{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "Euler",
     "pcm",
     "physique-chimie",
     "première-voie-technologique",
     "STI2D",
     "STL"
    ]
   },
   "source": [
    "# Chute d'un corps dans un milieu visqueux"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Présentation\n",
    "- **Voie et niveau de classe :** \n",
    " - Technologique: Première (STI2D-STL, spécialité physique-chimie et mathématiques)\n",
    "- **Référence au programme :** \n",
    " - Spécialité physique-chimie et mathématiques de première technologique : *Construire différents points d’une approximation de courbe intégrale par la méthode d’Euler.*.\n",
    "- **Description de l'activité :** cette activité permet d'utiliser la méthode d'Euler dans le contexte de la chute d'un corps dans un milieu visqueux."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un corps s'enfonce dans un milieu visqueux selon le modèle régi par l'équation :\n",
    "$$\n",
    "a(t) = k\\times v(t) + g_0\n",
    "$$\n",
    "où $a$ représente l'accélération, $v$ la vitesse et $g_0$ une constante gravitationnelle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constantes\n",
    "Fixons les constantes à $k=35$ et $g_0=8,22$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 35\n",
    "g0 = 8.22"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Méthode d'Euler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La fonction `acceleration` prend en paramètre un flottant `v` représentant la vitesse et renvoie l'accélération."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def acceleration(v):\n",
    "\treturn -k*v+g0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Suggestions pédagogiques\n",
    "</div>\n",
    " \n",
    "*  **Écrire un programme**\n",
    " \n",
    " Écrire la fonction `acceleration`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La fonction `euler` prend en paramètres `v0` représentant la vitesse initiale, `n` représentant le nombre d'itérations de la méthode d'Euler et `dt` le pas de temps. Elle renvoie la liste des vitesses et des accélérations calculées au fur et à mesure avec la méthode d'Euler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0, 0.08220000000000001, 0.13563, 0.1703595, 0.192933675],\n",
       " [8.22, 5.343, 3.472950000000001, 2.2574175000000007, 1.467321375000001])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def euler(v0,n,dt):\n",
    "\tlisteVitesses = [v0]\n",
    "\ta0 = acceleration(v0)\n",
    "\tlisteAccelerations = [a0]\n",
    "\tv =v0\n",
    "\ta = a0\n",
    "\tfor i in range(n-1):\n",
    "\t\tv = v + a*dt\n",
    "\t\tlisteVitesses.append(v)\n",
    "\t\ta = acceleration(v)\n",
    "\t\tlisteAccelerations.append(a)\n",
    "\treturn listeVitesses,listeAccelerations\n",
    "\n",
    "euler(0,5,0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Suggestions pédagogiques\n",
    "</div>\n",
    "\n",
    "* **Expliquer un programme**\n",
    "\n",
    " - Que représente `a0` ?\n",
    " - Expliquer l'égalité de la ligne 8.\n",
    "\n",
    "* **Compléter un programme**\n",
    "\n",
    " Le programme précédent étant fourni en remplaçant les lignes 4, 6 et 8 par `listeAccelerations = [...]`, `a = ...`, `v = ...`, demander aux élèves de compléter les lignes 4, 6 et 8."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Représentation graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "fig, (ax1,ax2) = plt.subplots(1, 2,figsize=(12, 5))\n",
    "\n",
    "def plotEuler(v0,n,dt):\n",
    "\tt0 = 0\n",
    "\tX = [t0 + i*dt for i in range(n)]\n",
    "\tlisteVitesses,listeAccelerations = euler(v0,n,dt)\n",
    "\tax1.plot(X,listeVitesses,'r--',label='Vitesse')\n",
    "\tax2.plot(X,listeAccelerations,'b--',label='Accélération')\n",
    "    \n",
    "plotEuler(0,30,0.01)\n",
    "ax1.legend(loc=\"lower right\")\n",
    "ax2.legend(loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Suggestions pédagogiques\n",
    "</div>\n",
    "\n",
    "* **Interprétation du résultat**\n",
    " - Commenter la forme des courbes. Est-ce cohérent ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Animation susceptible d'être présentée aux élèves\n",
    "La courbe de gauche donne la vitesse du corps en fonction du temps et la courbe de droite son accélération construite avec la méthode d'Euler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
       "css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<div class=\"animation\" align=\"center\">\n",
       "    <img id=\"_anim_imgb535f0ab83784c73b8fd97ce434c6f3b\">\n",
       "    <br>\n",
       "    <input id=\"_anim_sliderb535f0ab83784c73b8fd97ce434c6f3b\" type=\"range\" style=\"width:350px\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           onchange=\"animb535f0ab83784c73b8fd97ce434c6f3b.set_frame(parseInt(this.value));\"></input>\n",
       "    <br>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.previous_frame()\">\n",
       "        <i class=\"fa fa-step-backward\"></i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.reverse_animation()\">\n",
       "        <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "        </i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "        </button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"animb535f0ab83784c73b8fd97ce434c6f3b.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "  <form action=\"#n\" name=\"_anim_loop_selectb535f0ab83784c73b8fd97ce434c6f3b\" class=\"anim_control\">\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"once\" > Once </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"loop\" checked> Loop </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"reflect\" > Reflect </input>\n",
       "  </form>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgb535f0ab83784c73b8fd97ce434c6f3b\";\n",
       "    var slider_id = \"_anim_sliderb535f0ab83784c73b8fd97ce434c6f3b\";\n",
       "    var loop_select_id = \"_anim_loop_selectb535f0ab83784c73b8fd97ce434c6f3b\";\n",
       "    var frames = new Array(0);\n",
       "    \n",
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       "cLEAAAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animb535f0ab83784c73b8fd97ce434c6f3b = new Animation(frames, img_id, slider_id, 200.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,show,subplots,close\n",
    "import matplotlib.animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "#ctes: \n",
    "n =40\n",
    "v0 = 0\n",
    "dt = 0.01\n",
    "t0 = 0\n",
    "#Création des figures\n",
    "fig, (ax1,ax2) = subplots(1, 2,figsize=(12, 6))\n",
    "courbeVitesses, = ax1.plot([],[],'.-',color=\"#1e7fcb\")\n",
    "courbeAcceleration, = ax2.plot([],[],'.-',color=\"#C4151C\")\n",
    "#Réglage des axes\n",
    "ax1.set_xlim(( 0, 0.4))\n",
    "ax1.set_ylim(( 0, 0.3))\n",
    "ax2.set_xlim(( 0, 0.4))\n",
    "ax2.set_ylim(( 0, 9))\n",
    "\n",
    "def init():\n",
    "    global courbeVitesse\n",
    "    courbeVitesses.set_data([], [])\n",
    "    courbeAcceleration.set_data([], [])\n",
    "    return (courbeVitesses,) \n",
    "\n",
    "def animate(j):\n",
    "    global courbeVitesse,courbeAcceleration,v0,t0,n\n",
    "    listeAbscisses = [t0 + i*dt for i in range(j+1)]\n",
    "    listeVitesses,listeAccelerations = euler(v0,j+1,dt)\n",
    "    #print(euler2(0,5,0.1))\n",
    "    courbeVitesses.set_data(listeAbscisses,listeVitesses)\n",
    "    courbeAcceleration.set_data(listeAbscisses,listeAccelerations)\n",
    "    \n",
    "    ax1.set_title('Vitesse',color=\"#1e7fcb\")\n",
    "    ax2.set_title('Accélération',color=\"#C4151C\")\n",
    "    return (courbeVitesses,)\n",
    "\n",
    "close ()\n",
    "ani = matplotlib.animation.FuncAnimation(fig, animate, frames=n,init_func=init,blit=False,interval=200)\n",
    "# l'un ou l'autre\n",
    "HTML(ani.to_jshtml())\n",
    "#HTML(ani.to_html5_video())"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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