{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wheel on Inclined Plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import FloatSlider"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pysketcher import *\n",
    "\n",
    "def inclined_plane():\n",
    "    theta = 30.\n",
    "    L = 10.\n",
    "    a = 1.\n",
    "    xmin = 0\n",
    "    ymin = -3\n",
    "\n",
    "    drawing_tool.set_coordinate_system(xmin=xmin, xmax=xmin+1.5*L,\n",
    "                                       ymin=ymin, ymax=ymin+L+1,\n",
    "                                       #axis=True,\n",
    "                                       instruction_file='tmp_mpl.py'\n",
    "                                       )\n",
    "    #drawing_tool.set_grid(True)\n",
    "    fontsize = 18\n",
    "    from math import tan, radians\n",
    "\n",
    "    B = point(a+L, 0)\n",
    "    A = point(a, tan(radians(theta))*L)\n",
    "\n",
    "    wall = Wall(x=[A[0], B[0]], y=[A[1], B[1]], thickness=-0.25,\n",
    "                transparent=False)\n",
    "\n",
    "    angle = Arc_wText(r'$\\theta$', center=B, radius=3,\n",
    "                      start_angle=180-theta, arc_angle=theta,\n",
    "                      fontsize=fontsize)\n",
    "    angle.set_linecolor('black')\n",
    "    angle.set_linewidth(1)\n",
    "\n",
    "    ground = Line((B[0]-L/10., 0), (B[0]-L/2.,0))\n",
    "    ground.set_linecolor('black')\n",
    "    ground.set_linestyle('dashed')\n",
    "    ground.set_linewidth(1)\n",
    "\n",
    "    r = 1  # radius of wheel\n",
    "    help_line = Line(A, B)\n",
    "    x = a + 3*L/10.; y = help_line(x=x)\n",
    "    contact = point(x, y)\n",
    "    normal_vec = point(sin(radians(theta)), cos(radians(theta)))\n",
    "    tangent_vec = point(cos(radians(theta)), -sin(radians(theta)))\n",
    "    c = contact + r*normal_vec\n",
    "    outer_wheel = Circle(c, r)\n",
    "    outer_wheel.set_linecolor('blue')\n",
    "    outer_wheel.set_filled_curves('blue')\n",
    "    hole = Circle(c, r/2.)\n",
    "    hole.set_linecolor('blue')\n",
    "    hole.set_filled_curves('white')\n",
    "\n",
    "    wheel = Composition({'outer': outer_wheel, 'inner': hole})\n",
    "    wheel.set_shadow(4)\n",
    "\n",
    "    drawing_tool.set_linecolor('black')\n",
    "    N = Force(contact - 2*r*normal_vec, contact, r'$N$', text_pos='start')\n",
    "    V = Force(c, c + 0.001*tangent_vec, r'$V$', text_pos='end')\n",
    "    V.set_linecolor('red')\n",
    "    mg = Gravity(c, 3*r, text='$Mg$')\n",
    "\n",
    "    x_const = Line(contact, contact + point(0,4))\n",
    "    x_const.set_linestyle('dotted')\n",
    "    x_const.rotate(-theta, contact)\n",
    "    # or x_const = Line(contact-2*r*normal_vec, contact+4*r*normal_vec).set_linestyle('dotted')\n",
    "    x_axis = Axis(start=contact+ 3*r*normal_vec, length=4*r,\n",
    "                  label='$x$', rotation_angle=-theta)\n",
    "\n",
    "    body  = Composition({'wheel': wheel, 'N': N, 'mg': mg})\n",
    "    fixed = Composition({'angle': angle, 'inclined wall': wall,\n",
    "                         'wheel': wheel, 'V': V, 'ground': ground,\n",
    "                         'x start': x_const, 'x axis': x_axis})\n",
    "\n",
    "    fig = Composition({'body': body, 'fixed elements': fixed})\n",
    "    fig.draw()\n",
    "    return (fig,normal_vec,tangent_vec,c)\n",
    "\n",
    "def position(t):\n",
    "    \"\"\"Position of center point of wheel.\"\"\"\n",
    "    global tangent_vec,c\n",
    "    return c + 7*t**2*tangent_vec\n",
    "\n",
    "def speed(t):\n",
    "    global tangent_vec\n",
    "    return 0.14*t*tangent_vec    \n",
    "\n",
    "t = 0\n",
    "\n",
    "def move(change):\n",
    "    global fig,t\n",
    "    dt = change.new - t \n",
    "    t = change.new\n",
    "    drawing_tool.erase()\n",
    "    x = position(t)\n",
    "    x0 = position(t-dt)\n",
    "    displacement = x - x0\n",
    "    fig['fixed elements']['V']['arrow']['line'] = Line(x,x+speed(t))\n",
    "    fig['body'].translate(displacement)\n",
    "    fig.draw()\n",
    "    drawing_tool.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "slider = FloatSlider(\n",
    "    orientation='horizontal',\n",
    "    description='Time:',\n",
    "    value=0.0,\n",
    "    min=0.0,\n",
    "    max=1.0,\n",
    "    step = 1.0 / 30\n",
    ")\n",
    "slider.observe(move, 'value')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1af7c7deda7b418a8a170ec0b34505ec",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FloatSlider(value=0.0, description='Time:', max=1.0, step=0.03333333333333333)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slider"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "da53e1cea5d447b5af22e27766617152",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,normal_vec,tangent_vec,c = inclined_plane()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "speed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "position(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.5       , 4.90747729])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig['fixed elements']['V']['arrow']['line'].x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.5       , 4.90747729])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig['fixed elements']['V']['arrow']['line'].y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "speed(0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "position(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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