{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kapitza's Pendel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wichtige Module "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Parameters\n",
    "g = 9.81       # gravity\n",
    "m = 1.0        # mass of pendulum\n",
    "l = 1.0        # length of pendulum arms\n",
    "A = 0.5        # amplitude\n",
    "Omega = 20     # driving frequency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bewegungsgleichung in Matrixform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the equation of motion\n",
    "def eq_of_motion(t, y):\n",
    "    phi, omega = y\n",
    "    domega_dt = (A / l * Omega**2 * np.cos(Omega * t) - g / l) * np.sin(phi)\n",
    "    return [omega, domega_dt]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerische Lösung der Differentialgleichung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y0 = [0.1, 0]  # initial conditions: [phi, omega]\n",
    "t_span = (0, 10)\n",
    "t_eval = np.linspace(*t_span, 2000)\n",
    "\n",
    "sol = solve_ivp(eq_of_motion, t_span, y0, t_eval=t_eval)\n",
    "\n",
    "t = sol.t\n",
    "phi = sol.y[0]\n",
    "omega = sol.y[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zeitlicher Verlauf des Winkels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(t, phi)\n",
    "plt.xlabel(r'$t$')\n",
    "plt.ylabel(r'$\\varphi$')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Energien als Funktion der Zeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 0.5* m * (l**2 * omega**2 - 2 * l * omega * np.sin(phi) * A * Omega * np.sin(Omega*t) + (A * Omega * np.sin(Omega*t))**2)\n",
    "V = -m * g * (l * np.cos(phi) - A * np.cos(Omega*t))\n",
    "E = K + V\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t, K, '-r')\n",
    "plt.plot(t, V, ':g')\n",
    "plt.plot(t, E, '--b')\n",
    "plt.xlabel(r'$t$')\n",
    "plt.ylabel('Energy')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Erzeugung einer Animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Convert to Cartesian coordinates\n",
    "x = l * np.sin(phi)\n",
    "y = -l * np.cos(phi) + A * np.cos(Omega * t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\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",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\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",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img8e13b52106d34e499ddd01da71259eb2\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider8e13b52106d34e499ddd01da71259eb2\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim8e13b52106d34e499ddd01da71259eb2.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim8e13b52106d34e499ddd01da71259eb2.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select8e13b52106d34e499ddd01da71259eb2\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_8e13b52106d34e499ddd01da71259eb2\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_8e13b52106d34e499ddd01da71259eb2\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_8e13b52106d34e499ddd01da71259eb2\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_8e13b52106d34e499ddd01da71259eb2\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_8e13b52106d34e499ddd01da71259eb2\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_8e13b52106d34e499ddd01da71259eb2\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\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_img8e13b52106d34e499ddd01da71259eb2\";\n",
       "    var slider_id = \"_anim_slider8e13b52106d34e499ddd01da71259eb2\";\n",
       "    var loop_select_id = \"_anim_loop_select8e13b52106d34e499ddd01da71259eb2\";\n",
       "    var frames = new Array(400);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWgAAAFoCAYAAAB65WHVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "AElFTkSuQmCC\\\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",
       "        anim8e13b52106d34e499ddd01da71259eb2 = 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": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Animation\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.set_xlim(-2.1, 2.1)\n",
    "ax.set_ylim(-2.1, 2.1)\n",
    "ax.set_aspect('equal')\n",
    "ax.grid()\n",
    "\n",
    "line, = ax.plot([], [], 'r-', lw=2)\n",
    "bob, = ax.plot([], [], 'ro', markersize=8)\n",
    "origin, = ax.plot([], [], 'ko', markersize=5)\n",
    "\n",
    "\n",
    "# Initialization function\n",
    "def init():\n",
    "    line.set_data([], [])\n",
    "    bob.set_data([], [])\n",
    "    origin.set_data([0], [A * np.cos(Omega * t[0])])\n",
    "    return line, bob, origin\n",
    "\n",
    "# Update function\n",
    "def update(i):\n",
    "    xi = [0, x[i]]\n",
    "    yi = [A * np.cos(Omega * t[i]), y[i]]\n",
    "    line.set_data(xi, yi)\n",
    "    bob.set_data([x[i]], [y[i]])\n",
    "    origin.set_data([0], [A * np.cos(Omega * t[i])])\n",
    "    ax.set_title(f't = {t[i]:.2f} s')\n",
    "    return line, bob, origin\n",
    "\n",
    "ani = FuncAnimation(fig, update, frames=range(0, len(t), 5), init_func=init, blit=True)\n",
    "plt.close(fig)\n",
    "HTML(ani.to_jshtml())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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