard.    \n",
    "\n",
    "Les valeurs de l'étude statistique du nuage de points sont calculées par `linregress(I,U)` et rangées dans l'objet `Modele`, puis les deux premières valeurs de `Modele` sont affectées dans cet ordre aux variables `m` pour la pente et `p` pour l'ordonnée à l'origine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import linregress\n",
    "Modele = linregress(I,U)\n",
    "m,p = Modele[0],Modele[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">\n",
    "**b. Affichage de la modélisation**\n",
    "\n",
    "Le principe d'affichage est le même que précédemment grâce à l'instruction `plt.plot(I,m*I+p)` qui trace les points d'abscisses dans `I` et d'ordonnées dans `m*I+p`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure('Etude d\\'un dipôle',figsize=(10,6))# Initialise la figure\n",
    "plt.title('Caractéristique Tension-Courant',fontsize = 14)# Titre du graphe\n",
    "plt.xlabel('I (en mA)',fontsize = 14)       # Label de l’axe des abscisses\n",
    "plt.ylabel('U (en V)', fontsize = 14)       # Label de l’axe des ordonnées\n",
    "\n",
    "plt.plot(I,U,'r+',ms=14,label='Points expérimentaux') # Points expérimentaux \n",
    "\n",
    "plt.plot(I,m*I+p,'g:',label='Régression linéaire')# # Points d’abscisses\n",
    "                                      # dans I et d’ordonnées dans m*I+p\n",
    "                                      # en vert reliés par des petits points\n",
    "\n",
    "plt.grid()                                  # Affiche une grille\n",
    "plt.legend(fontsize=14)                     # Affiche la légende\n",
    "plt.show()                                  # Affiche les courbes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c. Equation de la caractéristique**   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t Modélisation de la caractéristique de la résistance :\n",
      "\t U (en V) = 0.96 x I (en mA)\n",
      "\t La résistance estimée vaut R = 9.6e+02 Ω.\n"
     ]
    }
   ],
   "source": [
    "print('\\t Modélisation de la caractéristique de la résistance :')\n",
    "print('\\t U (en V) =','{:.2f}'.format(m), 'x I (en mA)') \n",
    "print('\\t La résistance estimée vaut R =','{:.1e}'.format(1000*m),'Ω.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t m = 0.958230958230958 (en V/mA) \n",
      "\t p = 0.04054054054054124 (en V)\n"
     ]
    }
   ],
   "source": [
    "print('\\t m =',m,'(en V/mA) \\n\\t p =',p,'(en V)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Remarque :   \n",
    "La comparaison des coefficients* `a` *et* `m`, *d'une part, et* `b` *et* `p`*, d'autre part, montre que les deux méthodes sont équivalentes dans le cas étudié.*"
   ]
  }
 ],
 "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",
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 },
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