{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trajectoire d'un boulet de canon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons intégrer les équations du mouvement pour un boulet de canon soumis à des forces de frottement \"turbulentes\" (non-linéaires):\n",
    "$$\n",
    "\\ddot{\\mathbf{r}} = \\mathbf{g} - \\frac{\\alpha}{m}v\\times\\mathbf{v}.\n",
    "$$\n",
    "\n",
    "Cette équation différentielle non linéaire du 2d ordre doit être réécrite sous la forme de deux équations différentielles couplées du 1er ordre:\n",
    "$$\n",
    "\\begin{cases}\n",
    "\\dot{\\mathbf{r}} &= \\mathbf{v} \\\\\n",
    "\\dot{\\mathbf{v}} &= \\mathbf{g} - \\frac{\\alpha}{m}v\\times\\mathbf{v}.\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Il s'agit donc de résoudre *une seule* équation différentielle du 1er ordre en $\\mathbf{z} = (\\mathbf{r},\\mathbf{v})$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Valeurs numériques pour un boulet de canon de [36 livres](http://fr.wikipedia.org/wiki/Canon_de_36_livres):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Masse du boulet: 17.42 kg\n",
      "Coefficient de frottement par unité de masse: 0.0003718994604243878 S.I.\n"
     ]
    }
   ],
   "source": [
    "g = 9.81        # Pesanteur [m/s2]\n",
    "cx = 0.45       # Coefficient de frottement d'une sphère\n",
    "rhoAir = 1.2    # Masse volumique de l'air [kg/m3] au niveau de la mer, T=20°C\n",
    "rad = 0.1748/2  # Rayon du boulet [m]\n",
    "rho = 6.23e3    # Masse volumique du boulet [kg/m3]\n",
    "mass = 4./3.*np.pi*rad**3 * rho            # Masse du boulet [kg]\n",
    "alpha = 0.5*cx*rhoAir*np.pi*rad**2 / mass  # Coefficient de frottement par unité de masse\n",
    "print(f\"Masse du boulet: {mass:.2f} kg\")\n",
    "print(f\"Coefficient de frottement par unité de masse: {alpha} S.I.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conditions initiales:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0 = 450.            # Vitesse initiale [m/s]\n",
    "alt = 45.            # Inclinaison du canon [deg]\n",
    "alt *= np.pi / 180.  # Inclinaison [rad]\n",
    "z0 = (0., 0., v0 * np.cos(alt), v0 * np.sin(alt))  # (x0, y0, vx0, vy0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Temps caractéristique du système: $t = \\sqrt{m/(g\\alpha)}$ (durée du régime transitoire). L'intégration des équations se fera sur un temps caractéristique, avec des pas de temps significativement plus petits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temps caractéristique: 69.1 s\n"
     ]
    }
   ],
   "source": [
    "tc = np.sqrt(mass / (g * alpha))\n",
    "print(f\"Temps caractéristique: {tc:.1f} s\")\n",
    "t = np.linspace(0, tc, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Définition de la fonction $\\dot{\\mathbf{z}}$, avec $\\mathbf{z} = (\\mathbf{r},\\mathbf{v})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def zdot(z, t):\n",
    "    \"\"\"Calcul de la dérivée de z=(x, y, vx, vy) à l'instant t.\"\"\"\n",
    "    \n",
    "    x, y, vx, vy = z\n",
    "    alphav = alpha * np.hypot(vx, vy)\n",
    "    \n",
    "    return (vx, vy, -alphav * vx, -g - alphav * vy) # dz/dt = (vx,vy,x..,y..)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intégration numérique des équations du mouvement à l'aide de la fonction [scipy.integrate.odeint](http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.odeint.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "zs = odeint(zdot, z0, t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le tableau `zs` contient les valeurs de $z$ à chaque instant $t$: il est donc de taille `(len(t),4)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "temps de coll. t(y~0) = 36 s\n",
      "portée x(y~0) = 3966 m\n",
      "vitesse(y~0): 140 m/s\n"
     ]
    }
   ],
   "source": [
    "ypos = zs[:,1]>=0 # y>0? \n",
    "print(f\"temps de coll. t(y~0) = {t[ypos][-1]:.0f} s\") # Dernier instant pour lequel y>0\n",
    "print(f\"portée x(y~0) = {zs[ypos, 0][-1]:.0f} m\") # Portée approximative du canon\n",
    "#print(f\"y(y~0) = {zs[ypos, 1][-1]:.0f} m\") # ~0\n",
    "print(f\"vitesse(y~0): {np.hypot(zs[ypos, 2][-1], zs[ypos, 3][-1]):.0f} m/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(zs[ypos, 0], zs[ypos, 1])\n",
    "ax.set(xlabel=\"x [m]\", ylabel=\"y [m]\", title=\"Trajectoire du boulet\");"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.12"
  },
  "nbsphinx": {
   "orphan": true
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": true,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}