{
 "metadata": {
  "name": "",
  "signature": "sha256:1af223da3d90aaca19fd8e6022bb86b0a809e2850967301ad7afb00495d5a986"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from ipywidgets import StaticInteract, RangeWidget, RadioWidget"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Ex = 0\n",
      "#Ey = 5\n",
      "\n",
      "m = 1\n",
      "q = 1\n",
      "\n",
      "dt = 0.1\n",
      "\n",
      "def main(Ex,Ey):\n",
      "    def force():\n",
      "        return [Ex,Ey]\n",
      "\n",
      "#    def euler_step(x,Vx,y,Vy):\n",
      "#        array = force()\n",
      "#        Fy = Vy\n",
      "#        fy = array[1]\n",
      "#        Fx = Vx\n",
      "#        fx = array[0]\n",
      "#        return [fx*dt, Fx*dt, fy*dt, Fy*dt]\n",
      "\n",
      "    def rk2_step(x,dx,y,dy):\n",
      "#        array = force()\n",
      "#        F1y = Vy\n",
      "#        f1y = array[1]\n",
      "#        F2y = Vy\n",
      "#        fy = array[1]\n",
      "#        F1x = Vx\n",
      "#        f1x = array[0]\n",
      "        F1x = dy\n",
      "        f1x = fn(k,m,y)\n",
      "        F2x = dy +f1*h\n",
      "        f2x = fn(k,m,(y+F1*h))\n",
      "        return [(f1+f2)*h/2., (F1+F2)*h/2.] # [dy, y] update\n",
      "\n",
      "    i = 0\n",
      "    \n",
      "    x = 0\n",
      "    y = 0\n",
      "    Vx = 1\n",
      "    Vy = 1\n",
      "\n",
      "    xposn = []\n",
      "    yposn = []\n",
      "\n",
      "    while i<100:\n",
      "        array = euler_step(x,Vx,y,Vy)\n",
      "    #        array = rk2_step(k,m,y,dy)\n",
      "        Vx += array[0]\n",
      "        x += array[1]\n",
      "        Vy += array[2]\n",
      "        y += array[3]\n",
      "        #print y,dy\n",
      "        xposn.append(x)\n",
      "        yposn.append(y)\n",
      "        i +=1\n",
      "    return [xposn,yposn]\n",
      "    \n",
      "def plot(Ex,Ey):\n",
      "    fig, ax = plt.subplots(figsize=(4, 3),\n",
      "                           subplot_kw={'axisbg':'#EEEEEE',\n",
      "                                       'axisbelow':True})\n",
      "    ax.grid(color='w', linewidth=2, linestyle='solid')\n",
      "    alist = main(Ex,Ey)\n",
      "    xlist = alist[0]\n",
      "    ylist = alist[1]\n",
      "    ax.plot(xlist, ylist, lw=5, alpha=0.4)#, label = Ex/Ey)\n",
      "    ax.legend(loc='upper right')\n",
      "    #ax.set_xlim(0,2*np.pi)\n",
      "    #ax.set_ylim(-1, 1)\n",
      "    return fig"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "StaticInteract(plot, Ex=RangeWidget(0., 1., 1.), Ey=RangeWidget(0., 1., 1.))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "    <script type=\"text/javascript\">\n",
        "      var mergeNodes = function(a, b) {\n",
        "        return [].slice.call(a).concat([].slice.call(b));\n",
        "      }; // http://stackoverflow.com/questions/914783/javascript-nodelist/17262552#17262552\n",
        "      function interactUpdate(div){\n",
        "         var outputs = div.getElementsByTagName(\"div\");\n",
        "         //var controls = div.getElementsByTagName(\"input\");\n",
        "         var controls = mergeNodes(div.getElementsByTagName(\"input\"), div.getElementsByTagName(\"select\"));\n",
        "         function nameCompare(a,b) {\n",
        "            return a.getAttribute(\"name\").localeCompare(b.getAttribute(\"name\"));\n",
        "         }\n",
        "         controls.sort(nameCompare);\n",
        "\n",
        "         var value = \"\";\n",
        "         for(i=0; i<controls.length; i++){\n",
        "           if((controls[i].type == \"range\") || controls[i].checked){\n",
        "             value = value + controls[i].getAttribute(\"name\") + controls[i].value;\n",
        "           }\n",
        "           if(controls[i].type == \"select-one\"){\n",
        "             value = value + controls[i].getAttribute(\"name\") + controls[i][controls[i].selectedIndex].value;\n",
        "           }\n",
        "         }\n",
        "\n",
        "         for(i=0; i<outputs.length; i++){\n",
        "           var name = outputs[i].getAttribute(\"name\");\n",
        "           if(name == value){\n",
        "              outputs[i].style.display = 'block';\n",
        "           } else if(name != \"controls\"){\n",
        "              outputs[i].style.display = 'none';\n",
        "           }\n",
        "         }\n",
        "      }\n",
        "    </script>\n",
        "    \n",
        "    <div>\n",
        "      \n",
        "    <div name=\"Ex0Ey0\" style=\"display:block\">\n",
        "      <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAADICAYAAADofFQ1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
        "AAALEgAACxIB0t1+/AAADhlJREFUeJzt3W9sJPV9x/G3OTtNYsp5naZHUpCcHDmgeXBpcgXu4MLS\n",
        "uiKNri0PoiZRIAjalAdpemnUNlCpkZ80SiNFSauqEmmbCFRK05AoSlCb5u7IHlR2C0nApWDOBRoV\n",
        "qDiqWx9Hrn/Ohu2DWR++vV3v7MzszG9m3y/J8q49u/5q7fn4O7/9zfxAkiRJkiRJkiRJkk77EnAU\n",
        "eHTD16aBA8Ay8B1gqoC6JGXknD7f/zLwno6v3UoUAjuAQ+37kipshjM7gSeAbe3b57fvSyqpfp1A\n",
        "N9uIDhFof962ybaSAjee8vGt9sdZdu7c2VpcXEz59JISeAq4KO7GSULgKNFhwPPAm4AXum20uLhI\n",
        "s9lM8PTFqNVqzM3NsX///qJLiaVs9YI1Z+3IkXN48MFxXn751a9NTk5yyy1j2wd5niSHA98Ebmzf\n",
        "vhH4RoLnkJTQ6ircf/84CwtnBkBS/TqBu4GrgZ8AngE+BXwG+Fvg14AfAr+avgxJcTSbYxw+PM6L\n",
        "L451/f7ExODP2S8EPtjj67OD/6jw1ev1oksYSNnqBWtOo1v7v1Gt1uK66+Dmmwd73u5xko1W2cYE\n",
        "AFZWVgquJJ6y1QvWnNTqKiwsjPP0072P3nfseIXLLlvjjW+sMTY2BgPs22nfHZA0RCsrYzQam7f/\n",
        "u3ev8da3vpL4ZxgCUqCWl6P2f22t+/drtRbXXLPKeeel+zmGgBSYOO3/xRdH7f+WLel/niEgBSSP\n",
        "9r+TISAF4siRc3jooeG3/50MAalgebf/nQwBqUBxJv9k3f53MgSkgsSZ/DOM9r+TISDlbJDJP+M5\n",
        "7KGGgJSjIkb/+zEEpJzEmfxTr6+xdWvXS3QMjSEgDVnc9v/yy4cz+t+PISANUQij//0YAtKQxBn9\n",
        "L6L972QISBkLvf3vZAhIGWo2o9H/EyfCbf87GQJSRkKZ/DMoQ0BKqei5/2kZAlIKcdr/K65YY/v2\n",
        "cNr/ToaAlFBZRv/7MQSkAYU29z+tEpQohSPO3P/Q2/9OhoAUU5wr/5Sh/e9kCEh9rC/7VZX2v1Oa\n",
        "km8DrgdeAR4FbgL+L4uipFA0m3DwIDz3XPcACHHyz6CShsAM8BHgUqId/yvAB4A7silLKt7y8jk8\n",
        "9hiVa/87JQ2BE8Aq8Hrg5fbn57IqSirSxtH/ycnu24Q09z+tNGsR/gbwOeB/gH8Abuj4fqvVKndC\n",
        "avQcOwaHDsHx492/PzEBe/fCRRflW9cg8lqLcDvwcaLDgheBrwIfAu7auNHc3Nzp2/V6PZjVXaVu\n",
        "lpZgfp6ek3+mp2F2Fqam8q2rn0ajQaPRSPz4pJ3A+4FfAH69ff8G4Argoxu2cVXiISpbvRBuzZtN\n",
        "/plsHw9ccMFLwc7936hWy29V4ieAPwBeB/wvMAs8mPC5pMLEufLP3r3whjf0GB2sgKQhsAjcCXyP\n",
        "6C3CHwBfzKooKQ9x5v5fd13U/gfWvGQqzTyBz7Y/pFIZZO5/aMf/w1DC+U1SciFe979ohoBGRlGr\n",
        "/obOEFDlle3Cn3kzBFRptv/9GQKqrFCX/QqNIaDKqdqVf4bNl0CVYvs/OENAlVHVK/8MmyGg0iv7\n",
        "df+LZgio1OLM/S/bhT/zZgiotKpy3f+iGQIqHUf/s+VLpFKx/c+eIaDSsP0fDkNAwbP9Hy5fMgUt\n",
        "Tvvv5J90DAEFy/Y/H4aAguOpv/kyBBSUZjOa+3/ihO1/XgwBBSNO+z+KV/4ZNkNAhbP9L5YhoEI5\n",
        "+l88Q0CFcfQ/DIaAcufkn7CkeYmngL8A3g60gJuBf8qiKFVXswn33jth+x+QNCHwx8DfAe9rP0+P\n",
        "ldylyNISLCzQMwBs/4uRNAS2AnuBG9v314iWKJfOst7+Hz3aexvb/+IkXZr8HcDtwOPATuD7wH7g\n",
        "vzds02q1TPRRd+wYHDoEx493//7EBFx1FbztbfnWVWV5LU0+DrwT+E3gIeALwK3ApzZuNDc3d/p2\n",
        "vV6nXq8n/HEqo6UlmJ+n5+j/9DTMzjISi34OU6PRoNFoJH580k7gfGABeEv7/lVEIbBvwzatZrOZ\n",
        "uLC81Wo1AFZKsgZ1yPX2Gv2fnIyGjU6ePFma9j/k17mbWq2WWyfwPPAMsANYBmaBxxI+lyokznX/\n",
        "9+71yj8hSZPDHwPuAl4DPAXclElFKq1+1/1fb/9bLQMgJGlCYBH42awKUXnFnfxz7bUwPg4l6axH\n",
        "RuBHZArdIKf+hn78P6r8tSgx5/5XgyGggXnqb7UYAhqIq/5WjyGg2JaXo/bfVX+rxRBQX576W23+\n",
        "yrSpOO2/y36VmyGgnvpN/rH9rwZDQGex/R8t/gp1hjiTf2z/q8UQ0GlO/hlNhoBitf8XXxy1/07+\n",
        "qR5DYMTZ/ssQGGG2/wJDYCQ5+q+N/BWPGOf+q5MhMELizP131d/RYwiMANt/bcZfecU591/9GAIV\n",
        "5tx/xWEIVJBX/tEgDIGKaTbHOHzY0X/FZwhUiJN/lIQhUAHO/VcahkDJxWn/Hf3XZtKGwBbge8Cz\n",
        "wC+lL0eDWFqCAwcmbP+VStoQ2A88Dvx4BrUoptVVuO8+ePLJ3st+O/lHcaX5E7kAeC/wh8AnsilH\n",
        "/ay3/73e+7f916Bir2HexVeBTwPnAb/D2YcDrVbLNjRLS0swP9/7v//6qr9TU/nWpbCMjY3BAPt2\n",
        "0k5gH/AC8DBQ77XR3Nzc6dv1ep16veem2sTqKjzwQNT+93LppbBnD47+j6BGo0Gj0Uj8+KSdwKeB\n",
        "G4A14LVE3cDXgA9v2KbVbDYTF5a3Wq0GwEpg62b3Gv2fnJwE4NSpk6WZ/BPqa7yZstVcq9Vy6wR+\n",
        "v/0BcDXR4cCHe2+uJPpN/pmehl27Vh39VypZjR37V5ihOJN/LrkErrwSTpzwpVc6WYTA4faHMhDn\n",
        "wp+7d6/xrnflXJgqy3eRAxJn7r9X/lHWDIEAeOqvimQIFMy5/yqaIVAgT/1VCAyBAtj+KySGQM5s\n",
        "/xUaQyBHtv8KkSGQA6/7r5D5JzdkLvul0BkCQxTnuv9O/lHRDIEh8MKfKhNDIGNx5/7b/isUhkCG\n",
        "nPuvMjIEMuDkH5WZIZCSy36p7AyBFJz8oyowBBJw9F9VYggMyNF/VY0hMADbf1WRIRCDc/9VZf7J\n",
        "9hGn/ffUX5WZIbAJ23+NAkOgC0f/NUoMgQ5xTv21/VeVJA2BC4E7gZ8kWn3oi8CfZFVUUZaW4ODB\n",
        "iU1P/bX9V9UkDYFV4LeBR4Bzge8DB4CljOrK1eoq3HdftOpvrwBw7r+qKmkIPN/+APgR0c7/ZkoY\n",
        "Autz/3vt/E7+UdUlXZp8oxmitQjfThQI61qtVtht89ISzM+z6aq/s7MwNZVvXVIaeS1Nvu5c4B5g\n",
        "P2cGAABzc3Onb9frder1esofl43VVXjggaj97+WSS2DPHpz8o+A1Gg0ajUbix6fpBCaAe4G/B77Q\n",
        "5futZrOZ4umHo9epv5OTkwCcOnWyFKP/tVoNgJWVlYIric+ah69Wq+XWCYwBfwk8TvcACFK/yT/T\n",
        "07Br16qj/xopSUPgSuB64F+Ah9tfuw34dhZFZS3O5J/19v+llwwAjZakIfCPQO89KiBxl/3atSvn\n",
        "wqRAVHrYy7n/Un+VDAHn/kvxVS4EXPZLGkylQsBlv6TBVSIEbP+l5EofAp76K6VT6hCI0/47+i9t\n",
        "rpQhYPsvZad0IeDov5StUoWAo/9S9koRArb/0vAEHwIu+yUNV9Ah4Nx/afiCDAGX/ZLyE9wu5LJf\n",
        "Ur6CCgHbfyl/QYSA7b9UnMJ3qbhX/rH9l4aj0BCw/ZeKV0gI2P5L4ch9F7P9l8KSawjY/kvhySUE\n",
        "bP+lcA19l3PuvxS2oYZAnPbfU3+lYqVZReg9wBPAvwGf7LbBwkLvANix4xX27QsrANKs7FqEstUL\n",
        "1hyipCGwBfhToiD4aeCDwKVxHjgxAe9+9xp79oR37n/ZftllqxesOURJDwcuA54Efti+/zfArwBL\n",
        "mz3I0X8pPLHXMO/wPuBa4CPt+9cDlwMf27BN6/bbX93Z11f9dfRfGq6xsTEYYN9OukvG+Vf+1C23\n",
        "jG1P+PySkntqkI2ThsBzwIUb7l8IPNuxzUUJn1tSCYwTpc0M8BrgEWIODEqqjl8EjhANEN5WcC2S\n",
        "JCkkfScSBeRC4LvAY8C/Ar9VbDkD2QI8DHyr6EJimALuIXob+XHgimLLieU2or+LR4G/Bn6s2HK6\n",
        "+hJwlKjGddPAAWAZ+A7Ra5+rLUSHCDPABOGPF5wPvKN9+1yiQ5yQ693oE8BdwDeLLiSGO4Cb27fH\n",
        "ga0F1hLHDPA0r+74XwFuLKya3vYCP8OZIfBZ4Pfatz8JfCbvonYD395w/9b2R1l8A/j5oouI4QLg\n",
        "IHAN4XcCW4l2qDKZJvqHUCMKrW8Bs4VW1NsMZ4bAE8C29u3z2/d7SnPuQC8/BTyz4f6z7a+VwQxR\n",
        "qv5zwXXE8Xngd4EynH75FuC/gC8DPwD+HHh9oRX11wQ+B/wH8J/AcaLQLYNtRIcItD9v22TboYRA\n",
        "WecEn0t0zLof+FHBtfSzD3iBaDwg6azPPI0D7wT+rP35JOF3h9uBjxP9Y3gz0d/Hh4osKKEWffbJ\n",
        "YYRAnIlEoZkAvgb8FdHhQOj2AL8M/DtwN/BzwJ2FVrS5Z9sfD7Xv30MUBiHbBcwDx4A14OtEr3sZ\n",
        "HCU6DAB4E9E/jFyVbSLRGNEO9PmiC0noasIfEwC4H9jRvj0H/FFxpcSyk+jdotcR/Y3cAXy00Ip6\n",
        "m+HsgcH1d+VupYCBQSjXRKKriI6rHyFqrx8meouzLK6mHO8O7CTqBBaJ/quG/u4ARCPs628R3kHU\n",
        "MYbmbqIxi1NEY3E3EQ1qHqTAtwglSZIkSZIkSZIkSVKY/h/ZgtxSoZxq4wAAAABJRU5ErkJggg==\n",
        "\">\n",
        "    </div>\n",
        "    \n",
        "    <div name=\"Ex0Ey1\" style=\"display:none\">\n",
        "      <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQIAAADICAYAAAADS+82AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
        "AAALEgAACxIB0t1+/AAAFndJREFUeJzt3WtwVOd9x/Hvnt2VQAJLQgghQEaYq+wYycSAudhINthu\n",
        "4jp90cm003QySZrxi0zittMmcWfa+lXqZqaTvOikk0mbjNsmadLcpvYkjQEjsDGIO5URIImLQQIB\n",
        "MpIlZAG7e7YvnlWQtWels6u9nd3fZ2ZH2t1j8UTR+e05z+0PIiIiIiIiIiIiIiIiIiJJqQR+BpwG\n",
        "OoGNwDxgJ9AFvBE7RkQK2KvA52PfB4AK4JvAV2OvfQ14JQftEpEsqQDOO7x+BqiNfb8w9lxEClQz\n",
        "0A78ADgGfA8oBwYnHOOb9FxEPMRycUwAWAd8J/Z1FPj6pGOiscdHNDU1RSe8p4ceemTv0UMSfC6O\n",
        "WQgcAJbFnm8FXgIeAFqBfqAO2AOsmfTfRm/evJlMe3KmqqqKl19+mRdffDHXTXFNbc48r7T37l14\n",
        "7bUgIyM+ysvLeeEFH7g7vwF3VwT9wGVgVez5duAU8Brw2dhrnwV+5brVIpJWBw4EGBlxfd7HCbg8\n",
        "7svAD4ES4BzwOcAP/BT4AnAR+HTKrRCRlHV1WVy44OYzPTG3QXASWO/w+vYZ/et5pqWlJddNSJra\n",
        "nHn53N7BQR+HDrk9jRNL/VrCHU/1EQAMDnpn8ENtzrx8bm84DK+/HmRo6KOncab6CEQkD7W3B+JC\n",
        "AGDN5C57FxQEIh507pxFd3f86VtZGWXz5uR/noJAxGM++MDHgQPx/QKBALS0hAmk0GWgIBDxkHAY\n",
        "2toChMPx723cGKayMprSz1UQiHhIe3uAwcH4foHly21WrrRT/rkKAhGP6Olx7heoqIjy2GMOlwhJ\n",
        "UBCIeMDQkI+DBxP3CwSDM/v5CgKRPBcKwZ49ifsFqqpS6xeYSEEgkucOHAjwwQfx/QIrVsysX2Ai\n",
        "BYFIHjtzxuL8eef5AjPtF5hIQSCSpwYGnNcRBIPQ2prafIFEFAQieejOHTNfwHa48t+0KUxFxcz7\n",
        "BSZSEIjkmWgU9u0LcOuW0zqCCA88kJ5+gYkUBCJ55uRJP3198afm/PlR1q+PZOTfVBCI5JHeXh8n\n",
        "TvjjXi8thW3bQvjj30oLBYFInhgZgbfeip8Z5PPB44+HmDs3c/+2gkAkD5jFREHu3Il/r6kpwpIl\n",
        "6e0cnExBIJIHDh4M8P778Z2DixfbNDVlpl9gIrcjkReBYSAChIANmNqHPwGWcm/z0qG0t1CkwJ0+\n",
        "bdHTE/+ZPHdulCeeCOPL9IaCuL8iiAItwCOYEABT5GQnZpvz3cQXPRGRaVy75uPw4cSLiUpLs9OO\n",
        "ZG4NJufS85jiqMS+/kFaWiRSJD78EPbuDTpOGtq4MUx1dWb7BSZye9FxHvgAc2vwXUz9w0GgasLP\n",
        "uTnh+bhoNJq9/zEiXhGJwOuvw7Vr8e89+CBs3Tqzn+/zJbeLsds+gi3AVaAGczswufLxeL21OC+/\n",
        "/PLvvm9pacnrPeJFsuWdd5xDoLaWlDYfbWtro62tLeX2pNIN8ffALeCLmH6Dgql9CPm5f30ianPm\n",
        "ZaK9Z89ajpuPlpXBc8/dpaxsZj+/qqoq6SsCN30EZcD4VIZy4GmgA/gfVPtQJCnXrvlob48PAcuC\n",
        "lpbQjEMgVW5uDWqBX044/ofAG8ARVPtQxLXRUTNpKFHn4IIFuetPcxMEF4Bmh9dvUmC1D0UyJRKB\n",
        "PXuCjI3Fv7d6tc3q1elfUZgMzSwUyYL9+wMMDMTfstfWRtmwIX07DaVKQSCSYe++63fcbqy8PLMr\n",
        "CpOhIBDJoN5eH0ePxp/pfj+0tuauc3AyBYFIhgwN+di3L4jTnLrNm8PMn58/k+0UBCIZcOcO7N4d\n",
        "4O7d+Pc+9rEIy5fntnNwMgWBSJrZthkmHBmJ7xxcssTm4x/P/LLiZCkIRNKsvT3A1avxIVBRkb1l\n",
        "xclSEIikUWenxdmz8adVaSk89VSIkpIcNMoFBYFImvT2Ou8tYFlmmPC++3LQKJcUBCJpMDjoY+9e\n",
        "5xGCDRvCLFqUPyMEThQEIjM0NmZGCEKh+PfWrImwZk1+jRA4URCIzEAkAm++GXSsSrR4sc3Gjfk3\n",
        "QuBEQSCSomgU3norwI0b8SFQWRll27b8HCFwoiAQSdGxY34uXow/hWbNyu8RAicKApEUdHVZdHQ4\n",
        "ryF48snMViXKBAWBSJL6+nwcPOi8lceWLbndYCRVCgKRJIwPEzrtMrRuXWZKlmeDgkDEpdHRxAuJ\n",
        "VqywWbvWGyMEThQEIi6EQrB7t/MwYV1dlM2bc7/L0Ey4DQI/cBx4LfZ8Hqa+QRdmI9PK9DdNJD+Y\n",
        "1YQBbt50HiZsbQ1hefwj1W3zXwQ6uVfERHUPpWjs2wd9ffGnSlkZbN/urWHCRNwEwRLgE8C/cq9g\n",
        "guoeSlE4fBi6uuJfDwbNXIE5c7LfpkxwM+/pv4FvAPcBfwX8Pu7qHoJqH4qHdXbC22/Hv25Z8Mwz\n",
        "UF+f/Ta5le7ah88B1zH9Ay0JjklY9xBU+1C86cIF2L/f+b2tW/MvBDJd+/AbwJ8CYWAW5qrgF8B6\n",
        "pq97CKp9mFFqc2b09/vYuTNIJALl5eUAjI6OAtDcHKG5Ob+HCTNR+/BvgHpgGfBHwJuYYFDdQylI\n",
        "g4M+3nzThMBkq1bZeR8CqUp20GP8FuAVYAdm+PDJ2HMRTxsZgZ07g44ThpYssdm0ydtzBabipvbh\n",
        "uL2xB6juoRSY27dNCHz4Yfx7CxaYNQReWVKcCo9PgxCZuVAIdu0KMjzsNGEInn0WAsl8ZHqQgkCK\n",
        "mqlS7FygtLwcPvEJs79AoVMQSNGKRmHfvgBXrjhvP75jR+FMGJqOgkCKUjQK77wT4L334k+BQMDM\n",
        "GqysLJ7JcAoCKUpHjvjp7o7/87csaGkJeXJzkZlQEEjROXHCz6lT8duMAWzdGmbJkuIKAVAQSJHp\n",
        "7LQ4ccI5BDZuDHt2h6GZUhBI0ejqsjh0yHkc8JFHIjQ2FmcIgIJAisSFCxYHDjiHwEMPRWhqKsyp\n",
        "w24pCKTgXbpk8dZbAce6hKtW2axfX9whAAoCKXC9vT7a2gKOuw4vW1bY6weSoSCQgnXlio89e5y3\n",
        "Hq+vt3n88cJeP5AMBYEUpP7+xMuJFy+2aWkJe37D0XTSr0IKzvXrPnbvDhJ2uOpfuDBKa2sYv/MI\n",
        "YtFSEEhBuXHDx65dQUKh+PdqaqI89VSo4FcSpkJBIAVjYMCXcGOR+fOj7NgRIhjMfru8QEEgBWFg\n",
        "wMcbbziHwLx5JgQKof5ApigIxPOmCoGqqihPPx2itDT77fISBYF42lQhUFlpQqAYNhaZqemCYBbQ\n",
        "DpzAlDz7h9jrqn0oOXf9euIQqKiI8swzIWbPzn67vGi6ILgNtALNwNrY91tR7UPJsWvXzOhAohB4\n",
        "9lmFQDLc3BqM7+tagqmKPIhqH0oO9fcrBNLNzQRLCzgGLAf+Bfgqqn0oOdLXB7/9LY6ThebNg09+\n",
        "EoUA6a99CGBjbg0qgN9ibg8mUu1DyYr33oNdu3CcNlzsIZDp2oeT/S0wBvwZqn2Yc8XU5osXLfbt\n",
        "c15FWF1t5glkYnTAq7/jdNc+nM+9EYHZmDJnx1HtQ8minh6LvXudQ6CmRkOE6TDdrUEdpjPQij3+\n",
        "AzNKcBz4KfAF4CLw6cw1UYrZ6dMW7e3Of6a1tWbtgGYMztx0QdABrHN4XbUPJeM6OvwcPeq8TLCu\n",
        "LsqTT2rtQLpoHZbkpaNH/XR0OIfAkiW2lhKnmYJA8ko0CgcOBOjqcu6+amiweeIJbSqSbgoCyRuR\n",
        "iKlF6FSGDGDFCrvgy5PnioJA8kIoZKoSOxUkBWhsjLBhQ0QhkCEKAsm5sTHYtSvI++87n+XNzRGa\n",
        "m7XleCYpCCSnhodh584gIyPOIbBhQ5gHHyzeCkTZoiCQnHn/fbN4aGws/j3Lgi1bwixfrhDIBgWB\n",
        "5ERfn4+2NudNRgMBU5q8GKsS54qCQLKuqwt273YuPFJaCk89FWLBAoVANikIJKuOHYMjR3AMgTlz\n",
        "ouzYEaaiQiGQbQoCyQrbhoMHA/T1Ob9fVRVl+/YQ5eXZbZcYCgLJuLt3Ye/eAH19luOJXlcXpbVV\n",
        "i4dySUEgGXXrlukPGBx0Hh5ctsxm61atG8g1BYFkzI0bphrxhx86v//wwxHWrdNswXygIJCMuHjR\n",
        "4u23A457C/p8sGlTmNWrNUcgXygIJO1OnvRz/LjztX4wCNu3w5w5CoF8oiCQtIlEYP/+AOfPOy8c\n",
        "Ki+H55+H6mrw0BaARUFBIGkxOgp79gQZGHC+4a+uNtuKVVdrfDAfKQhkxgYGfLz5ZuJOwfvvN5uJ\n",
        "BPTXlrfc7PNSj9mu/BTwLvCV2Ouqfyj09Fj85jeJQ2Dt2gitrQqBfOcmCELAXwAPAY8BXwIaUf3D\n",
        "ombbcOiQn7ffDjgWHPH74fHHwxoe9Ag3Od0fewDcAk4DizH1D7fFXn8VaENhUBTGxmDfviBXrzqf\n",
        "4WVl0NoaoqZGawa8ItmsbgD2Ah8DLjF9/UPVPiwwN27Azp1mxqCTmhp4+mm0ZiDHMlH7cNwc4OfA\n",
        "i8DIpPcS1j9U7cPCceYM7N/vXHsQYOVKeOIJNF04B7JV+zAIvA78Bvh27LUzTF//ULUPMyhbbY5E\n",
        "oL098RbjlgWPPupuSzGv/Z691l7ITO3D8R/2b0An90IAVP+wKAwPw69/HUwYArNmwY4dIe0r6HFu\n",
        "bg22AJ8B/g9T8xDgJeAVVP+woL33nsX+/QHu3nV+f/78KC0tIebMyW67JP3cBMHbJL5yUP3DAmTb\n",
        "cOSIn87OxDf7q1bZbNyo5cOFQtM85CNGRszQ4I0bzreXfj889liYlSt1K1BIFATyO9PdCsydG6Wl\n",
        "JUx1tYaEC42CQAiHza3AmTOJr/Pvv9/sJKTtxAqTgqDIDQ762Ls3wNCQ861AMkOD4l0KgiLW2Wlx\n",
        "9KjzWgEw24tv2xbWVOEioCAoQmNjZgOR3t7E00iWLrXZvDlMaWkWGyY5oyAoMpcuWbzzToDbt53f\n",
        "9/th/fowa9boVqCYKAiKRCgEhw4F6O5OfBVQWWluBaqqdCtQbBQERaC/38f+/YGEpccB1qyJsH59\n",
        "RBOEipSCoICFw3D0qJ/TpxOf3bNnw5Ytqjxc7BQEBcrNVUB9vekQnD07iw2TvKQgKDChEBw7NvVV\n",
        "QDBoOgRXrVKHoBgKggLS1+fj4MGprwIWLoyyZUuIuXOz2DDJewqCAnD7Nhw5EqCnJ/GIQCAA69aF\n",
        "aWy0tZmoxFEQeFx3N+zaVZJwXgBAba25Crjvvuy1S7xFQeBRw8Nw4AD09pIwBHQVIG4pCDwmEoGO\n",
        "Dj8dHX5mzUp8XF1dlE2bdBUg7igIPKS310d7+9SdgSUlZrWgRgQkGQoCDxgZgcOHA1y6NPVesw0N\n",
        "Nhs2hCkry1LDpGC4CYLvA58ErgMPx16bB/wEWMq9jUuHMtC+ohYOm9uAd9/1J1wqDGbnoI0bw5od\n",
        "KClzs535D4BnJ72muocZFI3CuXMWv/xlCSdPJg4By4LmZvjUpzRFWGbGzRXBW5hSZxOp7mGGXL/u\n",
        "4/DhQMLNQ8fV1UV55hmoqgIP1d6QPOV2UKkBeI17twaDTF/3EFT70LXhYTh0CM6fn/q4sjLYtAmW\n",
        "L89Ou8SbMln7MJGEdQ9BtQ+nc/s2HD8Op06ZegKJWBasXQuPPGLWCohMlK3ahw189IrATd1DUO3D\n",
        "hEIh6Oz0c+qUP+H24ePuv9/m0UfDcXMCvFqXD7zTZq+1F1KrfZjqFcF43cN/RHUPkxKJwNmzFh0d\n",
        "AcbGpj62qirK+vVhFi3S7ZVklpsg+DGmY3A+cBn4O1T3MGm2Dd3dFh0dfm7dmjqoy8qgudlUE9LU\n",
        "YMkGN0HwxwleV91DF2wbenpMAEw1IxDMvf9DD0V46KGI+gEkqzSzMEMiEXMFcOrU9AFgWbBqVYSm\n",
        "poh2C5KcUBCkWSg0HgABRkenPtbngwcesGlqiu8IFMkmBUGa3L4NZ86Y+oFT7Q0wbulSm+bmiLYO\n",
        "l7ygIJih4WEzDNjT4yccnv74+noTAKooLPlEQZCi/n4fnZ1+Ll+2cDN5UgEg+UxBkIRwGC5csDh9\n",
        "2s/Nm9OP6/l85hZg7doI8+YpACR/KQhcGB6Gs2fN5f+dO9Mfb1mwfLnNww+rE1C8QUGQgG2bgqHd\n",
        "3RZ9fW5Wa5vdgVaujPDggxHKyzPcQJE0UhBMMjTko7vb4tw5d73/AHPmRGlstFm5MkJJSWbbJ5IJ\n",
        "CgLM0N+pU2Zr8AsX3E/pq62N0tgYYelSTQUWbyvaIAiH4fJliwsXLHp7Ldcz+vx+WLbMprFRIwBS\n",
        "OIoqCCIRuHLFnPyXL1uEQu7/2/vui7J6tc2KFRFKSzPXRpFcKPggCIWgr8/i0qXkT36/3wz/rVwZ\n",
        "oa5On/5SuAoyCEZHobfXnPhXr1pT7gDspLo6yooVER54wNanvxSFgggC2zabfvb1maE+N5N9Jisv\n",
        "hxUroKYmpPn/UnQ8GQTRqBnmu3rVx5UrFteuJXfJP66kxBQFWbYsQmOjmQk4OKgQkOLjiSCwbbh5\n",
        "08f16z76+y2uX7dcj/FPVlJi9gBsaDD3/X6/eV3Df1LM8jIIRkdhYMBiYMDHjRvmq5uVfYmUlZlF\n",
        "P/X1ERYtimK5mygoUjRyGgS2DcPDPgYHfdy8Of6wpt3U041586LU19ssWWIzf35Un/giU5hpEDwL\n",
        "fBvwA/+K2dU4zp075oSf+Bga8vHBB74p9/JPRmkp1NXZLFpks3ixndJc/7a2NpqamtLToCxRmzPP\n",
        "a+1NxUyCwA/8M2YT0z7gMGab89MTD/rRj0qm3bc/FYEA1NbaLFwYpa7Oprp65p/6Xvw/XG3OPK+1\n",
        "NxUzCYINQA9mO3OA/wI+xaQgSFcIzJoFNTU2tbVRFiwwl/u61xdJj5l8hv4h8AzwxdjzzwAbgS9P\n",
        "OCb63e8mPxzn90N1NdTUwIIF5lFRMYOWihSZbNY+dHOGn3vhBZ/KdYpk37lkDp5JEPQB9ROe1wO9\n",
        "k45ZMYOfLyIeEMCkTgNQApwAGnPZIBHJjd8DzmI6DV/KcVtEREQk3zwLnAG6ga/luC1u1AN7gFPA\n",
        "u8BXctsc1/zAceC1XDfEpUrgZ5gh5k7gsdw2x5WXMH8XHcCPgHxcmP594BqmjePmATuBLuANzO8+\n",
        "q/yYW4UGIIg3+g4WAs2x7+dgbnfyvc0Afwn8EDORywteBT4f+z4A5PugcANwnnsn/0+Az+asNYk9\n",
        "DjzCR4Pgm8BXY99/DXgl243aBPzvhOdfjz285FfAU7luxDSWALuAVrxxRVCBOam8ZB7mQ6EKE1yv\n",
        "YWbS5qMGPhoEZ4Da2PcLY88TysTcvMXA5QnPe2OveUUDJl3bc9yO6XwL+GsgTas1Mm4ZcAP4AXAM\n",
        "+B5QltMWTe8m8E/AJeAKMIQJXy+oxdwuEPtaO8WxGQkCL+/sMQdzD/sicCvHbZnKc8B1TP+AV9ZV\n",
        "BoB1wHdiX0fJ/yvF5cCfYz4cFmH+Pv4klw1KUZRpzstMBIGbiUb5KAj8HPhPzK1BPtsMPA9cAH4M\n",
        "PAn8e05bNL3e2ONw7PnPMIGQzx4F3gHeB8LALzC/ey+4hrklAKjDfHBklRcnGvkwJ9K3ct2QFGzD\n",
        "G30EAPuAVbHvXybBsvU80oQZRZqN+Rt5FfhSTluUWAPxnYXjI3ZfJwedheC9iUZbMffaJzCX28cx\n",
        "Q6BesA3vjBo0Ya4ITmI+XfN91ABMz/v48OGrmCvHfPNjTB/GXUz/3OcwHZ27yOHwoYiIiIiIiIiI\n",
        "iIiIiIiIiHjT/wPf3Rl1MQY9mwAAAABJRU5ErkJggg==\n",
        "\">\n",
        "    </div>\n",
        "    \n",
        "    <div name=\"Ex1Ey0\" style=\"display:none\">\n",
        "      <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQIAAADICAYAAAADS+82AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
        "AAALEgAACxIB0t1+/AAAFk9JREFUeJzt3WtwVOd9x/HvXgRCQpYlYRCIiwSSQIAkxKXYBoJ8rXNp\n",
        "O5nJNMk0ridpU79IE9pO01xmmtGrNO1Mp+lMpzNpc5m0k0nbxG3G6dUhtmxjwBh0AUkIcbeAIAEC\n",
        "YUs27J49ffEsRrBX7eWcs6vfZ0aj3dXR6j+S9rfP85znPA+IiIiIiIiIiIiIiIiIiKTl+8AYcGzG\n",
        "Y9XAL4AR4CXgQRfqEpEc8qf4+g+AZ+577KuYIGgGfhm9LyJFrp57WwTDwJLo7drofREpYKlaBPEs\n",
        "wXQXiH5ekuRYESkAwSy/345+xGhvb7f7+/uzfHoRycBpoHE235BJEIxhugSXgaXAeLyD+vv7mZiY\n",
        "yODp86Oqqoquri727Nnjdikf8GJN4M265nJN1675OHEiwJkzfsLh5MeWl5fz/PO+NbP9GZkEwYvA\n",
        "c8BfRj//LIPnEJEkIhE4d87P8HCA8XFfWt/j98OaWUeAkSoIfgzsBhYBo8A3gG8B/wb8HnAO+O3M\n",
        "frSI3G96Gk6cCHDyZIDp6fS+Z+FCm+bmCE1NFsuWlWf0c1MFwacTPP5kRj/NZZ2dnW6XEMOLNYE3\n",
        "6yrmmsbGfAwPBzh/3k8kkt731NVFWLcuwvLlEXzpNRoSyvLbk7K9NkYAcP36dZcrucuLNYE36yrG\n",
        "miwLzpwxzf9r19J7Kc6fD42NFmvXWjzwQPyafCYVZvXazvasgYjM0tSUaf6PjAR4//30vqe62mbd\n",
        "OovVqyME8/CqVRCIOGR83Mfx4+k3//1+WLUqwrp1FkuWxD1LnzMKApE8ujP6f/x4gCtX0mutl5VB\n",
        "c7NFc7NFWVmeC4xSEIjkwfvvw8hIgBMnAkxNpfc9ixeb5n99fQR/JnN+s6AgEMmhyUkfQ0MBTp9O\n",
        "PfkHTPO/oSFCS4vFokX5bf4noyAQyYFLl3wMDga4eDG9t/IFC2DtWjP6v2BBnotLg4JAJEOWBadO\n",
        "wYEDJVy/nl7/v6bGZv160/wPBPJc4CwoCERm6f33zem/CxfMTMCpqeQh4POZ0f+WlvyP/mdKQSCS\n",
        "pps3YWgowKlTAcJhKE8xm3fePGhqsmhpsVi40JkaM6UgEElhfNz0/99+24+dxht6RYVNS4tFU1OE\n",
        "kpL815cLCgKROGwbRkf9DAykf/Vfba3p/69Ykf3cf6cpCERmMAOAfgYHA9y8mfrV7PfD6tUR1q93\n",
        "9/RfthQEIsCtW2YA8PjxAO+9l/r4efOgrQ02boRQKI0JAx6nIJA5bWrKDACOjAQIhVIfv3ChTUuL\n",
        "ufZ/yRIzWuihCyIzpiCQOWly0sfAgJkBmM4FQNXVNhs2WDQ0OD/91wkKAplTrl71cexY+mcA6upM\n",
        "/7+urnD7/+lQEMic8KtfmQC4dCn127nfD/X1ETZutKiuLu4AuENBIEXLtuHCBT9Hj6Z3CXAwaCYA\n",
        "rV9vUVHhQIEeoiCQomPbcPasn2PHAmldAzB/PqxbZ2YAlpY6UKAHKQikaEQicPq0aQG8807qAFi4\n",
        "0EwAKqQZgPmiIJCCZ1kwMmImAb37buoAqKy02bjRYs2a4jwDkAkFgRSscNgEwMBAMK09AGpqbNra\n",
        "LFauLLwpwPmmIJCCEwqZWYCDg+nNAqyttWltDRf9KcBsKAikYIRCcOyYCYB0lgGvq4vQ2mpRW6sA\n",
        "SCWbIPga8BkgAhwDPgvcykVRIjOFQtDXB0ePwrVrqZf1WbkyQltbYV8E5LRMg6Ae+DzQgnnx/yvw\n",
        "KeCHuSlLxATA8LBpAaRa1svnM5OA2tosqqoUALOVaRDcBEJAGWBFP1/MVVEyt80MgDtdgESrAfl8\n",
        "5jLgtjaLykoFQKayGTv9A+CvgfeA/wOeve/rtp3OZG6RqHAYhoZMNyDVGIDfD42N0NEBlZXO1Fco\n",
        "nNz7cA3wR5guwiTwE+B3gB/NPKirq+uD252dnZ7czVbcZ1lw/LgJgFSnAf1+aGoyARBvE9C5qLu7\n",
        "m+7u7qyeI9MWwSeBp4Dfj95/FngY+MKMY7QbcgperAmcqysSgZMnzVTgVBOBKirKaWqC+vrrngkA\n",
        "L/79nN4NeRj4c2AB8D7wJHAow+eSOca2zXbgfX2ppwL7fLBmTYTdu00LwEOvuaKSaRD0A/8EHMac\n",
        "PuwB/iFXRUnxOn/eT29vgBs3UgfA6tUR2tvDPPCAugH5ls08gr+KfoikdOmSj56eIFevpm6xNjRE\n",
        "2LRJZwGcpJmFkldXr/ro6UlvQZCVKyN0dGgegBsUBJIXk5MmAM6fTx0AdXUmADQT0D0KAsmpqSno\n",
        "7w9y8mTqNQGXLLHZvDns2f0A5xIFgeTE7dswMBBgaMjsC5hMTY1NR0eY5csVAF6hIJCsWBacOOHn\n",
        "6NFgytmAlZU2HR0Wq1ZpPQCvURBIxs6e9dPTk3ouQHk5tLeHaWpSAHiVgkBmbWzMx+HDwZQrA8+f\n",
        "D62tZlHQVFcPirsUBJK2mzfhyJFgyjMBgQC0tFi0tlrMn+9QcZIVBYGkdOsW9PcHGB4OJN0e7M50\n",
        "4E2bwixc6Fx9kj0FgSQUicDwsJ/+/iC3Uqw9VVcXYcuWubMzULFREEhcb78Ne/eWMDmZfBygutpm\n",
        "69Ywy5YpAAqZgkDuceOGjwMH4MIFmJpKHALl5dDREWbNGp0JKAYKAgHMOEBfX4ATJwIsWJD4uGDQ\n",
        "nAnYsMEiqP+eoqE/5Rxn22aTkN7e5BOCfD5obIzQ0RGmrMy5+sQZCoI5bGzMx6FDQa5dS962r621\n",
        "2bYtTE2NxgGKlYJgDpqeNvMBTp9OPh+gosJm61YzJViKm4JgDolE4PjxAH19AUKhxMeVlMCmTbBi\n",
        "RUgzAucIBcEccfmyj4MHgymXCGtsjPDEE1BWpvUB5xIFQZGbnobDh4OcOZO8G1BTY7N9e5jFi20N\n",
        "Bs5BCoIiZdtmVmBvb5DbtxMfV1pq5gM0N2s+wFymIChCV6+abkCyhUJ9Pli71qKjQxcGiYKgqNy+\n",
        "Db295uKgZMuELV5sugE6HSh3KAiKxPnzfg4dCjI1lfiY0lLYsiVMY6O6AXIvBUGBm5qCgweDjI4m\n",
        "Hwxsbo6wZUtY3QCJK5sgeBD4LrABsIHPAQdzUZSkdmcwsKcnmHROQHW1zcMPm7MBIolkEwR/C/w3\n",
        "8Ino8yTYwV5y7cYNH/v3BxkfT9y+Dwaho8Ni/XpL3QBJKdMgqAR2Ac9F74cx26NLHkUicPRogKNH\n",
        "k68UtGJFhO3btUqQpC/T94pNwHeAIaAdOALsAWbubm/bqXa4kLRduQKvvgrJdpovK4NHH4XVq52r\n",
        "S7zHyW3Rg8Bm4A+Bt4BvA18FvjHzoK6urg9ud3Z20tnZmeGPm7ssC44cgf5+kp4SbGmB7dth3jzn\n",
        "ahNv6O7upru7O6vnyLRFUAscABqi93diguBjM46xJ5K9fTmsqqoKgOsemkCfqqYrV3zs2xdMulxY\n",
        "ZaXNI4+Eqa3NXeurEH9XbvBqTU62CC4Do0AzMAI8CQxm+FxyH8syqwUNDCSeGOT3w8aNFu3t2jNA\n",
        "spfNWYMvAj8C5gGngc/mpKI57to1H6+/nvwqwZoamx07wloxWHImmyDoB7blqpC5Lp0zAn4/bNpk\n",
        "sXGjhT/1buMiadPMQg+YnDStgGQXCS1aZLNzZ5gHH1QrQHJPQeAi24bBQXjllZKEW4nfaQW0tmpi\n",
        "kOSPgsAl09N8sH9AohCoqTGtgKoqtQIkvxQELjh/3s+BA8GEo/1+v9k7oL1dYwHiDAWBg8JhOHQo\n",
        "yMiIeXWXx7k6o7LSZteuMIsWqRUgzlEQOGRiwserryafHLRuncXWrdpBSJynfzkHDA35OXIkiGXF\n",
        "/7q5RiDE8uVqBYg7FAR5dOsW7NuXfNGQ+npobb1NaalzdYncT0GQJ2NjZm7Au+/G7woEg7Brl7lY\n",
        "yENT1WWOUhDkmG3DwECA3t7EMwSrq2127w5TX+9oaSIJKQhy6NYteP31IBcuJO4KtLSYAUFdKCRe\n",
        "oiDIkStXzFmBRF2B+fNh584wK1ZoQ1HxHgVBDgwPm6XEE3UFliyx2bUrpKXDxLMUBFkIh+HAgeTb\n",
        "i7e2mt2ENENQvExBkKF33jEXC01MJO4K7NqluQFSGBQEGbh40cdrr5Vw61b8rz/0kM3u3eoKSOFQ\n",
        "EMzSwECAI0cSLyG2bp3Ftm06KyCFRUGQJsuCN94IcuZM/M5+MAiPPBJmzRqdFZDCoyBIw9SUGQ9I\n",
        "tIJQRYXNY49pDUEpXAqCFK5e9fHyyyVMT8f/el1dhA99SJuLSmFTECRx7pyfffuCCVcQ2rDBzBLU\n",
        "EmJS6BQECRw9GqCnJ/6IXyAAjz6q8QApHgqC+0QiZpLQyZPxBwXLyuCxx0I89JDGA6R4KAhmuH0b\n",
        "uruDXLoUPwRqamwefzwUd4kxkUKmIIiamoK9e0u4fj1+h3/Vqgi7doW1jJgUpWz/rQPAYeAC8BvZ\n",
        "l+OOGzd87N2b+MrBjRsttmzRoKAUr2yDYA8wBFTkoBZXjI2Z04Pxpgv7/bB9e5i1azUoKMUtm2vi\n",
        "lgMfAb5L5turu2p01M9LL8UPgZISePzxkEJA5oRsXsA/Ab4JPAD8KbFdA9tONCHfA0ZG4LXXiLuG\n",
        "QFkZPPMMLFrkfF0i2fKZPuysXtuZdg0+BowDvUBnooO6uro+uN3Z2UlnZ8JDHTUwAPv3x/9aZSV8\n",
        "5CNQUbCdHZlruru76e7uzuo5Mm0RfBN4FggDpZhWwQvA7844xp6YmMiquFyqqqoCoLv7Jr298ScK\n",
        "PfSQzRNPhBxbWvxOTdc9toyxF+tSTempqqrKqEWQ6RjB14EVQAPwKeBl7g0BTzp0iIQhUFcX4emn\n",
        "nQsBES/J1Vlx7w4GRO3fb7oE8dTXmwuHtJyYzFW5CIJXox+eZNvw5psBRkfjf725OcIjj4Q1R0Dm\n",
        "tKJ+D7wTAsPD8bsD69dbPPqoQkCkqCfMJguBtjaLzZsT7EoqMscUbRAcPJg4BDo6LNrbFQIidxRl\n",
        "ELz1VuIQ2LzZoq1NISAyU9EFQV9fgMHB+CGwbRvU1ysERO5XVIOFQ0N++vrih8DWrdDR4XBBIgWi\n",
        "aILg1Cmz/2A87e0Wmzc7XJBIASmKIBgd9bN/f/wQ2LDB7D0oIokVfBCMj5vtyONdRbh2bYRt2xQC\n",
        "IqkUdBBMTvr45S9L4i433tAQ4eGHE6xDLiL3KNggeO892Ls3GHdRkbo6s76gZgyKpKcggyAchpdf\n",
        "LuGdd2Jf6YsW2XR26gIikdkouJeLbcO+fUGuXIkNgYoKs55ASYkLhYkUsIILgr6+AOfOxZZdWgpP\n",
        "PRViwQIXihIpcAUVBGfP+unvj50wFAiYhUYfeMCFokSKQMEEwcSEjzfeiD9XYOfOMIsXe35tFBHP\n",
        "KogguHULXnkl/q7EmzZZNDRoyXGRbHg+CGwbXnstGPcMQX19RJcTi+SA54Ogvz/AxYuxZVZX2+zc\n",
        "qbkCIrng6SC4eNEXd3Bw/nyzNbk2JBXJDc8GwfQ07NtXwv2bJfl8sGtXSBuQiOSQJ4PAtuGNN4K8\n",
        "917s19rbLZYv1xkCkVzyZBAMDsYfF1i2TIODIvnguSCYmPDR0xM7LlBWhi4kEsmTTINgBfAKMAgM\n",
        "AF/KRTGWZU4VxltbYMcOTR8WyZdMx91DwB8DfcBC4AjwC+B4NsX09AS4cSP2LX/jRou6Oo0LiORL\n",
        "pi2Cy5gQAHgXEwDLsilkfNzH0FBsl6C62tZSYyJ5losedz1m78MNmFC4w7bvP/eXgGXBCy/AjRv3\n",
        "Ph4IwMc/DtXVOahSZI7IZFv0bKfkLAR+Cuzh3hAAoKur64PbnZ2ddHZ2xn2S3t7YEADYskUhIJJK\n",
        "d3c33d3dWT1HNi2CEuA/gf8Bvh3n6/bExETKJ7lxw8eLL5bEDBAuWmTz0Y+GcnaWoKqqCoDr16/n\n",
        "5glzwIs1gTfrUk3pqaqqyqhFkOkYgQ/4HjBE/BBI28GDsWcJ/H7YsUOnCkWckmkQ7AA+AzwG9EY/\n",
        "npntk5w54+fy5dhXe2urRVWVzhKIOCXTMYJ9ZDkZKRSCw4djf3xFha1NSkUc5trMwmPHAkxPxz6+\n",
        "fXuYQPztC0UkT1wJgnffJe6OxStXRnRBkYgLXAmC3t4g1n2t/0AAtm3TzkQibnA8CCYmfJw5E/tj\n",
        "16+3tMaAiEscD4Le3kDMYiOlpeZMgYi4w9EguHrVx+ho7I9sawszb56TlYjITI4GQV9f7ABhRYXN\n",
        "2rVajlzETY4FwbVrPi5ciNcasHS6UMRljgXBsWPxWwONjWoNiLjNkSC4eRPOn4/9Ua2tlq4nEPEA\n",
        "R4Lg+PHYMwXl5bBmjVoDIl6Q9yC4fRtOnYrtFrS0aGxAxCvyHgSnTvkJhe59rKQEmps1b0DEK/Ie\n",
        "BCdOxL7tNzZamjcg4iF5DYKxMR+Tk7GjgevWaWxAxEvyGgTxxgaWLrWprNQVhiJektcgOHcu9umb\n",
        "mjQ2IOI1eQ2C+wcJ582DVavULRDxGkevNaivj+iUoYgHORoEDQ3qFoh4kWNBsGAB1NZqkFDEixwL\n",
        "glWrdF2BiFc5FgTLl2uQUMSrHAmCYNDMHxARb3IkCJYu1dkCES/LJgieAYaBk8BXkh24dKk3ugXZ\n",
        "7hibD16sCbxZl2rKn0yDIAD8HSYM1gOfBloSHbxsmTe6BV78o3mxJvBmXaopfzINgl8DTgHngBDw\n",
        "L8BvxTuwtBRdWyDicZme0PsE8OvA56P3PwNsB7444xj7O9+xqa+Hp5/OvEARmR2fOU8/q9d2prsh\n",
        "p/MWf/r5531rMnx+Ecnc6dl+Q6ZBcBFYMeP+CuDCfcc0ZvjcIlIggpjUqQfmAX0kGSwUkeL1YeAE\n",
        "ZtDway7XIiIiIl6U9mSjPPo+MAYcm/FYNfALYAR4CXjQ4ZpWAK8Ag8AA8CUP1FUKvInp3g0Bf+GB\n",
        "mu4IAL3Azz1S0zngaLSmQx6piejP/ClwHPM33O6FugKY7kI9UIJ74we7gA7uDYK/Av4sevsrwLcc\n",
        "rqkW2BS9vRDTtWrxQF1l0c9B4CCw0wM1AfwJ8CPgxeh9t2s6i3mBzeR2TQA/BD4XvR0EKr1Q1yPA\n",
        "/864/9XohxvquTcIhoEl0du10ftu+hnwJN6pqwx4C9jggZqWA3uBx7jbInC7prNAzX2PuV1TJXAm\n",
        "zuOzqisfFx3VAaMz7l+IPuYFSzDdBaKflyQ5Nt/qMS2WN3G/Lj+m5TbG3a6L2zX9DfBlYOaFKm7X\n",
        "ZGPC6TB3J9O5XVMDcAX4AdAD/CNQPtu68hEEhTKf2Ma9WhcCLwB7gHfu+5obdUUwXZblwIcw78Ju\n",
        "1vQxYBzTF080Q86N39MOTHh/GPgCpvvpdk1BYDPw99HPU8S2wFPWlY8gSGeykVvGMM0kgKWYfzan\n",
        "lWBC4J8xXQOv1AUwCfwXsMXlmh4FfhPTFP8x8Djm9+X27+lX0c9XgP/AXHPjdk0Xoh9vRe//FBMI\n",
        "l2dTVz6C4DDQxN3JRp/k7mCP214Enovefo67L0Sn+IDvYUZ2v+2RuhZxd0R5AfAU5p3YzZq+jnkD\n",
        "aQA+BbwMPOtyTWVARfR2OfA0ZvzJ7f+py5iueHP0/pOYrt3PXa4L8MZkox8Dl4DbmF/UZzEjvntx\n",
        "75TKTkwzvA/zYuvFnGp1s65WTN+yD3Nq7MvRx93+Xd2xm7tvJG7W1ID5HfVhTv3e+b/2wu+pHdMi\n",
        "6Af+HTOA6IW6REREREREREREREREREREpAD9Pw5EDbp2oXucAAAAAElFTkSuQmCC\n",
        "\">\n",
        "    </div>\n",
        "    \n",
        "    <div name=\"Ex1Ey1\" style=\"display:none\">\n",
        "      <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQIAAADICAYAAAADS+82AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
        "AAALEgAACxIB0t1+/AAADslJREFUeJzt3W+MHPdZwPHv2XtJmkvxXQhyosbCpv5DUkrSUDeGO8gF\n",
        "ua2LjsALBEVqFbVQ5UXVWiCaNJUAvyqhb+gLVBSVNoqqKAXSuCSOCnZozsIWNo3itGn+nJ1/IoE4\n",
        "reS74BgIu/h48ZvNndc73tk/M/Ob3e9HWu3u3Nzdc7uzz80zv/nNA5IkSZIkSZIkSZLUlUngAeBZ\n",
        "4BngRuBy4ABwHNifrCNpiN0LfDJ5XAPWAV8Cbk+W3QHcVUJckgqyDnixzfLngPXJ4yuT55KG1PXA\n",
        "UeAe4Angq8AEsLhqnbGW55IqZE2GdWrADcBXkvszwOdb1llObue47rrrlld9zZs3b8XdnqcLYxnW\n",
        "uRL4F2BT8nwGuBP4GeBm4CRwFfAY8LMt37t86tSpbuLJ1dTUFHv27GH37t1lh/I2Y8ouxrjKjKle\n",
        "h6NHazz//Ln/zycmJrjttjHI9vkGsu0RnAReAbYmz3cCTwMPA7cmy24Fvp31l0rqz9LSGI88Mn5e\n",
        "EuhVLeN6nwHuAy4CXgA+AawF/hb4PeBl4LcHEpGkCzpxYg1Hj9ZoNNp/fWqq+5+ZNRF8H9jeZvnO\n",
        "7n9luWZnZ8sO4TzGlF2McRUVU1opsNqWLWfZtav7n525huhRdMcIABYX4xngMKbsYoyrqJiWlsZ4\n",
        "7LEab7zR/iNbq8GOHQ02bz7L1NQUY2PdHSPIukcgqSSdSoHJyWVmZxtMTi73/DtMBFKkGg04cqRz\n",
        "KXDjjQ1qfX6STQRShJaWxpifr7G01LkUGAQTgRSZIkqBViYCKRJFlgKtTARSBIouBc77+bn8VEmZ\n",
        "lVEKtDIRSCXJeoJQHqVAKxOBVIJuThAqgolAKlgMpUArE4FUkDJHBToxEUgFKHtUoBMTgZSzGEuB\n",
        "ViYCKScxjQp0YiKQchDbqEAnJgJpwKpQCrQyEUgDUqVSoFVk4UjVVLVSoFXWRPAy8J/A/wF14AOE\n",
        "3od/A/w0KxcvXRp4hFLkFhZg//7xSpUCrbJeC3kZmAXeR0gCEJqcHCBc5vyfOL/piTTU6nWYn4eD\n",
        "B0lNAlu2nGVurh51EoDuSoPWfZ5bgJuSx/cC85gMNCKaJwjV6+2/Hnsp0CrrVU5fBN4glAZ3E/of\n",
        "LgLNK6iPAadWPW9aXl6OOxNK3VpYgMOH0/cCpqZg587e+gsMSl5XMZ4GXgN+ilAOtHY+bvZbO8+e\n",
        "PXvefjw7OxvldemlLOr1kACOH09fZ9s2mJ6m8FGB+fl55ufne/7+Xvoa/CnwJvApwnGDSvU+hNG8\n",
        "Ln43YowJyo0rbVRgYmICgLfeOhNNKdBLX4MsBwsvBd6ZPJ4APgQ8BTyEvQ81Ak6cWMO+feOpQ4NT\n",
        "UzA3V48iCfQqyw7MemDvqvXvA/YDj2PvQw2xLCcINUuB06erfSwsSyJ4Cbi+zfJTVLD3oZRF1hOE\n",
        "trfrCFpBnlkotajiXIF+mQikRJXnCvRryP4cqTdVnyvQLxOBRt4olgKtTAQaWaNcCrQa8j9Pai/2\n",
        "i4kWzUSgkWMpcD4TgUaGpUC6EftzNapGfVSgExOBhp6lQGcmAg0tS4HsRvzP17CyFOiOiUBDx1Kg\n",
        "eyYCDQ1Lgd75cmgoWAr0x0SgyrMU6J+JQJVlKTA4vjyqJOcKDJaJQJVjKTB4WRPBWsLFSl8Ffh37\n",
        "HqoEzb4Cx46lb7aWAr3J2vtwN/AMK01M7HuoQi0tjbF3b3pzkVoNZmYaTE+bBHqRJRFcDfwa8Nes\n",
        "NEy4hdDvkOT+NwcfmhQ0+wospexzTk4uV76vQNmydEL5O+CLwE8Af0QoDbL0PQR7H6oPMbcYi92g\n",
        "ex/OAT8CjhHam7WT2vcQ7H2o3iwuwoEDpO4FhFIAtm4tNq5Y5d378IvAx4EGcAlhr+BBYDud+x6C\n",
        "vQ87MqbzpY0KNPsMjo+/Gc2oQNmvVTt59D78ArAB2AR8FPguITHY91ADV6/DoUM1Dh9OHxrcti30\n",
        "GYwhCQyTbiur5qt/F/Y91ABlmSswOxtKgYj++Q6NbhLBweQG9j3UAGU9QWjTpmLjGiUea1VpsswV\n",
        "2Lz5LDt2eG5A3nx5VQqnDcfFRKDCOVcgPiYCFcZpw/Hy5VYhnDYcNxOBcmcpED8TgXLTaMCRI5YC\n",
        "VeDLr1xYClSLiUADZylQPSYCDYyjAtXl26GB8AShajMRqG+WAtVnIlDPnCswPHx71BNLgeFiIlDX\n",
        "LAWGj4lAmTkqMLx8u5SJpcBwMxGoI0uB4WciUCpLgdHR6e27hHCdwouBi4C/B+7E3odDb3ER9u0b\n",
        "txQYEZ0uZ/4/wM3A9cDPJ49nsPfhUFtYgL17SU0CthgbPll26P4rub+I0BV5kdD78KZk+b3APCaD\n",
        "ymtOG37ttfR1LAWGU5ZOKGuAJ4B3A38F3I69D4fO4iI8+mh6zwBbjFXLoHsfApwllAbrgH8klAer\n",
        "2fuw4hYWQrPRtFGBqSnYuTPcK0559z5s9cfAfwO/j70PB6LMmNKuINTsMXjmzJmoSgHfv2zy6H14\n",
        "BTCZPH4H8EFCZ2R7H1bc0tIY+/aNpw4NhlKgwfR0HElA+er0Fl9FOBi4Jrl9gzBKcAx7H1ZWpxOE\n",
        "mqVAqAo1CjolgqeAG9ost/dhBWU9QWjXrrBHENHernLmTt+I6GaugKXA6PEtHwHOFVAnJoIhZl8B\n",
        "ZeXbP6TsK6BumAiGkKWAumUiGCJOG1av3ByGhFcQUj9MBEPAUkD9MhFUmKWABsXNo6IsBTRIJoIK\n",
        "shTQoJkIKsRSQHlxc6kISwHlyURQAZYCypuJIGKWAiqKm0+kLAVUJBNBhCwFVDQTQUQsBVQWN6dI\n",
        "OG1YZep0FWOADYTLlT8N/BD4bLL8ckLbs+PAflaudqwuLSyEPoNpScAWY8pblkRQB/4AeA+wA/g0\n",
        "cA32P+xbvQ7z83DwYHpzkS1bzjI3V/d4gHKVpTQ4mdwA3gSeBd6F/Q/70hwVSEsAlgIqUredjjYS\n",
        "2qT/HPBvdO5/aO/DNmwxprzl0fuw6TLgW8Bu4HTL11L7H9r7cEWjAYcOwfHj6ets2wbT0zgqoK4U\n",
        "1ftwHNgHfAf4crLsOTr3P7T3YSJtVKDZZ/Ctt85EUwrE2M8P4owr1pjy2CMYA74GPMNKEoCV/od/\n",
        "jv0PLyhLi7H3v98DgipPlkQwDXwM+AGh5yHAncBd2P/wgrL0FWiWAqdPmwRUniyJ4BDpw4z2P0yR\n",
        "da7A9u0FBya14SGpHDhXQFVjIhigLKXA5s1n2bHDuQKKi5vjgDhXQFVmIhgASwFVnYmgD04b1rBw\n",
        "8+yRVxDSMDER9MBSQMPGRNCFLKWAowKqIjfXjCwFNMxMBBlYCmjYmQguwFEBjQo33xSWAholJoI2\n",
        "LAU0akwEqzgqoFHl5pxwroBGmYkASwFppBOBowJSMLKbt6WAtGIkE4GlgHSuLC3Pvg68Djy1alkl\n",
        "+x42GqHF2OHD6Ulg82ZbjGn0ZEkE9wC7WpZVru/h0tIYDz6Y3lykVoOZmQYzMx4P0OjJssn/M6HV\n",
        "2WqV6nvYLAUuvrj91y0FNOqydkLZCDwMvDd5vkjnvodQcu/Dej30GLTFmEZNnr0P06T2PYTyeh8u\n",
        "LsKBA7C01P7roRSArVsLCUfKVVG9Dzdy7h5Blr6HUFLvw7RRgWafwfHxN6MpBWLtnQdxxQRxxhVr\n",
        "TEXtEUTZ9zDLCULbtsG119YtBaRVsnwc7iccGLwCeAX4EyLse5jlBKHZ2VAKRJS8pShkSQS/m7I8\n",
        "mr6HWU8Q2rSp2Likqqj0DrLThqXBqOzHwysISYNTyUTgXAFpsCqVCJw2LOWjMh8XSwEpP5VIBJYC\n",
        "Ur6iTgSNBhw5Yikg5S3aj4+lgFScKBOBpYBUrKgSgaMCUjmi+ThZCkjliSIRWApI5So1ETgqIMWh\n",
        "tI+XpYAUj1ISgaWAFJdCE4GjAlKcCvu42WJMilchicBSQIpb7ong0CFLASl2WVqeXcguwqXNTwB3\n",
        "tFshLQk0W4xNTxebBPq59ntejCm7GOOKMaZu9ZMI1gJ/SUgG1xIucnpNlm+cnFxmbq5eyvGAGN80\n",
        "Y8ouxrhijKlb/fwv/gDwPOFy5gDfBH4DePZC32QpIMUncyeUNn4L+DDwqeT5x4Abgc+sWmf57rvD\n",
        "AUBbjEnFKbL3YZZD/C/cdtvYu/v4HZJ680I3K/eTCP4d2LDq+Qbg1ZZ1Nvfx8yVVQI2QdTYCFwFP\n",
        "kvFgoaTh8hFggXDQ8M6SY5EkSbHpeKJRQb4OvA48tWrZ5cAB4DiwH5gsOKYNwGPA08APgc9GENcl\n",
        "wFFCefcM8GcRxNS0FjgGPBxJTC8DP0hi+tdIYpoEHiAM3T9DGL0rOybWEkqFjcA45R47+GXgfZyb\n",
        "CL4E3J48voPQ4r1IVwLXJ48vI5RW10QQ16XJfQ04AsxEEBPAHwL3AQ8lz8uO6SXCh2y1smO6F/hk\n",
        "8rgGrIsgJn4R+IdVzz+f3MqykXMTwXPA+uTxlcnzMn2b0GI+lrguBb4HvCeCmK4GHgVuZmWPoOyY\n",
        "XgJ+smVZmTGtA15ss7yrmPqda9DOu4BXVj1/NVkWi/WEcoHkfv0F1s3bRsIey1HKj2sNYe/tdVZK\n",
        "l7Jj+gvgc8Dqc9HLjmmZkJweZ+VkujJj2gT8GLgHeAL4KjDRbUx5JIIqzSVeprx4LwO+BewGTrd8\n",
        "rYy4zhJKlquBXyH8Fy4zpjngR4RaPO0MuTJep2lC8v4I8GlC+VlmTDXgBuAryf0Zzt8D7xhTHokg\n",
        "y4lGZXqdsKsEcBVhYyvaOCEJfINQGsQSF8AbwCPAL5Qc0y8BtxB2xe8HfpXwepX9Or2W3P8Y2EuY\n",
        "c1NmTK8mt+8lzx8gJIST3cSURyJ4HNjCyolGv8PKgZ4YPATcmjy+lZUPYlHGgK8Rju5+OZK4rmDl\n",
        "qPI7gA8S/hOXGdMXCP9ENgEfBb4LfLzkmC4F3pk8ngA+RDj+VGZMJwmleHMWz05CWfdwiTG9LZYT\n",
        "je4H/gP4X8KL9QnCEd9HKW9YZYawG/4k4cN2jDDcWmZc7yXUl08ShsY+lywv+7VquomVfyZlxrSJ\n",
        "8Bo9SRj6bW7bZb9O1xH2CL4PPEg4gFh2TJIkSZIkSZIkSZIkqaL+H0DUsOXsMl4yAAAAAElFTkSu\n",
        "QmCC\n",
        "\">\n",
        "    </div>\n",
        "    \n",
        "      <b>Ex:</b> <input type=\"range\" name=\"Ex\" min=\"0.0\" max=\"1.0\" step=\"1.0\" value=\"0.0\" style=\"width:350px\" oninput=\"interactUpdate(this.parentNode);\" onchange=\"interactUpdate(this.parentNode);\">\n",
        "<br>\n",
        "<b>Ey:</b> <input type=\"range\" name=\"Ey\" min=\"0.0\" max=\"1.0\" step=\"1.0\" value=\"0.0\" style=\"width:350px\" oninput=\"interactUpdate(this.parentNode);\" onchange=\"interactUpdate(this.parentNode);\">\n",
        "    </div>\n",
        "    "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<ipywidgets.interact.StaticInteract at 0xb035b0ac>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "testing\n",
      "==="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bz = 1\n",
      "\n",
      "m = 1\n",
      "q = 1\n",
      "\n",
      "x = 0\n",
      "y = 0\n",
      "Vx = 1\n",
      "Vy = 0\n",
      "\n",
      "dt = 0.1\n",
      "\n",
      "xposn = []\n",
      "yposn = []\n",
      "\n",
      "def force():\n",
      "    return [Vy*Bz,-Vx*Bz]\n",
      "\n",
      "def euler_step(x,Vx,y,Vy):\n",
      "    array = force()\n",
      "    Fx = Vx\n",
      "    fx = array[0]\n",
      "    Fy = Vy\n",
      "    fy = array[1]\n",
      "    return [fx*dt, Fx*dt, fy*dt, Fy*dt]\n",
      "\n",
      "i = 0\n",
      "while i<100:\n",
      "    array = euler_step(x,Vx,y,Vy)\n",
      "#        array = rk2_step(k,m,y,dy)\n",
      "    Vx += array[0]\n",
      "    x += array[1]\n",
      "    Vy += array[2]\n",
      "    y += array[3]\n",
      "    #print y,dy\n",
      "    xposn.append(x)\n",
      "    yposn.append(y)\n",
      "    i +=1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(xposn,yposn)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb13715ac>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb140d9cc>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bz = 1\n",
      "\n",
      "m = 1\n",
      "q = 1\n",
      "\n",
      "x = 0\n",
      "y = 0\n",
      "Vx = 1\n",
      "Vy = 0\n",
      "\n",
      "dt = 0.1\n",
      "\n",
      "xposn = []\n",
      "yposn = []\n",
      "\n",
      "def force():\n",
      "    return [Vy*Bz,-Vx*Bz]\n",
      "\n",
      "#def euler_step(x,Vx,y,Vy):\n",
      "#    array = force()\n",
      "#    Fx = Vx\n",
      "#    fx = array[0]\n",
      "#    Fy = Vy\n",
      "#    fy = array[1]\n",
      "#    return [fx*dt, Fx*dt, fy*dt, Fy*dt]\n",
      "\n",
      "def rk2_step(k,m,y,dy):\n",
      "    array = force()\n",
      "#    \n",
      "    F1x = Vx\n",
      "    f1x = array[0]\n",
      "    F2x = Vx +f1x*dt\n",
      "    f2x = array[0]\n",
      "#    \n",
      "    F1y = Vy\n",
      "    f1y = array[1]\n",
      "    F2y = Vy +f1y*dt\n",
      "    f2y = array[1]\n",
      "#    \n",
      "    return [(f1x+f2x)*dt/2., (F1x+F2x)*dt/2., (f1y+f2y)*dt/2., (F1y+F2y)*dt/2.] # [dy, y] update\n",
      "#    return [fx*dt, Fx*dt, fy*dt, Fy*dt]\n",
      "\n",
      "i = 0\n",
      "while i<100:\n",
      "    array = rk2_step(x,Vx,y,Vy)\n",
      "#        array = rk2_step(k,m,y,dy)\n",
      "    Vx += array[0]\n",
      "    x += array[1]\n",
      "    Vy += array[2]\n",
      "    y += array[3]\n",
      "    #print y,dy\n",
      "    xposn.append(x)\n",
      "    yposn.append(y)\n",
      "    i +=1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#plt.hold(True)\n",
      "#plt.hold()\n",
      "plt.subplot(121)\n",
      "plt.plot(xposn,yposn)\n",
      "plt.subplot(122)\n",
      "plt.plot(xposn1,yposn1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb0f932ec>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0f35d0c>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure()\n",
      "ax1 = fig.add_subplot(111)\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "ax1.plot(xposn,yposn)\n",
      "ax2.plot(xposn1,yposn1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEACAYAAACZLPCyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n0wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0d6f46c>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bz = 1\n",
      "\n",
      "m = 1\n",
      "q = 4\n",
      "\n",
      "x = 0\n",
      "y = 0\n",
      "Vx = 1\n",
      "Vy = 0\n",
      "\n",
      "dt = 0.1\n",
      "\n",
      "xposn1 = []\n",
      "yposn1 = []\n",
      "\n",
      "def force():\n",
      "    return [(q/m)*Vy*Bz,-(q/m)*Vx*Bz]\n",
      "\n",
      "#def euler_step(x,Vx,y,Vy):\n",
      "#    array = force()\n",
      "#    Fx = Vx\n",
      "#    fx = array[0]\n",
      "#    Fy = Vy\n",
      "#    fy = array[1]\n",
      "#    return [fx*dt, Fx*dt, fy*dt, Fy*dt]\n",
      "\n",
      "def rk2_step(k,m,y,dy):\n",
      "    array = force()\n",
      "#    \n",
      "    F1x = Vx\n",
      "    f1x = array[0]\n",
      "    F2x = Vx +f1x*dt\n",
      "    f2x = array[0]\n",
      "#    \n",
      "    F1y = Vy\n",
      "    f1y = array[1]\n",
      "    F2y = Vy +f1y*dt\n",
      "    f2y = array[1]\n",
      "#    \n",
      "    return [(f1x+f2x)*dt/2., (F1x+F2x)*dt/2., (f1y+f2y)*dt/2., (F1y+F2y)*dt/2.] # [dy, y] update\n",
      "#    return [fx*dt, Fx*dt, fy*dt, Fy*dt]\n",
      "\n",
      "i = 0\n",
      "while i<10:\n",
      "    array = rk2_step(x,Vx,y,Vy)\n",
      "#        array = rk2_step(k,m,y,dy)\n",
      "    Vx += array[0]\n",
      "    x += array[1]\n",
      "    Vy += array[2]\n",
      "    y += array[3]\n",
      "    #print y,dy\n",
      "    xposn1.append(x)\n",
      "    yposn1.append(y)\n",
      "    i +=1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}