{
 "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": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as N\n",
    "import scipy.integrate as SI\n",
    "import matplotlib.pyplot as P"
   ]
  },
  {
   "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": 2,
   "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.*N.pi*rad**3 * rho            # Masse du boulet [kg]\n",
    "alpha = 0.5*cx*rhoAir*N.pi*rad**2 / mass  # Coefficient de frottement par unité de masse\n",
    "print(\"Masse du boulet: {:.2f} kg\".format(mass))\n",
    "print(\"Coefficient de frottement par unité de masse: {} S.I.\".format(alpha))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conditions initiales:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0 = 450.           # Vitesse initiale [m/s]\n",
    "alt = 45.           # Inclinaison du canon [deg]\n",
    "alt *= N.pi / 180.  # Inclinaison [rad]\n",
    "z0 = (0., 0., v0 * N.cos(alt), v0 * N.sin(alt)) # (x0, y0, vx0, vy0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Temps caractéristique du système: $t = \\sqrt{\\frac{m}{g\\alpha}}$ (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": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temps caractéristique: 69.1 s\n"
     ]
    }
   ],
   "source": [
    "tc = N.sqrt(mass / (g * alpha))\n",
    "print(\"Temps caractéristique: {:.1f} s\".format(tc))\n",
    "t = N.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": 5,
   "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 * N.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": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "zs = SI.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": 7,
   "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(\"temps de coll. t(y~0) = {:.0f} s\".format(t[ypos][-1])) # Dernier instant pour lequel y>0\n",
    "print(\"portée x(y~0) = {:.0f} m\".format(zs[ypos, 0][-1])) # Portée approximative du canon\n",
    "#print \"y(y~0) = {:.0f} m\".format(zs[ypos, 1][-1]) # ~0\n",
    "print(\"vitesse(y~0): {:.0f} m/s\".format(N.hypot(zs[ypos, 2][-1], zs[ypos, 3][-1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccd9ee9ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = P.subplots()\n",
    "ax.plot(zs[ypos, 0], zs[ypos, 1])\n",
    "ax.set(xlabel=\"x [m]\", ylabel=\"y [m]\", title=\"Trajectoire du boulet\");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python3",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}