{
 "metadata": {
  "name": "",
  "signature": "sha256:26664603ec2241f7bf487888c0bb8fff196730959e439a36979f72379d125918"
 },
 "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",
      "    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": [
      "Ex = 0\n",
      "Ey = 5\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 [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",
      "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": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(xposn,yposn)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb1277aac>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb12cbeec>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}