CDPM-2.7.ipynb

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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/envs/py2p7/lib/python2.7/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(self.msg_depr % (key, alt_key))\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, init_printing\n",
    "import sympy\n",
    "import sympy.physics.mechanics as me\n",
    "init_printing(use_latex='mathjax')\n",
    "import seaborn as sns\n",
    "# sns.set_context(\"notebook\", font_scale=1.5, rc={\"lines.linewidth\": 2.5})\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import ode, odeint\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import InputShaping as shaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Create the variables\n",
    "x, y, beta = me.dynamicsymbols('x, y, beta')\n",
    "\n",
    "# Create the velocities\n",
    "x_dot, y_dot, beta_dot = me.dynamicsymbols('x, y, beta', 1)\n",
    "\n",
    "# Create the constants\n",
    "m, k, L, g, H, c, D,t, Izz, k_beta, c_beta = sympy.symbols('m k L g H c D t Izz k_beta c_beta')\n",
    "L_1_init, L_2_init = sympy.symbols('L_1_init L_2_init')\n",
    "# m = mass\n",
    "# k = spring k\n",
    "# L = spring equilibrium length\n",
    "# g = gravity\n",
    "# c = spring c\n",
    "# c_beta = rotational c\n",
    "# k_beta = rotational k\n",
    "# D = rod length\n",
    "# Izz = moment of Inertia about the end of a rod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
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   "source": [
    "# Create the world frame\n",
    "N = me.ReferenceFrame('N')\n",
    "\n",
    "# Create the rod frame\n",
    "B = N.orientnew('B', 'axis', [beta, N.z])\n",
    "\n",
    "# Set the rotation of the rod frame\n",
    "B.set_ang_vel(N, beta_dot * N.z)\n",
    "\n",
    "# Create the Origin\n",
    "O1 = me.Point('O_1')\n",
    "\n",
    "# Set origin velocity to zero\n",
    "O1.set_vel(N, 0 * N.x)\n",
    "\n",
    "# Create the second attachment point\n",
    "O2 = O1.locatenew('O_2', H * N.x)\n",
    "O2.set_vel(N, 0 * N.x)\n",
    "\n",
    "# Locate the point in the N frame\n",
    "# P = me.Point('pen')\n",
    "P = O1.locatenew('P', x * N.x + y * N.y)\n",
    "\n",
    "# P.set_pos(O1, x * N.x + y * N.y)\n",
    "\n",
    "# Set the point's velocity\n",
    "P.set_vel(N, x_dot * N.x + y_dot * N.y)\n",
    "\n",
    "# Create the rod center of mass\n",
    "G = P.locatenew('G', D/2 * B.y)\n",
    "\n",
    "# Set the velocity of G\n",
    "G.v2pt_theory(P, N, B)\n",
    "\n",
    "# Create the rod\n",
    "I_rod = me.inertia(B, 0, 0, Izz)\n",
    "rod = me.RigidBody('rod', G, B, m, (I_rod, G))\n",
    "\n",
    "# Create the distance from the point to each attachment point\n",
    "L1 = O1.pos_from(P).magnitude\n",
    "L2 = O2.pos_from(P).magnitude\n",
    "L1_vector = O1.pos_from(P).normalize\n",
    "L2_vector = O2.pos_from(P).normalize\n",
    "\n",
    "# Create the height from the center of gravity to the datum\n",
    "h = G.pos_from(O1) & N.y\n",
    "\n",
    "# The forces at the connection point\n",
    "forceP = c * (x_dot + y_dot) * L1_vector() + c * (x_dot + y_dot) * L2_vector()\n",
    "\n",
    "# The forces on the beta frame\n",
    "forceB = -c_beta * beta_dot * N.z\n",
    "\n",
    "rod.potential_energy = (-m * g * h + 0.5 * k * (L1() - L_1_init)**2 + 0.5 * k *(L2() - \n",
    "                        L_2_init)**2 + 0.5 * k_beta * beta**2)\n",
    "\n",
    "Lag = me.Lagrangian(N, rod)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# x_eq = ((sympy.diff(sympy.diff(Lag, x_dot), t) + sympy.diff(-0.5 * c * x_dot**2, x_dot) - \n",
    "# sympy.diff(Lag, x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# y_eq = ((sympy.diff(sympy.diff(Lag, y_dot), t) + sympy.diff(0.5 * c * y_dot**2, y_dot) - \n",
    "# sympy.diff(Lag, y)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# beta_eq = (sympy.diff(sympy.diff(Lag, beta_dot), t) + \n",
    "#              sympy.diff(0.5 * c_beta * beta_dot**2, beta_dot) - sympy.diff(Lag, beta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "LM = me.LagrangesMethod(Lag, [x, y, beta], forcelist=[(P, forceP), (B, forceB)], frame=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "EqMotion = LM.form_lagranges_equations()\n",
    "# sympy.simplify(EqMotion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lrhs = LM.rhs()\n",
    "# me.mprint(LM.forcing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "# def Length1(t):\n",
    "#     # This is essentially a step input with a linear rise time\n",
    "#     # set the velocity\n",
    "#     v = 1\n",
    "    \n",
    "#     # set the inital cable lengths\n",
    "#     init_length = 10.0\n",
    "    \n",
    "#     # set begin motion time\n",
    "#     time1 = 2\n",
    "#     time2 = 6\n",
    "#     move = v*t\n",
    "    \n",
    "#     return (((((t>=time1) * (t<=time2)) * (init_length + move)) + (t<time1)*init_length) + \n",
    "#              (t>time2)*(init_length + v*time2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# def Length2(t):\n",
    "#     # This is essentially a step input with a linear rise time\n",
    "#     # set the velocity\n",
    "#     v = 0.5\n",
    "    \n",
    "#     # set the inital cable lengths\n",
    "#     init_length = 15.0\n",
    "    \n",
    "#     # set begin motion time\n",
    "#     time1 = 2\n",
    "#     time2 = 6\n",
    "#     move = v*t\n",
    "    \n",
    "#     return (((((t>=time1) * (t<=time2)) * (init_length - move)) + (t<time1)*init_length) + \n",
    "#              (t>time2)*(init_length - v*time2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def s_curve(CurrTime, Begin, Amp, RiseTime, StartTime):\n",
    "    \"\"\"\n",
    "    This was copied from Dr Vaughan's Input shaping Library\n",
    "    I edited it to allow for a beginning value\n",
    "    \n",
    "    Function to generate an s-curve command\n",
    "    \n",
    "    Arguments:\n",
    "      CurrTime : The current timestep or an array of times\n",
    "      Amp : The magnitude of the s-curve (or final setpoint)\n",
    "      RiseTime : The rise time of the curve\n",
    "      StartTime : The time that the command should StartTime\n",
    "      Begin : The beginnning value\n",
    "      \n",
    "    Returns :\n",
    "      The command at the current timestep or an array representing the command\n",
    "      over the times given (if CurrTime was an array)\n",
    "    \"\"\"\n",
    "\n",
    "    Amp = Amp - Begin\n",
    "    scurve = 2.0 * ((CurrTime - StartTime)/RiseTime)**2 * (CurrTime-StartTime >= 0) * (CurrTime-StartTime < RiseTime/2) \\\n",
    "            +(-2.0 * ((CurrTime - StartTime)/RiseTime)**2 + 4.0 * ((CurrTime - StartTime)/RiseTime) - 1.0) * (CurrTime-StartTime >= RiseTime/2) * (CurrTime-StartTime < RiseTime) \\\n",
    "            + 1.0 * (CurrTime-StartTime >= RiseTime)\n",
    "    \n",
    "    return (Amp * scurve) + Begin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "# Going with 500rpm\n",
    "# example_shaper = shaping.EI(0.329, 0.101)\n",
    "example_shaper = shaping.ZVD(0.32, 0.032272678421545214)\n",
    "# example_shaper = shaping.ZV_EI_2mode(.466053, 0.032272, .466053, 0.032272)\n",
    "# example_shaper = shaping.UMZVD(.46605358040201028, 0.032272678421545214)\n",
    "# example_shaper = shaping.ZVD_2mode(0.40160804, 0.07159188, 0.047746, 0.0)\n",
    "Shaper = example_shaper.shaper\n",
    "\n",
    "# a = shaping.shaped_input(s_curve, t, Shaper, 10.0,13.0,5.0,3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
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   "source": [
    "length_of_rod = 1.0\n",
    "mass = 1.0\n",
    "inertia = length_of_rod * (1.0/3.0) * mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
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   "source": [
    "# Define the states and state vector\n",
    "w1, w2, w3, w4, w5, w6 = sympy.symbols('w1 w2 w3 w4 w5 w6', cls=sympy.Function)\n",
    "w = [w1(t), w2(t), w3(t), w4(t), w5(t), w6(t)]\n",
    "\n",
    "# Set up the state definitions and parameter substitution\n",
    "sub_params = {x : w1(t),\n",
    "              y : w2(t),\n",
    "              beta: w3(t),\n",
    "              x_dot: w4(t),\n",
    "              y_dot: w5(t),\n",
    "              beta_dot: w6(t),\n",
    "              m : mass,\n",
    "              g : 9.81,\n",
    "              k : 10.0,\n",
    "#               L_1_init: shaping.shaped_input(s_curve, t, Shaper, 15.62,25,9.0,3.0),\n",
    "#               L_2_init: shaping.shaped_input(s_curve, t, Shaper, 15.62,20.61,9.0,3.0),\n",
    "              L_1_init:s_curve(t, 15.62, 25.0, 9.0, 3.0),\n",
    "              L_2_init:s_curve(t, 15.62, 20.61, 9.0, 3.0),\n",
    "#               L_1_init: 15,\n",
    "#               L_2_init: 15,\n",
    "              H : 20.0,\n",
    "              c : 1.0,\n",
    "              D : length_of_rod,\n",
    "              Izz: inertia,\n",
    "              k_beta: 1.0,\n",
    "              c_beta: 1.0}\n",
    "\n",
    "# set this parameter to enable array output from sympy.lambdify\n",
    "mat2array = [{'ImmutableMatrix': np.array}, 'numpy']\n",
    "\n",
    "# Create a function from the equations of motion\n",
    "# Here, we substitude the states and parameters as appropriate prior to the lamdification\n",
    "eq_of_motion = sympy.lambdify((t, w), \n",
    "                              lrhs.subs(sub_params), \n",
    "                              modules = mat2array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
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    "scrolled": true
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   "source": [
    "end_time = 60.0\n",
    "\n",
    "x0 = [10, 12, 0.0, 0.0, 0.0, 0.0]\n",
    "\n",
    "# Positive beta is to the left when facing the structure\n",
    "sim_time = np.linspace(0.0, end_time, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
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   "source": [
    "# Set up the initial point for the ode solver\n",
    "r = ode(eq_of_motion).set_initial_value(x0, sim_time[0])\n",
    " \n",
    "# define the sample time\n",
    "dt = sim_time[1] - sim_time[0]   \n",
    "\n",
    "# pre-populate the response array with zeros\n",
    "response = np.zeros((len(sim_time), len(x0)))\n",
    "\n",
    "# Set the initial index to 0\n",
    "index = 0\n",
    "\n",
    "# Now, numerically integrate the ODE while:\n",
    "#   1. the last step was successful\n",
    "#   2. the current time is less than the desired simluation end time\n",
    "while r.successful() and r.t < sim_time[-1]:\n",
    "    response[index, :] = r.y\n",
    "    r.integrate(r.t + dt)\n",
    "    index += 1\n",
    "    \n",
    "np.savetxt(\"response.csv\", response, delimiter=\",\")\n",
    "# np.savetxt(\"response_shaped.csv\", response2, delimiter=\",\")\n",
    "# np.savetxt(\"sim_time.csv\", sim_time, delimiter=\",\")"
   ]
  },
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   "execution_count": 34,
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l2W9iDQCPzF4WczWSJEmbn0KC4v3ApWEYTu20LBOGYTXZ6xMf7NXKesF7p44C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\n9qvaeAzlFM8TwGnA4cD+mXmvfdBZEfEEv3pnFtu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea402d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VhQIc1hRnY1eKlzoTtCWzrGnp5bCmeNG/RQ+n2w+raX8oZWYsxLzqMFVBk76sw7aeNFt7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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4a61d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RiilMioiIiEjFFCZFREREpGIKkyIiIiJSMYVJEREREamYwqSIiIiIVExhUkRE\nREQqpjApIiIiIhVTmBQRERGRiilMiuyG67o4rlvrZoiIiOzXQrVugMj+qD2dx+pJk3VcpsfDHNJS\nRzBg1LpZIiIi+50Rh0nTNE8AHMuyHjRNcw7wA+AA4DeWZX292g2Ufas7U6AjkydrO9QFA0ytC9Mc\nnVjvOXqyBVZ0pUrfb0vlAVjSGq9Vk0RERPZbI+rmNk3zLcC9wJn+TT8AXgVsBy4xTfP86jZP9pWC\n4/JkZ5LHOpNsTuRoTxfYmMjxSEeSJzqTFJyJ0d3ruC7P9qQBqA8FmFUfAbxA2ZMt1LJpIiIi+6WR\njpn8NHAL8H+maU4GXgN81bKsVwOXAB+scvtkHyg4Lo91JOnIeGGpIRxgejxMfch7enRmCjzVncKd\nAOMHt6XypAoOAIe2xlnUEqMh7B2HjQPZfd6eguOSd5x9vl8REZHhGmmYXAL8wLKsPPBa/+f/5N/3\nH2B+Fdsm+4DrujzTk6I/bwOwsDnG8qkNLGmNc9y0Bg5ujgFeoCyGzRez55M5AKbEQjRFghiGwbzG\nKOAdg6y9b4Kd67qs6k1z95Z+7t4ywFPdKewJEOZFRGT8GWmYzAAR/+tTgC7Lslb4388AeqrVMPHk\nHZf2dJ7ebGFMKoMvJPO0p72QuKA5xtzGKIbhTTQxDIMDGiK0RoMAbKhBZW5fGsjZ9Oe8UD27IVK6\nfUpdmKA/96Yjnd8nbVnXn2VTIkfxjG9L5XnO734XERHZn4x0ZsXjwAWmabYBZwA3ApimuQy4CHig\nus2b2HqzBZ7sSpH3xyu2RkMc1hYnVKVZxVnbYU2fF1Cm1IWYWxagigzD4IDGKN3ZFP05m0TepiEc\nrMr+9zdbUl5Vsi5o0Fo26ShoGLTFwrSnveA9uyE6pu1I5u1ScJ8eDxMJGGxK5NiayjMjXqA1NrEm\nRImIyP5tpJXJ84FDgV8D/cCl/u3/AJqAz1WvaRNbznYGBUmA7myBld2pqq19uKYvQ8GFkAGLWupK\nFcmdtUZDRP0A276PKnP7muu6parj9Hhkl2Mxtc4LcD3ZwqBzMhbWD2RxgVjQ4JCWOhY0x2gKF6vD\nmTHd91CytkMib0+IMbMiIjJyIwqTfpf2AuA44CDLstb7d70LONSyLKvK7Zuw1vVnyTsuQQOOm9bA\nAn/sYlemUJXu5kTeZqu/5M2BTTGiwd0/FQzDYEpdGIDO9Itz3GQi75CxvbBU/F3LTY6FMQAXxnRW\nd8522O64K6FAAAAgAElEQVSfl3mNUYIBwxu32eRVQ7uzNkl/fOtYc10XqzfNvVsHeHB7gge2JxjI\n7Zt9i4jI+DHiK+BYljUAPAIcZJrma0zTbAL+a1lWf9VbN0HlbIct/kSQ+Y1RGsJBDmiMlpapWd+f\nHXWgWNfvVbhiQWPQ+MDdKXatDuTtF+UyQR0ZL8BFgwaN4V3/LEIBg0a/Otg7hmFyezqPCwQMr0Ja\nNDkWIuoP3CxOEhpra/oybE7s2Feq4PBYZ3KfTUISEZHxYcRh0jTNs4CNwJPAX4CDgZ+bpnmjaZoa\nzFUFzydzOEDQYND4vAXNMaJBAxd4rjddcbdjf65QmnRzYFOMwG66t8tN8ifhuEBv7sVXnSxWXKfE\nwrvt7i8eg57s2FXntia9UDu1LjxobGzAMEpvJran8mPe5dyf89YZBZhZH+aIyfUEDW9C2HO9mggk\nIiI7jHTR8tOA3+BNxPkgUPxvdzvehJzPVrV1E5DrumxNFv+JRwYFilDAwGypA7xAU+n4xTV9Xjd5\nfSjAjPiuXbrlcgWHZ7YN8NCGHvqTWVzXfdF1dRYct7Q00p4mt7REx7Y6my44pXYMdV6m+t3vOcel\nb4zPwdp+7zkSDwVY1FJHWyzEQv+515EulGa97wt9uQKPdyT5z9Z+nuxK7rNufhERGZ6RVhK/iHfZ\nxHeZphkEfgJgWdZV/iLm7wa+WuU2TigDeYe0P3ZvRnzX7ucpsRBt0RBd2QKr+jK0xcIjmt3dky3Q\nnd1RlRyqCmc7Lvev7+afq9r5z7pukmXBYdakOt5z3FzmN8VG+qvtt8rHQE7aw6UjW6I7ZrH35gpM\nju05iI9Up9/VHjSGbkd9KEA8FCBVcOhI50vhttr6cwW6MsXnSLRUuZ4RD7NxIEuq4LCuP8OyyfVj\nsv9yXZk8T3amKHasZ9IFujMJjprSQFPkxbmqgIjIeDPSbu7iTO6h3AXMHVVrpFRtjO1m7J5hGCxs\niWEAWdsd0WQc13VZ2+eNlWwMB0ozlIuSuQI3PvYCZ173CJ/609P847mOUpAsRs4XetJ88x+ruHtt\n58h/uf1UMUw2hoOE9xDMw4FA6apAY1GZKwa4tlhoyKEHhmEwxa+cjuUC8i/4lfF4KMC0sslIAcNg\nftkC7pnC2I6dzNoOK7vSOHjLNR3UFCUcMLBdWNmVwt7HY3dd1yVjO1o8XkRkJyMtbfQD03Zz3yxg\nYHTNmdhc12W7Hyan1e1+7F69PyFnw0CWjQNZZsTD1O9h7cfedJ5t/RkyjktHziYcDAyqSr7Ql+am\nJ7bwp6e2DapCHj6ziVebUzj5wDYmN0S5Z10337xjNd3JHP/3l2f5wZmHsWxWcxWPQG0UK7Wt0b1X\nuhojQZIFp+ph0nbdUjv2VPGcUhdmYyJHquCQLjjUhUY87HnP7XBctvmzyWfVD7FEUjyM1Zuh4Lps\nTeXGtEK9ts/bT9CAI6c0UBcK0BYL80h7grTtsH4gW7pC01jbnsqzqi9N1nYJGDC7PsLBzcMbbywi\n8mI30jD5V+Arpmk+BKz2b3NN02zFGy95WzUbN9Ek8l5AAO+f9p7Ma4yyNZUja7us6s2wbHJ8l3/8\n96/v5toHNvLM9sEZv6UuzIGtcdrqI2zqTWO1J0r3hYMGr1k0lbcdMYsFUxoG/dxJB06i1z2YH9+1\nhq5Ejgv/8gy/eueRTBnjRbzHUsFxSeS9Yz6cbuOmcJBt5Bmo8ri9vqxNsdDWtodxm02RIEEDbNcL\nwbNCe5+JPxIdmTy261Wipw/xHAwaBtPjYZ5P5tiSzDOv7IpJ1ZTI22wpW7qqGJqbIkHmNkTYmMix\ncSDL7IYIsT0sa1UNLyRzPFt29SHHhU2JHMm8M+TfnYjIRDPSV+H/A/LACrxJOC7wQ7xg2Qp8vqqt\nm2C2l3VxN+3lKjOhgLFj7cns4Otm247Ld+5ayydufWqXIAlepfKxF/q4fVVHKUi2xsN86LgD+NMH\nlnPRKeYuQRK8bt6pDRHe/ZL51IUDdKfyXPT358b1UkHlFcbmYYzBK47Ty9puVZfIKc6Qj4cCe1zz\nM2AYpdDbPQZd3cU1Lltjod22Y6Y/qzxtOwzkx6are6M/fKMuaDBnp6Wr5jfFCBneqgabx/gSn/25\nQukylk3hIEdPqecAvz1d2UJpotK+kLMd1vRleKQ9wWMdCTYnslW7gIGIyGiMqDJpWdZ20zSPAj4J\nvBpYixdIfwJcbllWe/WbODG4rlsaLzl1D13c5abVhXkhmqMna7OqN01rNETQgG/fuYbfr9gKwNIZ\nTbzv2Dn0A4mcTS5XoM6F5/sydCdzTG2McsSsZo6e00JkGF2mDeEgU5tivO+E+fzg7rU89nwfP31w\nI2efMG80v37N9Pkhri4UIDKMClf5pSQHcjbRuupUxYqzs4cTaFujIboyBXr867VXqzJW3tU+dQ9d\n7Y3hAHVBg7TtPWerPREmZzulrvY5DdFdupJDAS9grh/I8nzS62qv1iVGyzmuy9PdaVy8kH/klHpC\nAS/M2663hNeGgSxT60I0RcZ2VbRE3ubxjiTZQVfEsulIF1jaFt/jWF8RkbE24ldAy7J68WZ1f7H6\nzZm4kgWHVLGLe4grsAzFMLylgh7aniBjuzzbk+apjd2lIHn6kulc8MoFrOnLkEnmaIuEWD6tbVTX\n1o77gXPJ7GbOOGwGt6zYys8e2sQRs5o59oBJFW+3VkYS4sALMvWhgDduMm8zeZjnak9c16XPD3HN\nwwglxeuG5xyXVMHZ43jZkejNFvAXEmBy3e7bUbwi0qZEjvZ0noOaqtvVvSWZw8Wb1V6sgu5sTkOE\njQNZbBe2pXJjcr30LckcSf9vcvGkukGBdWFLjO5sgVTBwerNcPSU+jHr7s4UnFKQDBjeWNac7Y2v\n7s4WeLIzyZFT6vfJ+M2c7bA5kaMzk8dxvVUH5jZGiIc0s15kIhtxmDRNMwy8DzgVmOl//VLgEcuy\nHqtu8yaOYvdiNGgMO9iAVyk7uDnG6r4Md63t5Nf3bQDgpANb+ewrF9CezpeumDLPv5rOaBT/aaQK\nDp986UGs3NrP6o4kF9/2HNeetYy5k+pGtf19yXXdUjf3SI55cRJOtdbbTBUcCn6IaxnGJKCGcKA0\nbrI3Z1ctTHakd8xq31NXO3hveDb5E4GqGWhd1y1d5nN6PLLbimMkGGBKXZjt6Txbkvmqh0nbdVnv\nd6FPj4d3GU8bMAwWNsd4oitFX86mM1MY8jKco+W6Lk91p8j6l1Y9cnI9zX5bJiWyPNeboTdns6Yv\nU1oHdKz0ZQus6E6RtXdUR5OFHFuSORa31g26YtNYc13vjZTtesOChtOrICJjZ6SLlrcADwLXAEcC\nxwJx4E3APX4XuIxQ+Szu4XZxl5vbECGbzvPbBzfhAnNb6zj/FQvYmMjytD/eqzkSZH7T6P/h1vvL\nFeUcl2DA4GuvP4T6SJDuVJ6P/n4Fz+40RrNgO/Skcvvl2K6M7ZLzuw1H0lVbvKxif5Um4fT6oTRo\nUFp6aE8Mw6DFr2BW69KOruuW1rmcvIcJQEXNkR3LKHVVcezmQN4pVQP3tqB+8YpA/Xm76gvpb03m\nydouBt5am0OZXBemxX/ebBjIjslViZ5P5krPj8WT4qUgCd7Vseb64zc3JXKlIRtjYSBn+5fS9Kqj\ncxoizG+MEgkYOMBT3Wm2psb+Mp+u67I9lecB/1rxD7cnuHfrAE92Jks9OyKy7420MnkZMBs4ClgJ\nFF893gr8C/gScFq1GjdRDOR3dHFPr6C6saU/ww/uXEPOdmiKhXj7CfN51l9PErzwc3hbvCrdYPGy\nsJMs2BwwKc533riE8/6wku0DWd5/4xO8ZH4r0xqjrO9KsXJrP9mCQ2s8zDknzOP0pTNG3YZqKf7z\nDbAjIA5H+SScnO2MuipSbEdzJDTsNxLN0SBd2UIpaIxWsuCQ8StOw6mwGYZBWzTEtnSerkyBuY3V\nqQxu8wNJXSiw12rxpGiQWNAg43f5NlZp7KbrumxOeFXJqXXhPXbhzm+K8ninV53szdl7XPR+pAqO\nyzp/gs+0ujDThgjXBzfH6Mx43e3P9aQ5dmpD1bvb847DE11JbBciAYMjp9SXejjmNER4ojNFf97m\nme408WBgUOCtJtd1ea43U1oHtXQ73rqr3dsHWNoar8rQk70pOC7PJ7J0ZArkHJdIwKAtFmJ2fURV\nUpmQRvpXfzrwecuyHvevgAOAZVl9pml+A29m9z5lmubHgU/grX/5APBRy7Ksfd2O0Sj9Aw0GSkGl\nPZHlpse3cN/6LjoSORqiIQ6Z1sCrzSm8ZH4bUT/UrelM8qk/PkVHMkc8HOTi1x1CIBIkY7ulMWcH\nVXGCQiRgEDKg4EIy79AcgSNmN3PNWw7nC397luf7MtyztmuXn+tO5fnav1aTzNm886jZVWnLaBW7\nuBsjwREF7fLgOZC3aRttmMyOvKvdq0xmSRccsraz127pvSlWFyOBoRfLH0przAuTPdkCtusSHGWI\nKZ+Etqd1VosMw2Cav+7m9lSuamM3e7J2qTo6t2HPXbet0RAN4QCJvMPziVxVw+SmRJa84xKA0soN\nOwsYBota6nisM8lA3qE9nWdalbubn+3JeBVJYNnk+kFDZSLBAMsmx3mkPUnadniqO83yaQ1VnxDl\nui7P9qbZ4l+7vjUa5KCmGLFQgK5MgdV9GfKOy5NdKQ5ri4/JkIOijnSeZ3rS5MsmQ6Xxxl9vHMiy\nqKWOGbsZ61tNjuvSmSnQmcmTKXgV4+ZIkOnxSNXXnxXZm5G+8jUBG3dzXx+w63oyY8g0zQ8C3wY+\nBzzrf77dNM1FlmWl9mVbKmWXjRErVh5+98QWrrx33aArjPRnC2zpz/Dv1Z3UR4IcPacFw4D/rOum\n4LiEgwbffMNijp07Cdd1sV2v27TaVQrDMIiHgvTn7UHdSounN3LDu4/i9lUdPLChh4FsgdnNMZbM\naGJOSx0/fnAjD23s4ar/rOfE+a0c0BqvarsqUQyTI52NHAoY1AUDpaVx2kaxbnbecUvBZSRhsjkS\nxMCryvTlbKaOclZ58SpAk6LDr44W18N08Lrb20Z5eclEfkd1dOerM+3OtLi35mTa9q6vPpwJTHuz\nxa98NYaDe31uGIbBnIYoz/akaU/nqxLswZvoUlweaXZDhNgewkFrLERbzJvhv7Y/y5S6cNUm43Rl\n8qWAv6AlNuTxiAQDLG2LlxaTX9OXYVGVx04X1zUFb3jDopYdF12YWR+hNRbisQ6vq3tld4qjx+hy\nmxsHsqz2e30CwIz6CPXhAKm8w9ZUDtuFp3vSJAoOB1d5Ylq57kyB53rTu3Ttd/rPgeKi+mOxykE5\n23VpT+XpyhZKayTHQwEmx8JMqRv6Sl5jrZorXMjwjfSV9xngLOD2Ie57DfDcqFs0Ml8AvmNZ1rcB\nTNO8F9gE/C81qJJWYlsqT97xxmZNjYW49PZV/Pnp7QA0xUK8ccl0Fkyupzud5z/ruvnv5l6SOZu7\ny6p/UxsifP1/FrN0RhPg/YMLjeHfUjwc8MPk4C7WWDjIaYdO57RDp+/yM5f9z2Le+stH2T6Q5Xv3\nrOO7py8ZuwYOg+u6pYXHR9LFXdQYCZBOOyRGOW6yv2yc20i6B4MBg8awF+p7s4VhrwAwFMd1S2Gy\ndRjjJYuiwUCpKteVGX2Y7MjsmIQ23HPiLVPkBfvtqfyow2TBcWnPFEPL8MYvT68Ls7o3TcH1gmg1\nrgq0OZErvSGcN4whBAc1xejKJEgVvGWVdjcLfiRc12WNH5yaIkFm72GbTf6Y7HX93nJNM+sjVQtz\nvdkCq3q9dkyJhQYFyaJYMMBRU+p5uD1B1nZZ2ZVk+bTGqoapzYkdQbIpHGRpW3xQBXB+U5Snu1N0\nZ70KpQFVX+kAYNNAllVlw5haIkEaI0EKjlepzDsuzydzdGcLHN4Wr9rkuHKu610pa3VfpjTuvKgv\nZ7M1lScaNDioKcaM+MjnAYzEQM5mSypHtz/cw8XrYWmJBplWF9lnobY4KcybGOYSChg0hIJ7fCP4\nYjLSV95vATeYplkH3IpXGDncNM03AucCZ1e5fbtlmubBeNcC/3PxNsuy+k3TvBs4hXEQJl3XZZNf\nfQi7Lp/4w0qe2upNYDn5wDYuOnUhzWX/oN9x5GzaE1nuWNXJqo4E2YLDUXOaOXXRVOrHeJ27csVx\nkyMZ8B6PBPnYifO56O/Pcd/6blZs6eeIOXu+FGNXxhuPFw8FmFkfqeoLQsZ2S8vgVBImG8JB2tOF\nUU/86PW7uOtDgRGvFdgc9cJk3yjb0J+zS8dipN20bbEwiXy2KpNwirPJp8SG/8/HMAymxcNsGMiy\nPZ1nQfOuQWMktqe9JW8MGHKM4lCCAYMZ9RE2J3I8n8yN+qpAtuuWxgXOGuYYvKZIkCl1ITrSBdb3\nZ5keH311cns6X1qUfjjHdV5jlG2pvL9cUroqyyXZrsszPTvW+jy0dfdXHIoGAxzeVuxyd3muN82S\nKvWA9GQLWH6gnRQNsqytnuBOf6/RYIBlk+t5qjtFe7rAhoEs4YDBAVUaTwzwfCJXCpIN4QCLJ8UH\nhXbb/5+yrj9LquDwSHuCwyfXV3X4Rd5xebo7RWfZ33xbNFQas9yfK9Cdtcna3rlrT+dZPKmu6mNJ\nUwWvCl6snJfLOS7t6QLt6QKxoMFBzTGmVzC5dTjSBYfNiSzt6XypZ6VcfSjAtHh4zMfT5myH7myB\nnqxNpuCQd1yCAe952RwJ0hYNER+DNxZFI120/EbTNKcBXwHejvea+1MgA3zFsqzrqt7C3VuIF2bX\n7HT7euCV+7AdFduU8NaxW7Wtnz88spk+/4/zg8vn8sHjDxjyn8HUhihvO3LWvm7qIOVhciRdCqeY\nU7ju4U2s7Urx28df2GOYXNefKU0+AK+Ce8SU+lGPyysqViUNdsxQH4liAC2+C91buzb3pnlue4Jk\nrkBrPMJhM5toqQuPeJ3Lci2REJvJ+WGw8jGLxSvpxIIGdcGRbaMtGmLjQNabwFNwKn4Xnik4pXMy\nZZhd3EXT6rwwmbVd+nL2sC6LuTtb/RA3uS5EODD832W2HyaztjvqZYK2p/Klas+cESx5dGBjjI60\n19W8PZ1nxijGTjquy9o+7+9vciw0rDASMAwWtsR4wp+QtC2VH/XYwQ1+KAJY0hrfa6WxKRIqLZW2\nLZWnLZYb1XEAyNoOK7u8UVP1oQCHDxEkiwKGwZLWOCu6vLC1ui9DfShQlUlBW5M5nuv1VudoiQQ5\nYvKu7QgaBvObYrREQ6zoSpF3XJ7oTLKsSoEyVXB4sjNZGprTFgthttQNmpgJkMzbrO7L+GM6Czzc\nnuDwtvqqTZLbmsrxXE+69Ca4LugFtqZIkACQsh060wW6swUytnfxgS3RHIdMqqvamqg522Ftf7a0\nLm6RgdejUFzuLVlwWNefZUO/d/nX+U2xql5koC9XYNOAt+bv0OtJ2KWLQDRHgsyqj1TlzebORvTs\nMk2zzbKs75um+VPgBGAy0As8YFlWT1VbtndN/uedrxc4ADQOZwOO4+A4Drb/wu26lE5G6aSULffh\nFj/csseUvnZ3fviObflfOKXHuGzqz3Lvxl4e3dDNMy/0AVAfCXLxKSYvXzB5OM2vmeIfo+NC1nGJ\nDTOAGIbBW4+Yxdf+tZo7VnewrT9Da+uuw2y7MoVSkIwGDbK2W1pLz6zSWnrFimJ9OFDRH1UxTLp4\nL5xDXQHFcV3uXN3JLx7ZzHNl1z8HCBiwZHoT86Y1sHh2C4dUMMasuCali1dd3PmfRTpv05XMeR+p\nHMmcjeO6uK5XTWuIhpjWluaZrX1kXJc5jVH6MgXqwkEiQWNYbxJaojuuFd6VKTCrbMKK67pkCg7p\nvE06b5PJe1+n8l47goZBMGAQNAw6swW2pPJEggbphggdBYeIf1WicDCwxxDREA4QDwVIFbwQVQyT\nrutiO95lL3MFh5ztkC24ZAs2Odv7uw8YBgG/HXnHxepOEQoYzIwG6Urm/P0bhPbShvpwkJZIkN6c\nzQvJ3KAwaTsuedshb7vkHe9zwXEo2C42Lg0Zm8RAGsM1CAbgqZ40GdtlWjyEbTtkcAkHArsNMEWN\nkSCTYyE6MwU29Gd3qcQ4rkvBdik43v7zZV8XbO8VLBQwCAUMtqXzdKRyBA2DWa115AoOoaCx17+V\nybFwqQ1r+jJMrQuX2u26Lo7rHQ/H9fZt++eo/CMQ8M5H1nZ4pitFwPCqe/FQYFhvXuc2ROjKeEHC\n6kkzKRIqvckpPieK+3ZdMAJgpHL0pHLkCy6u65a91rs81Z2mP28TNGBRYz0DmTyGYWAYXnAw8L4G\n/NsMDm6M0p8tkCw4PN6R4OipDd5rhmF4P2N4r5/FY1L8XPz7dPA/+/88ujKF0vXhG8NBDmyIkMrZ\ng/ZLWVvqAgaHtcZ4vDNFtuDy6PYBjphcT0ssXNp/ccx1cf/F/eL6t/ltcP2v+3M2T3WnKPiV+4XN\nMWbUh8FxSedtDK8BGBiEDYPFLTG2pvOs6smQdFwe3j7Akrb4LsvflT8vCo6LbTv+/v3/q26xnd45\nW9OXLS1DFQl4VccZ8TABI1D63VoIMrMuTLLgsLYvQ2e2QHemwIPbEyxojjG7PrLb51Hp/JflAcpu\nc1yXrck8awcypSFq4YDB7PoIU+rCNESCBA0D2x9K1ZHOsyWZw8FgUyLH1lSeg5tjzBxm93+xPezU\npmSuwJqBLJ3pHRViAy8wNvlLtxX8rve+rE3BdenNFujL2azrzzCvMcqM+kjVCjQjfauy0jTNT1qW\n9Vvgn1VpQeWKb4WGCuPDWvDtoC/8vXqtGaVDpjXw9dMWM2eMFx6uhsayhbWzjkP9CN5tvv7QaVx9\n33r60gVuXbmNxfMmEwgMfmFZ3edfCzkSZPn0Btb2elXKzYkcBzRFqzIGKFEoTr4JERxhNQ4g4kIq\n461F2JuNMqksPKTzNn9/ZjvX//cFNnTvmAcWCwVoioXoSuWxHZcVW/tZsbWfPz+xhSUzmjh0RiNT\n6iMYBnQl87QnsrQPZOlO5elJ58jbXgALBQ3qwkHqwkFsIBQ0uDkWJho06M8U6E3n6UnlSY1iPGfQ\ngLpIkPpIiLpwkFg4sCP8+QEwGPD+6XSn86TzfpXahUzBJpWzB00gG4nv7KY94WCAaCgwxGeDZM4m\nkbMp2A4GkMk7ZAs7uu+rIeC3IRQwSiEz7IfdcNAgW3C8NjguAVxyBS/IFt+sjtX+Q0HvfBQcb6mq\ndN7bpwGl0FawnaocCwPv+RbynwchP+QWQ6jreksJpfPOjmBUFuCqIWhAIOAF25D/ORCg9PwM+Mci\nU/COgxeU/LC6/y13KzVSDJ6DQuM+2m/xC4MdoR72fVvK27Pua68f1XZGGibrgI5R7bF6+vzPDXgr\nMxQ1lt233zt8djPvPm4epy+btdfKw/4ktnXACwuR8JDVxT056+i5/PjedfzxqW185nWLaWmpL923\ntT9Dwh+ndewBrUxuiDJpUgNbn9lGOm+zLedwzLQ9j7UcjuQWr6A9vaVuRO1f25Hgin+v5t/PbSdZ\nNlaxrT7CjOYYjgtrOhLkyoLUSxdO4UMnHsjy+a2EggGS2QL3re3kd/99nntWd5ArOKzc2s/Krf3D\na0Qe+ncao7h+Lz8SDQVo9qtEhmFQsB2S2cKg36Gc7UIia5PIVncx8ErZLth+V3qtOC5kCw5ZIMm+\nPy613j94/+jytku+lMr2fTtsF2zbq1tl9/pokaGV9zLu6/0Wv9gf3ttUqw0jDZM/BS4yTfN5y7JW\nVakNlVqNF6oPZHDAnQ8Mq23ffesyspm8V1HxbxsU5/xwVz4axCg+ouxdRem+8rcc7OhKGHyfd1tT\nNMQBrXEa/S65vt7kcJq834gFDTIF6OhL0zrCYXKvW9jGj+9dR/tAljuea2f5rEYcv2qxcrvXHdwS\nDRLM5enu9sZ6zKkPs6rXZl1Xkjmx4KgGMudsp1S1CxZsursTe/kJz81PbOFbd6wZssJS7E4uCgYM\nXrVwCu86ejaLp3ujLvr7dlQpj57eQGz5XE46ZCovdCbpG8iypiPBQLaA40JLXZhpjVGmNkZoq48w\nqS5CJBTAcdxS5Seds9mWzPJ8f5aC7TK3MUJzXZgW/2NyvfezbfUR6iPBXbpUAgGDjak8jz/fR8CF\npW11pHJeN3Qq53VNJ3PFLmqvylfeHVnwrxUdCBhsTeUJBQMc3BKjLR4uVU7rwoGyr4OlKmcoYJS2\n90Iiy4qOFI7jcMy0elw/NHld0161rdhNveNrd8dtBYdgwGCrP2Zoen2E+S11xEJe5bL8IxIMEPG/\nDgYMHMebtNCdzvPf9iSO67K0rY5YIEC+1D3tdQnnil3VZV3WuYLjVQT9NvRkbQYKNnWhAIdNqSca\nCvrd9V5XeThglCqZoYDXlkkt9fT0JunL5HloWwLbcTmwOUprJESh2AZ/H3m/yljeZZ73q58hf5s5\n22FTIkfA7wJsqwsTChilfYaCBuHAjq774u0GkCrYPLR1gLzjMq0uzKyGiHeu/a754nkvlD0HCrZL\nwfXaZfjVQgxY15vBMbzFvA+eFCtVMYsVxGJ1s/y2YADSeYdHtw+Qs10mRUPMb4oO3p/fTe74lcZi\n5XPHZ0oV/BcSOa+LOmCwpC1OfSRYqqIW31iFAgZNTXGSiTSu673sZ/2xgQUXGkIBDm3zJv4M6gIt\n6w7H7wp23GJAcUtVps5UnrX9GVzXG386tzEKhtdGw8AfauENAyp9xhtr92x3qrRY/KFtcaLBwJD7\nLe5r530Xu6gz/qL2Of8KRgua66iPeEN8iv+nAqUu+GK7vDU1N/T7XcpBg0WT6ogFA0Psc+j97mij\nt1LC+r5MaeWI+lCA+U2x0t9iQ0OMZNKbXFQcPmC7LpsHsnRlC173ecDgoOYoTdHQLr8rQ+y3+Kn8\nvHVn8mwayJVex5siQeY0Rksz80vDF/zz3Ze1eSGRI+NX+yNBgwOaorRGQzsNext6vzu+3vHa25+z\n2ZgzCTkAACAASURBVNyfJeX3pID3P68lGvKuLub3lhUcSORturMF+rN26fcMBwxm1keYGg+XskV5\nSC3/vvzKXOXHKWs7bE/m6cx4kw5Ha6Rhcrn/8axpmhlg5wTkWpY1bfTN2jvLslaZpvkC8AbgIQDT\nNJvxrhN+4XC2cfrhs+juTvjvcmujlvsejbpggF68sDHS32FWUx1Hz2nh0c293PDwJo5542Js23vB\nK84KnlMfHbTdmfEIa/sy2C68MJAb1RVX+jI7qinxYGBY7f/ZQ5u45v4NgLcU03uPncusSXWsG8iR\nyOSZEQ3SkchhGAazW2IcNbuFNn/ywe6235MtEA4GeMWCyRxY4XIyibzNg34AP25aw26vve44MNR7\n0I5EjmjYG5Q9u7nyIRb3bR0gbTvMb4xy0G4W2N65PQYQMgz6cw51kSCt0QgzGytvw9q+DOsHskQD\nBifOaBzexDD/cD2fzNNUF6Y+FGBha+WzkJN5mwf887FkGItnB4MGrY1Rgvk87ZkCbQ1RogGDY2c0\njmqA/KPtCXpz9v9v787D47rq+4+/7+zaZUnet9iOc0ISJ4UEAoSlKWsIEGgotJS9LCUQKFAaCGvh\nVxq2sJSEsrSUtrQUKIS1bCFLgUCAJiQx5jiJ7Th2LNuyLGuf9f7+OHfGY1nLzJ0ZjWR9Xs/jJ/ad\nkXRyrzTz0bnnfL90JqI8sopd1b8/OkFvR4qYBxet7qhqE9JU+4Le4QBnL2+raGOU77vC432dLcQ8\nj8esaq+pbme24POLgyOk8z6t8QgXrGg/6bxGox49Pe0MDkbJB+tIf3VolL7OFuIRjwtXtNdc3uW0\nY5PsCSp39HUm5/x5P5bOccfAGKu6W0lEPC5Y0VbzxpHz1uT5zeExMgWfArB2WUupJelUBd9n59Ak\nuazPuh5XmP/hfW0111C90Pe5fzhdOhd5D1Z0JDmtK8WKvo7S+3He93loLMPu4TQdHSk6Otwu+nN6\nWutWx/X3QxMcCtYb5oBY0u14TsUi7s5MNs/B8SykIqwNqqqsaY2ztbulLhtofN/nobEsu4YnSZel\nuUkozbj7EYjGoixvSbAcFyI3tidZ356o253MdL7AvrHaW6FWGybv4+Td0830IeBaY8wYcBeuaPkQ\n8G9NHdUSEKY8ULk/Pnc1v35wiFvvPcy+oQlWd6ToD0o8xDzvpB29sYjHipY4B8az9E9kawqTxV3D\nqWCGZi7fvOdAKUheuKGbv3/mWbQnY4xk8oxFRlnZleKxq9qrerHPFo630Ayzk7uoLRYpdSQaSudn\nDJPTyRV8BoIXkZ4ad3r2pmLsG8twJJ1jSxUfVyjvCV7jjteVrXF2j6RJF6rb1Z33fQ4GC/pXt868\nML8Ss23EmU0mXyiVA1rXXnsZrE2dKe4YGGM4k2cwnS8VmJ/NWDZfGsNpnamagiS4YuL7xjKMZl2p\noEdOE+Sm6h/PlkrOnNGdqjk4xCMeZy1r5Y6gQ9C9c2zi832f7UfHS7uVz+lprUudwC2dScayeQ4H\nmwsL/sw1KAcnc/w2aF8ZD9pX1mMHcls8yvnL27hzYJyJfIEdRyc4MpllS2eqtA7d9/1SR6HiOehJ\nRtnW21aXAOV5Hqd3pehKRNlxdIJMwYXL3SNpVgxNEgk2zA2lc6X1rR6ubeiG9tp+NsslohG29bRy\ncMLVykznfY6m8xydYVlPT9JVCahnIXzP81jbnmB1W5z+8Sz9466bWGnWufg83HvEmrYEK8s2tNVL\nMhrhjDo0Gai2NNDLa/6KdWSt/QdjTCvweqAL107xqdbaxXXPeBEqvrhNVFkeqOiJW3rpaY0zOJ7l\nG3cd4IqLNpXe0Fe0Tl9kdlWrC5PDGVcwPewL7GgVxcp/uusI1/z4XgDOX9fFRy87h0Tw5tIWj5QW\nT49kClWN51jZi1YthbY9z6Mr6bqfHMvkWEflZVCKL1zgfuuvRU8QJoczebKFQsVB5GjZm8aKGoue\nt8ejtMUijE3Z1T2XwxPZUhmPVW21l3BZ255gaHCCgclcxeWSHhzNBLdnXZisVU/S7egczuTZPTxJ\nb2rudcE7j03i4yoorK/DGCKexxldx1s97h5OzzprPRnUpwT3y8nqCut8zqU3FWNDe4K9oxkeHM3Q\nEo1M+8uo7/vYoclSvdOtXamKQnglPM/dZr87KBm0ZyTNWDaPCZZjgPvlbs/I8Vm7ZBAk61l0vC0e\n5VEr27j7yASD6VxQi3G0VOd2PFc4oQj5xvYEW7pSdS8js7wlTlciyq7hNPvH3Pd+/8jJK2BXtcbZ\n0plqSHtIz/NY1ZpgRUucgckchybce0smXyDiebTEIixLuu/DRhR+L4p47pb1mrYEuYLPeC7PZD64\npR7xaI9HF8V+impLA22Y5eECMGqtHaptSNWx1n4Q+OB8fk05PjNZANJ5n1SVLXfi0QiXbVvFF375\nIN+6p58/v2BdqUDyqpbp38iWJWMkIp4rSDue5bTOcD/gpc43c/yWece+Y7z9uzvI+3B6XxsfetbZ\npSAJ7kWgPR5hJOs64ayk8je/Yn3JttjsJWcq0Z2IcmQyVyqAXqlifcmOeKTmYro9yVgpWA9O5iru\nD128zdQRr0+niJWtcXYNpzk4nuWMCguYF9v09aZipOpwC21FS5ydEVc2ZP9YZs7b/rmCKxUGbjav\n1hlBcG+UmzuS3HlknKFMnsHJ3KzdjQYmsqUlJlu7UnUrF9KTirEumKHcM5KmLxWbttNTwfe5Kyg7\nE/PgYcta6lpg+vSuFKNZV9R5Z9DHe1NnshSSsvkCdw2Ml+rxrW2Lz9mXvVpRz+Pc3la2D05wcCLL\n4ckcA/0jrjai514TijmuLRbhvL7WutVELBePRHh4XysPjQe3WPPHW7oWdSeibO1KVdWVq1qJaIQz\nl7WwpSvJwGSOdCTC6HiGiOdeD1a0xOtyS3suEc/d9aqli1i9xCIenYlYqe7hYlLtd8oe5tj8Y4wZ\nAD5mrb0m7KBk4SsvUjseslj1c7et5l9uf5DB8Sz/fXc/G1Z1EvO8Uv3EqSKeR18qxkPj7oX4tBA/\ncQXfZywIrbPdEt7eP8ybv3kP6VyBVR1JPvacc+iY5s24PR5lJHu84HalSsXKa5wRBIIZuDQT+UJV\nvaGLYbKnxhlBcC+CXcHt3SMVhknf9zkcLG2otBf3XFa0uDCZKbjapHMVap7IuYABbl1uPUQ9j9Wt\ncfaWdcSZbWZh96Bbx+YBG6ooUj6X3lSMzqDlph2a4MKV099mzhd8bNBVpTsRZWWd31S3dqUYTLtW\nd789Mn7S+r+C73PP4DjDwc/EWT2tdQn15SJBkLtzYIyhTJ7dI65jyYqWOL4H/fuHS5UCVrfGObO7\nvmG2fBzn9LTQMxbjvmEXass7WEWA9e0JNnemGjob5Xkea9sSrG6NczSdK3XBSkQ9epKxqpbL1Coe\nibCuIxmsW23uHgYJr9qf2JcAGeBG4BXAM4CXAd/Fhcz3A18C3mOMeVX9hikLTTTikQxe7Kb26K7U\n2u4WnrltDQD/9Zt9ZPMFelOz91Etrqs7FtyOqNZotlD6bWi629y5fIGv3Lmfv/zKXYxl8vS0xvnU\n5eeycoY1msXPUU2Y9H2fY0FP7lp7SYPrE1w8Y5W2VswWCqU373rdyit+noHJ3Ak7CGdyLJMv3VKr\npWNMueKtboD+8bkXlReLH8cjJ6/TrcWG9iQelGYnZ5Iv+Gzvd2WqVrbG63o7z/M8zDI3K1rswjGd\nnccmmQiC1BkNCFHRiAtyMc+1ufvVoTHXrcP3Gc3muWNgrDRDvakj2bAZoljE4+F9bawJljKM5Qrs\nHnGdSSZzhdLavLPqPCs6VXGt3ONWd3BOTwsb2xNsaE/wsO4WLlrdwdbulnm7rRnxPHpTcTZ1poJ1\nicl5DZJy6qj21fP5wNestS+ecvzfjDGfAc611v6xMeYocAXwuXoMUhamlliEdCYfehMOwF89eSvf\nu/shjo5nuWnHQf7q8ZtnfX757dQj6VzVrdKK6yWjHqXOPaPpHLftGeSnuwf5xZ6jHA1my1Z1JLn2\nOeewYZbFycVb5emgdEwlt4tHs8cLSHfXYUF3NOLREcxADaVzFb0ZFxeae8CyVKwuxcaWt8S5P5gV\nrGQDTHFWsjUWKQXAeljTlii109va5c+4jKBQ1gO73u3FUrEIq1vjPDSeZc9ImjVtiWnHsXckXeoe\nsrmzfrOSRV2JGOvbXavHPSNpOuLRE3qOPziaLp2DzZ3Jum4wKNcej3JeXxu/HRgjW/C568j4Sc/Z\n2J5oyDkoFw025KxpzfFQsDnI82B1dwsr4h4Jr/G3VUtjCdbsrapP+3CRpqo2TD4JeO4Mj30N+Ebw\n91uBq8IOShaH1niEoRrD5Oa+dp61bTU33HWAW3Yc4tKtfazZMnM7yVjEY1kyxmA6x8BE9WGyOIPY\nHotw+94hvr29n1vuO0K6bJbTA5525gre/Idb6J4jmJX/Fj+aLdBTQZgszkrGPO+knrZhdSddmCzW\ncJtL8RZ3bxBy6nFrqS0WoSUWYSJX4PAcG2B83+dQECaXt1TWVqxSq1vj3BeUkeofz7BuhlvHhyZc\nByNwvbXrbVNniv6gz/au4UnOmLKLeCJo9QZu000j1seBu818LJ1nOJvn7sFxJnJuY8lD425DCrgN\nO6fVUCGhEsuSMR61op0dQxMn7JpNRjzO6G45IeQ2WncyVvr+PF4aSLdYRcKqNkwOA4bpWymeCRR/\n3WzBlUuSU5h788vWFCYBLvuDtdy25ygHhyd5+3d28OrHbOSyc1axbIag2JdyYfLIZJaC71c1ozSS\nybGzf5hbdxxi18DxTf/RiMfD13Zx0aYenrClt+K2lvGI5wq4510f1tk2ORQNla2XrFeI6knG2Dua\nYSRbqGiGtLhOcGUd1+h5nseKVIwHRjMcnsxx+iy7/I9l8kwEb9yr6nxbMxGNsKIlzsGJLHtHM6yd\npg+v7/vsHXFBqi8Va8huzZZYhI0dSXaPpNk7mqEvFS99f+R9n+1BQepkzBV7b5SI53FenyuPM5ot\ncN/wJPeVNVvqSkQ5t7et7jt2p9Maj3L+8nbGsnkmcoXSWttG3lYWkcarNkx+Ffh/xphB3O3utDGm\nBbgct17yy8G/Xw3cUd+hykJTnFWbyBWqDnXlhrN5XvK4Tfz7z3Zz4Ngk1/9sD9f/bA+rOpJs6m3l\nsaf18IyHrSxtgOlribHzmKuteKyCTRZFR8bSXHfzLrbvP95t8+xVHTzzrJU8xSynM+RGlI54lMl8\nruJ1k0NBkFtWx1uK3WW3/4+m86xsnTlMjueO17hc1ZGCbLZu41jREueB0QzjuQLD2fyMa0IPBLtm\n22IR2uP1v7W4sSPJwQn3i87BiSyrpvxicmgix3Bwveq56WWq0zqSHJ7MMpotcPfgONt6WmmPR/jd\n0YnSLxWPXN9NolBo6KxYMhrhguXt7ByaoH88SwG31GNDe/KEXc3zpS0ebWi5FRGZX9WGyauArbii\n4P9qjBnF9cb2gO8Df4PrSPN04Gl1HKcsQMUw6QOTeZ/WKssDgVuvOJYrsKwtwScv38aXf72Pb23v\nJ5v36R9J0z+S5rY9R/nC7Xt5x5PP4PFbemmNRWmNRRgPOuZUEiZvuX+Av/vRvQwFt1bPWtXBFRed\nxiPXd9c8K9KRiHJ4MldajzmbyVyBySA0VFoHsRLlu6kH07lZbxkWi4THIh597QmGjtYvTHYmjl+b\nA2PZacNkvlBeJLy+t7jLx9GXijEwmeP+Y2mWp44X+80XfO4fdjdOepKximaTwypuPrn9oFsr+H8D\nJ5bAPb0rxfru1opbetYiFvE4q6cVs8wnk/dJRr15D5Eicmqqtmj5BHCJMeaJwJOBPmA/cLO19qcA\nxpjbgDOstfvqPVhZWMp3nk7k8qHW/x0I3tSjHqzvTHHVk7Zy5eM3s71/mF1HxtneP8JN9w4wOJ7l\nLd/azlV/dDqXn7eG3lSM8dGMW/vXNfPnH03nuPbm+/nO7w4CkIhFuPS8Nbz1cacRq0M9Pzi+bnIs\nO/cM7dFgvWQE6r7ZoScVC0rzZPH9mWssDgQ7Z/vm2DkfhheUxbl/OE3/eIat3SfXLDww7oqEe7g+\n2o2ypTPFkclRJvKu88mZy1pcYepjE6WZ2dMraP1Yq9ZYlAtWtHHP4DijQVmqiOfGt6mrsesUpxP1\nPFpC/OInIjKTUL+SW2tvMcbcAawBduNaWxYf21unsckCF/U8klGPdN5nPFegN8TnKIbJnrJg05qI\n8sgNy3jkhmUA7HvMBFd/dwe/PzTKB39yHwUfLjbLeXA0w3A2P+MawV8/OMT7fmBLnRXOXNnOMx+x\njnXdLXULknC8PJCP2y3eOUu5n2JhcVeouL5v6H2pGLuG00zmfUazhWmLsucKfmmTTr3K8Uy1ujXB\nruE0OR8eGsuwvuw2su/7PDjqrseKlnjd6wmW60i4TSW7R9LsG8uQ9318KBWmbuTu5ana41EuXNHO\nSLZAruDTmYgSi3haKygip4SqX8mNMRcZY34ODAL3AGcD/26MUZHyJaiWHt0F3+dgECz6ZlmvuK67\nheufdy5/sNZVKf/wTfdxkz1cqq14ZMoO5tF0jg/eeC9XfO0u+kfSxKMeVz5+E295iqGnPVlRG8Vq\npKIeieAW6lxdaErrJRvQWaIjHiUZlDsq7pSe6tBEFh83K1jPuorlUrFI6Tb7npE0hbKak/3j2VK3\njQ0djZuVLNrUmSzVvzwQ9L8FWJ6KsanBu5en8jyPzkSUnlSs5q5HIiILSVVh0hhzEa5geQr4AJTe\nz+8H3mqMuaK+w5OFrljOJEyYPDqZIxcUre6dI1y1J2N8/DnbOG/N8UB59wNHAUpt4PIFn+/vOMif\n/uuv+e+7DgCwdXkbX3zhI3jxBesZyxc739R3Nswr69ozlJm5NE8mXygFqZm6/NQ6jmKNycOT04fJ\nYpjqS8WIN3BWsBjU0nmfB4KZ4WzB596gFE5fKlaXgu1ziXge5/W2cnpXio54hI54hK1dKbb1tmpW\nUESkTqp9Nf8AcBOu800UeCeAtfadxphO4DXA9XUdoSxotcxMDgQhsD0eqagdY2siysefew5v+Po9\n3H1gmP+4fS9n7T/GOWs6uT0e4fu/P8SewQnAtQX7i0dv5MXnryMWjZAv+KUx1ntmEqA7EePQhOuP\n7c9QEqd4e9mjPp1vprM8FefBUVeMeTiTP+E2bjp/vHXg1N3N9dYWj7K2LcH+sQz3D6ddkfnJHJmC\nTwROqrnYSBHP47SOZMPrKIqILFXVTk1cAFxvrfU5uWfGN4AtdRmVLBrFMDkZlAeqxuHiLFkVa/fa\nEjE+8dxzOH+923Xzu/3H+MqvHuQff/5AKUg+YXMvX3rR+bz8URuIBbNvo2UtH6dbS1ir4s7sTMEv\ntaabqhieu5PRht3mXJaMlq7JvtET2+ftDQpUxzxXXqnRtnalSrPAu4bTpVaPZllL3Yq1i4hI81X7\njpLG3eKeTk/wuCwh5eWBJnKFimvHjefypVu+1W4EaU/GuO7yc/n2Pf38528f4sDQJJ2pGI/ZuIzn\nbFvNWas6TvqYkSDIxCPH1zfWU0c8QtSDvO8KgrdOOQ++75dux/eGrGdZCc/zWNeWYGfQTvD0Lrc5\nKVvwS+FyXXvypB3WjRCLeDyir417j00yMJkjEfHY3Jma104nIiLSeNWGyZ8A7zbG3AQcDY75xpg4\n8EbglnoOTha+lliECFDAtSqsNEwWy9PEo269oV/lXfKI53HZttVsXdvFQ+NZuhNRLljRPuPzi7Ni\njeq24XkePakYhydyDEzmTmrhN5ItkAnWh/Y1sK4huN7U9w+7doL3Hpvk7J5W7g/aC0Y82NDe+I0v\nRYlohLN71HxYRORUVu29prfhygHtBG7ATUi9G7er+zyCNZSydEQ8r1RnsTj7V4niLd/VHamaSuQU\nZ/mOZfKlzTzTGc4cL8nTKMuDsQxO5shPGUuxSHcq6tHW4Fu8sWAGENwO5tsPjrJvzH39je3JOVst\nioiIVKOqdxVr7X3A+cC3gv/mgYuAO4FHW2t/V/cRyoJXXIM4kq1serG81uHarto2YhS7l/gc7zc9\n3dcr3lJvZJgszjgWOLFcUcH3S+0DV7We3Ce6ETa0J0rjKbYN7EnG2NSpTSgiIlJfVd1vM8ZswIXH\ne4I/+4D/tdbub8DYZJHoCDZZjGRn3slc7shkrrR7a3VnkrHhidBfOx60ETwWdH5ZMc36y+GyGdOu\nBobJRDRCd9DSsH88UxrLYDpXusW9ep7WC3qea+O3byzDcNrt6l7XnlD7PBERqbuKwqQxZj3waeAS\njteWBDch5Btjvg68wVrbX/8hykJXLLWTLfikCz6p6OyBpVhQe1kySjIWZWzWZ8+tLxXjWCbP4Ykc\nZ3afHGaPBbUfW6IR4nXsfDOd1W0JhjITHJ7IMZEr0BKLsHfE3WLuSkQrXlNaDxHPY0N7EmZeSioi\nIlKzOd9ZjTErgdtwM5IfAZ6E63pzNvB04GPAU4CfGmOWNW6oslC1x6Ol3zCG51g3mS/4pYLa9erL\nXJwBzBR8hqb5+oOlrjOND3KrWuIkIh4+sHNogv7xTOnrb1SdQxEROQVVMjP5DiAOXGCtvX/KYzuA\nHxljrgN+BrwVuLq+Q5SFLhrx6IhHGc7mOZrOTXuruejwZJbi3pR6lYhpi0dpi0UYyxU4NJE9oVVh\nvuCXWhz2NHgXNbhzsbkzxe+HJjg8meNwsbZkIsryefj6IiIi862Se36XAB+cJkiWWGv3AJ8Anl2n\ncckisywISkdn2ARTdGDMzUr2JGMk67iruBhgD41nTyiePpQ5vj6zpwH9sKezti3O2rJZ17ZYRO37\nRETklFXJu/la3G7tufwfsKm24chi1RPcQh7NFsjkp9/VPZ4rlHY5r63TLe6iVcEsZ7rgMzh5PNAe\nKWvZOF8lcTzP42HLWnjUinYe3tfKhSvb6xqcRUREFpJK3uFSUNEeiVFm7o4jp7juRKy0bnKm2cn9\nQQeWRMRjeZ3b+bXFo3QHO7X3BzUVfd/nYLDZp5FdZ2bSmYjSm4prB7WIiJzSKp0uqaTpcnWNmeWU\nEg1K9AAcmjg5TGbyhVLh7LVtjSlRsyaY7RyYzDGezTOYzpHOz29JHhERkaWmnmFSlrjihprDk9mT\nutE8MJIm70PUg/UNaue3sjVOMup2Um8/OsHOoUnAleRpn8eSPCIiIktJpfcaf2CMmX1nRfV9vuUU\ns7Ilzr1DkxR82DeW4bSgFM5wJs/eUTcrub6B7fyinsfWrhT3DE6UenEDbOnU6gsREZFGqSQAfrHh\no5BTQiIaYXVbgv1jGfYMT7KqJU7Eg3sGx/GBlqhXCpiNsrIlzlhHgT0jbn3m6V2peSkJJCIislTN\n+S5rrX35fAxETg2bO5P0j2fI+fDLQ6OA64zjAWf3tBKLNHYziud5bOlKsaEjiQcN/3oiIiJLneqV\nSF0loxHO7W0l4rkQmS34RDw4p6eF7nmq8wiuZ7eCpIiISOPp/p/UXW8qzqNXtnNwPIuHx8rWOC0x\n/d4iIiJyKlKYlIZojUXZ1Kkd1CIiIqc6TReJiIiISGgKkyIiIiISmsKkiIiIiISmMCkiIiIioSlM\nioiIiEhoCpMiIiIiEprCpIiIiIiEpjApIiIiIqEpTIqIiIhIaAqTIiIiIhKawqSIiIiIhKYwKSIi\nIiKhKUyKiIiISGgKkyIiIiISmsKkiIiIiISmMCkiIiIioSlMioiIiEhoCpMiIiIiEprCpIiIiIiE\npjApIiIiIqEpTIqIiIhIaAqTIiIiIhJarNkDCMsY4wEjQOuUh75srX1hE4YkIiIisuQs2jAJbMYF\nyecB+8qODzRnOCIiIiJLz2IOk+cCaeAGa22h2YMRERERWYoW85rJbcAOBUkRERGR5lnMM5PbAIwx\nNwKPAY4CH7fWfripoxIRERFZQhZkmDTGxIAtszxlL+429yrgzcDfAk8HPmCMGbPWXt/4UYqIiIjI\nggyTwFpgB+DP8PjFwMuAY9ba3wXHbjXGdALvASoOk5GIV8MwpRbFc69r0Bw6/82na9B8ugbNp2vQ\nXPU4757vz5TXFh9jzLOBbwBrrLUHK/iQU+d/XkRERCScmhLlQp2ZnJUxpgP4E+BGa+0DZQ+lgv+O\nVvq5hobGKBSUKZshEvHo7m7TNWgSnf/m0zVoPl2D5tM1aK7i+a/FogyTQAa4Dvg48Pay45cDv7XW\njlX6iQoFn3xe37zNpGvQXDr/zadr0Hy6Bs2na7B4Lcowaa1NG2M+DrzJGDME/AYXJP8YeGZTByci\nIiKyhCzKMBl4B64c0Ctxm24s8Dxr7Q+aOioRERGRJWTRhsmgWPmHgj8iIiIi0gSLuQOOiIiIiDSZ\nwqSIiIiIhKYwKSIiIiKhKUyKiIiISGgKkyIiIiISmsKkiIiIiISmMCkiIiIioSlMioiIiEhoCpMi\nIiIiEprCpIiIiIiEpjApIiIiIqEpTIqIiIhIaAqTIiIiIhKawqSIiIiIhKYwKSIiIiKhKUyKiIiI\nSGgKkyIiIiISmsKkiIiIiISmMCkiIiIioSlMioiIiEhoCpMiIiIiEprCpIiIiIiEpjApIiIiIqEp\nTIqIiIhIaAqTIiIiIhKawqSIiIiIhKYwKSIiIiKhKUyKiIiISGgKkyIiIiISmsKkiIiIiISmMCki\nIiIioSlMioiIiEhoCpMiIiIiEprCpIiIiIiEpjApIiIiIqEpTIqIiIhIaAqTIiIiIhKawqSIiIiI\nhKYwKSIiIiKhKUyKiIiISGgKkyIiIiISmsKkiIiIiISmMCkiIiIioSlMioiIiEhoCpMiIiIiEprC\npIiIiIiEpjApIiIiIqEpTIqIiIhIaAqTIiIiIhKawqSIiIiIhKYwKSIiIiKhKUyKiIiISGgKkyIi\nIiISWqzZA5iLMeZ84BdAm7U2U3bcA94PvAzoAn4IvN5ae6AZ4xQRERFZihb0zKQx5nTgBqYfM8RG\n+gAAD5NJREFU5/uBNwDvBV4CnAV8e94GJyIiIiILN0waY14E/BJomeaxDuCNwN9Yaz9vrf0GcCnw\nB8aYS+Z3pCIiIiJL14IMk8aYjcDngOuAt03zlAuBVspmIq21u4DtwFPnY4wiIiIiskDDJDAAbLXW\nvhvITvP4GUDaWrt/yvHdwOmNHpyIiIiIOPO+AccYEwO2zPKUvdbaMWBslud0AqPTHB8B1tcwPBER\nERGpQjN2c68FdgD+DI9fDNw6x+eIzPLxMx2f/hNFvGqeLnVUPPe6Bs2h8998ugbNp2vQfLoGzVWP\n8z7vYdJa+wC1314/BrRPc7wjeKxi3d1tNQ5FaqVr0Fw6/82na9B8ugbNp2uweC34OpMzuBdIGWNW\nWmsPlh3fBPygmk80NDRGoVDVZKbUSSTi0d3dpmvQJDr/zadr0Hy6Bs2na9BcxfNfi8UaJn8OZIBn\n43Z9Y4zZApwNXFXNJyoUfPJ5ffM2k65Bc+n8N5+uQfPpGjSfrsHitSjDpLV21BhzPfAxY0wcOAB8\nALjDWvv95o5OREREZOlYlGEycBVQAN4DJIAfA1c2dUQiIiIiS8yCD5PW2i8CX5zmeA54a/BHRERE\nRJpgoRYtFxEREZFFQGFSREREREJTmBQRERGR0BQmRURERCQ0hUkRERERCU1hUkRERERCU5gUERER\nkdAUJkVEREQkNIVJEREREQlNYVJEREREQlOYFBEREZHQFCZFREREJDSFSREREREJTWFSREREREJT\nmBQRERGR0BQmRURERCQ0hUkRERERCU1hUkRERERCU5gUERERkdAUJkVEREQkNIVJEREREQlNYVJE\nREREQlOYFBEREZHQFCZFREREJDSFSREREREJTWFSREREREJTmBQRERGR0BQmRURERCQ0hUkRERER\nCU1hUkRERERCU5gUERERkdAUJkVEREQkNIVJEREREQlNYVJEREREQlOYFBEREZHQFCZFREREJDSF\nSREREREJTWFSREREREJTmBQRERGR0BQmRURERCQ0hUkRERERCU1hUkRERERCU5gUERERkdAUJkVE\nREQkNIVJEREREQlNYVJEREREQlOYFBEREZHQFCZFREREJDSFSREREREJTWFSREREREJTmBQRERGR\n0BQmRURERCQ0hUkRERERCU1hUkRERERCizV7AHMxxpwP/AJos9Zmyo4/Kjhezgdea6397DwOUURE\nRGTJWtBh0hhzOnAD08+gbgMOA88EvLLju+ZhaCIiIiLCAg6TxpgXAZ/AzTZO51zgLmvtr+ZvVCIi\nIiJSbkGumTTGbAQ+B1wHvG2Gp20D7p63QYmIiIjISRbqzOQAsNVau88Y89IZnrMNGDPG3A0YYCfw\nVmvt/8zXIEVERESWunkPk8aYGLBllqfstdaOAWOzfI7VQG/wed4GTACvAb5pjLnAWntXHYcsIiIi\nIjNoxszkWmAHM6+FvBi4dY7PMQQ8DbjTWnsYwBjzY+BO4J3A8ysdTCTizf0kaYjiudc1aA6d/+bT\nNWg+XYPm0zVornqcd8/3Z8p0C0Nwm/ufgZby0kAzPPda4BJr7cPmZXAiIiIiS9xCXTM5q6Bk0JOB\nz1lr82UPpYDR5oxKREREZOlZkLu5K7AWuB4XKAEwxqSAS5j7FrmIiIiI1MminJkE/hf4GfB5Y8zb\ncWso3wJ0AB9u5sBERERElpJFOTNprS0Azwa+B1wDfBlIA0+w1vY3c2wiIiIiS8mC34AjIiIiIgvX\nopyZFBEREZGFQWFSREREREJTmBQRERGR0Bbrbu6aGGPeAPwVsBK4DXidtdY2d1RLgzHmOcCnrbWr\ny461ANcClwNx4OvAm6y1w80Z5anFGBPHtR19MbAGuBf4gLX2q8HjOv8NZoxJAO8HXgh0ATcDb7TW\n7g4e1zWYJ8aYblwXtk9ba98XHNP5bzBjzApg6gZZH/igtfZqXYP5YYx5FvA+wAAPAh+21n4+eCz0\nNVhyM5PGmFcCH8HVqXw+0AL8yBjT2tSBLQHGmAuBf+HkVpqfAy4DrgSuAJ4RPE/q4xrgr4FP4aog\n3Az8V/CiAjr/8+ETwCtw7V6fB/QAPwnq44KuwXz6KLBiyjGd/8bbBhSAxwOPDv48BrgueFzXoMGM\nMU8GvoErr3gp8DXgs8aYy4KnhL4GS243tzFmD/Bla+3bgn93AnuBt1trP93EoZ2yjDFR3DfnB4Bx\nIGOtXRM8tgXYCVxqrf1+cOyJwE3A2dbaHc0Z9akhmJUcBq6y1n6y7Ph3cL9IvRqd/4YyxnQBB4HX\nWmu/EBxbDzwAPBe4B12DeWGMuRg32xIBPmqtfV/QUc2i899Qxpg3AVdYa7dO85jeB+aBMeYXwP3W\n2j8vO/ZfwGHgY9RwDZbUzGTworEB+HbxWDB9ewvw1GaNawl4HPAe4Crc7Fi5i3E1Qn9UPGCtvQU4\nhq5JPXQBn8fVZC1ngdPQ+Z8Po7hZmK+WHcsG/02iazAvjDFJ4DO4JR/jZQ/p/M+PbcDdMzyma9Bg\nwTKDRwGfLT9urX2Btfb11HgNltqayTNwt1jvm3J8N/Ck+R/OkrEd2GytPWqMec+Ux84AHpjSYx3c\nrM3p8zK6U5i1dgA3K1xijPGApwO/R+e/4YJzeyeAMSaCO+fXAvuA/wHeha7BfHgvcNBa+xljzHvL\njm9F538+bANGjTG/BM4D9gN/a639V/Q6NB/OxuWfvDHmh8ATgEO4a/BP1HgNllqY7Az+OzLl+Aiu\nFaM0QBBoZtLJydcDdE0a6V3AmcAbgD9B538+fQS3+S8PvNRaOxIstdE1aCBjzLm47/cLpnlY57/B\ngl+izsK1Pn4zLsS8APiCMeYIugbzYTngAV8C/gm37Oy5uDWT+6nxGiy1MFm8rT/dQtGltXh04Ygw\n87nXNakzY8yVuBmaa6y1NxpjXoDO/3z6IvBN3Oa/fzPGZNDPQEMFQeZzwLUzrPvS+Z8flwJ7rLV7\ngn/fZIxZh3s9ugNdg0aLB//9WrGKAXCzMeZM4B24Cgehr8FSC5PHgv+2AxNlxzvKHpP5dQx3PabS\nNamz4Nbeu4FPWWuvDg7r/M8ja+1vg7/eYozZipul+Rm6Bo30RqAXuCbYDOgFxyPBv/Uz0GDW2gKu\nisRUP8RVm7gZXYNGG8WFwh9OOX4jbh3xbdRwDZbUBhxcfT0P2Dzl+CbcLiaZf/cCG4J1fOU2omtS\nN8aYT+Fub19jrX1D2UM6/w1mjFlpjHlZsAGk3G+BVbjzrGvQOM/GvcaP4DY+ZXClgd4d/F3nv8GM\nMauMMa8yxiyb8lAKGEPXYD7cj8s/U1+H4riQWdN7wZIKk9banbhFv88uHgvKdjwR+EmzxrXE/QRo\nA55cPGCM+UPc+o2bmzOkU4sx5mrgtcA7y2Yki3T+G28Z8M+4+m1AaRPUH+LKAt2ErkEjvRp4JG69\nZPHPIG5X6wXo/M+H4k765085/hzgVnQN5sN24ABunXy5pwM/p8ZrsBTrTF6J20n5HuAu4GpcV5Cz\nrbVjzRzbUhDs5n5Nsc5kcOy/cYVs34LbmPAR4DZr7eXNGeWpI6hneB9wO65webmMtfYOnf/GC87x\nRbjbSQeA1wCXAI+z1v5G12B+GWMOcGIHHJ3/BjPG/Afue/5qYBfwStw6yguttXfrGjRe0LTlM7gM\n9H3gz4CXAk+w1t5WyzVYamsmsdb+Q9Dt5vW4Gny3AU9VkGyqlwCfDP7kgBuANzV1RKeOZ+B+zh+L\n++2z3EHcL1IvxXVo0flvnBfh2in+LdAH/Bq42Fr7m+Bx/QzMr6mzKDr/jfcK3Gabv8G1Mr4DeIq1\ntlh7Utegway1nzfGZHE1n1+Hqzf8LGvtbcFTQl+DJTczKSIiIiL1s6TWTIqIiIhIfSlMioiIiEho\nCpMiIiIiEprCpIiIiIiEpjApIiIiIqEpTIqIiIhIaAqTIiIiIhKawqSIyBTGmIuNMd8r+/dGY0zB\nGHNFM8cVjOWPjDH3GGMqajphjHmzMearjR6XiCxdCpMiIie7Ajiz7N8HgEcDTQ1lxpgu4F+AN1pr\ncxV+2CeAs40xL27YwERkSVOYFBGZg7U2Y6293Vp7uMlDeQew11p7Y6UfYK3NA38HfMQYk2rYyERk\nyVpyvblFRGZjjLkJeGLw9zzwcuAWYDfwemvt9caYJwI3AZcAbwSeAIwCnwY+BHwY+NPgU34LeJ21\ndqLsa1wJ/CWwBTgM/AfwbmttepZxLQs+5q+nHH8+rteuATK4HuzvstbeUfa0bwD/CLwGN1MpIlI3\nmpkUETnRa3FBsXhr+7uzPPffgVuBZwI/Bt4D/AZoAV4AfAR4GfDW4gcYYz4GfAz4DnApcC3utvrX\n5hjX5UBr+fOMMRcBX8IFyEuDr7UO+KExpq34PGvtePD1XjLH1xARqZpmJkVEylhrf2+MGQTS1tpf\nARhj2md4+n9aa68JnvM74IXAuLX2L4LHbzTGvBC4KHjOFuBK4Bpr7TvLnrMb+Lox5qnW2h/O8LWe\nBOyy1g6WHbsINynw99bah4KvcR/wIqATGCt77i+BPzHG9Fprj1R2NkRE5qYwKSIS3s+Lf7HWHjLG\ngAtt5Y4Ay4K/PxnwgG8aY6Jlz/kBkAWeBswUJjfjbrWXuxkoAL8yxnwt+Dw/sdZePc3H7wq+9mnB\nmERE6kK3uUVEwhue5tjYNMeKenGB7pe48Fj8M4b75X7tLB/bPfVzW2tvB54C/B/wSuDbwGFjzD8Y\nY+IzjKt7lq8hIlI1zUyKiMyfIcDHrW88NM3jR2f52AGOz3CWWGtvBm4OwuNjcesiXwfsAT5a9tTi\nxzZ7R7qInGIUJkVETpav4Dl+iM97E25mcrW19vvFg8aYzcBnges4+VZ20R7chqASY8w7gVcAZ1hr\ns8AtxphbgT8HNk75+A3BmPeGGLeIyIwUJkVETnYUWGmMeTpw5wzP8ar9pNbaHcaYfwY+aYxZB/wU\nWIPbBd4F/HqWD/8f4E+NMWuKm21wO8jfBdxgjLkOd8v8ZUAU+MqUj3888Atr7VC14xYRmY3WTIqI\nnOwzwIPADRwvp+Nz4mzkdDOTU58z3XNfBbwX+DPge7ialL8BHmetfXCWMX0bmMCVIQLAWvsL4DJc\nEP1SMN5NwLOttT8tPs8Y0wJcjKtnKSJSV57vh7lTIyIi880Ycw3wVGvtI6r8uFfhZj+3zFYYXUQk\nDM1MiogsHh8EVhljLq30A4KNOX8NvENBUkQaQWFSRGSRsNYeBV4KfNgYU+ma9zcC91hrv9i4kYnI\nUqbb3CIiIiISmmYmRURERCQ0hUkRERERCU1hUkRERERCU5gUERERkdAUJkVEREQkNIVJEREREQnt\n/wNFTWZUw97hlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d00ab10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PP9CgQaM8tbNhwzq6detEcvJR73l/AwcOxu12c/jw4Ty18euvv9CyZWvq1WvgDXVr13pu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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea77090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8DbjttGt7gf+rRW1Spro5cT0nTsCpqViPEpMkqb+0Yo2d2qS6xq7eM2IfXDkj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\nUk78/ysLFGAFwUbMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d086ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_palette(\"Paired\")\n",
    "sns.set_context(\"talk\", font_scale=1.2)\n",
    "sns.set_style(\"darkgrid\")\n",
    "\n",
    "plt.figure(0)\n",
    "# plt.subplot(211)\n",
    "plt.plot(sim_time, response[:,1], label='Unshaped')\n",
    "plt.plot(sim_time, response2[:,1], label ='Shaped')\n",
    "plt.ylim(25,0)\n",
    "plt.legend()\n",
    "plt.title('Y Motion')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('meters')\n",
    "\n",
    "plt.figure(1)\n",
    "# plt.subplot(211)\n",
    "plt.plot(sim_time, response[:,0], label='Unshaped')\n",
    "plt.plot(sim_time, response2[:,0], label ='Shaped')\n",
    "plt.legend()\n",
    "plt.title('X Motion')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('meters')\n",
    "\n",
    "plt.figure(2)\n",
    "# plt.subplot(211)\n",
    "plt.plot(sim_time, np.degrees(response[:,2]), label='Unshaped')\n",
    "plt.plot(sim_time, np.degrees(response2[:,2]), label ='Shaped')\n",
    "plt.legend()\n",
    "# plt.plot(sim_time, np.degrees(response2[:,2]))\n",
    "plt.ylim(-15,15)\n",
    "plt.xlim(0,60)\n",
    "plt.title('Beta Motion')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('Degrees')\n",
    "# plt.savefig(\"Beta_Motion.pdf\")\n",
    "\n",
    "plt.figure(3)\n",
    "# plt.subplot(212)\n",
    "plt.plot(response[:,0], response[:,1])\n",
    "plt.plot(response[:,0] + 0.5/2 * np.sin(response[:,2]) , response[:,1] + 0.5/2 * np.cos(response[:,2]), label='Unshaped')\n",
    "plt.plot(response[:,0] + 1/2 * np.sin(response[:,2]) , response[:,1] + 1/2 * np.cos(response[:,2]), label='Unshaped')\n",
    "\n",
    "plt.plot(response2[:,0], response2[:,1])\n",
    "plt.plot(response2[:,0] + 0.5/2 * np.sin(response2[:,2]) , response2[:,1] + 0.5/2 * np.cos(response2[:,2]), label ='Shaped')\n",
    "plt.plot(response2[:,0] + 1/2 * np.sin(response2[:,2]) , response2[:,1] + 1/2 * np.cos(response2[:,2]), label ='Shaped')\n",
    "\n",
    "plt.legend()\n",
    "plt.title('Front View Motion')\n",
    "# plt.ylim(25,0)\n",
    "plt.ylim(25,0)\n",
    "# plt.xlim(0,20)\n",
    "plt.xlim(0,20)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "# plt.show()\n",
    "\n",
    "plt.figure(4)\n",
    "plt.plot(sim_time, s_curve(sim_time, 15.62, 20.61, 9.0, 3.0))\n",
    "plt.plot(sim_time, shaping.shaped_input(s_curve, sim_time, Shaper, 15.62,20.61,9.0,3.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# shaped_arr = np.array(shaping.shaped_input(s_curve, sim_time, Shaper, 15.62,20.61,9.0,3.0))\n",
    "# 20.6099\n",
    "# 226\n",
    "# print(sim_time[226])\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "X = response[:,0][226:]\n",
    "Y = response[:,1][226:]\n",
    "BETA = abs(response[:,2][226:])\n",
    "\n",
    "fig1 = plt.figure(5)\n",
    "ax1 = fig1.gca(projection='3d')         # set the 3d axes\n",
    "\n",
    "\n",
    "ax1.plot_trisurf(X, Y, BETA, cmap=\"YlGnBu\", \n",
    "                linewidth=0.0)\n",
    "ax1.set_axis_bgcolor('white')\n",
    "plt.title('Resedual Vibration Across Workspace')\n",
    "# plt.savefig(\"Low_Mode_Natural_Frequency.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# # Set the plot size - 3x2 aspect ratio is best\n",
    "# fig = plt.figure(4, figsize=(6, 4))\n",
    "# ax = plt.gca()\n",
    "# plt.subplots_adjust(bottom=0.17, left=0.17, top=0.96, right=0.96)\n",
    "\n",
    "# # Change the axis units to serif\n",
    "# plt.setp(ax.get_ymajorticklabels(), family='serif', fontsize=18)\n",
    "# plt.setp(ax.get_xmajorticklabels(), family='serif', fontsize=18)\n",
    "\n",
    "# # Remove top and right axes border\n",
    "# ax.spines['right'].set_color('none')\n",
    "# ax.spines['top'].set_color('none')\n",
    "\n",
    "# # Only show axes ticks on the bottom and left axes\n",
    "# ax.xaxis.set_ticks_position('bottom')\n",
    "# ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# # Turn on the plot grid and set appropriate linestyle and color\n",
    "# ax.grid(True,linestyle=':', color='0.75')\n",
    "# ax.set_axisbelow(True)\n",
    "\n",
    "# # Define the X and Y axis labels\n",
    "# plt.xlabel('Time (s)', family='sans-serif', fontsize=22, weight='bold', labelpad=5)\n",
    "# plt.ylabel('Displacement (m)', family='serif', fontsize=22, weight='bold', labelpad=10)\n",
    "\n",
    "# # Plot the data\n",
    "# plt.plot(sim_time, response[:, 0], linewidth=2, linestyle='-', label = r'$xy$')\n",
    "# # plt.plot(sim_time, response[:, 1], linewidth=2, linestyle='--', label = r'$R$')\n",
    "\n",
    "# # uncomment below and set limits if needed\n",
    "# # plt.xlim(0, 5)\n",
    "# # plt.ylim(-1, 5)\n",
    "\n",
    "# # Create the legend, then fix the fontsize\n",
    "# leg = plt.legend(loc='upper right', ncol = 2, fancybox=True)\n",
    "# ltext  = leg.get_texts()\n",
    "# plt.setp(ltext, family='serif', fontsize=20)\n",
    "\n",
    "# # Adjust the page layout filling the page using the new tight_layout command\n",
    "# plt.tight_layout(pad=0.5)\n",
    "\n",
    "# # Uncomment to save the figure as a high-res pdf in the current folder\n",
    "# # It's saved at the original 6x4 size\n",
    "# # plt.savefig('SpringBar_Pendulum_InitCondResponse_CartAndRadial.pdf')\n",
    "\n",
    "# fig.set_size_inches(9, 6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eq_of_motion(w, t, p):\n",
    "    \"\"\"\n",
    "    Defines the differential equations for the coupled spring-mass system.\n",
    "\n",
    "    Arguments:\n",
    "        w :  vector of the state variables:\n",
    "                  w = [x, theta, x_dot, theta_dot]\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "                  p = [m1, m2, k, l, g, wf]\n",
    "    \n",
    "    Returns:\n",
    "        sysODE : An list representing the system of equations of motion as 1st order ODEs\n",
    "    \"\"\"\n",
    "    x, y, beta, x_dot, y_dot, beta_dot = w\n",
    "    m, k, L, g, H, c, D, t, Izz, k_beta, c_beta, L_1_init, L_2_init = p\n",
    "\n",
    "    # Create sysODE = (x', theta', x_dot', theta_dot'):\n",
    "    sysODE = [x_dot,\n",
    "              y_dot,\n",
    "              beta_dot,\n",
    "              (-D*m*sin(beta)*beta_dot**2/2 + D*m*(-D*g*m*sin(beta)/2 + D*(-D*m*sin(beta)*beta_dot**2/2 + c*(H - x)*(x_dot + y_dot)/sqrt((H - x)**2 + y**2) - c*(x_dot + y_dot)*x/sqrt(x**2 + y**2) - 1.0*k*(-H + x)*(-L_2_init + sqrt((H - x)**2 + y**2))/sqrt((H - x)**2 + y**2) - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*x/sqrt(x**2 + y**2))*cos(beta)/2 + D*(D*m*cos(beta)*beta_dot**2/2 - c*(x_dot + y_dot)*y/sqrt(x**2 + y**2) - c*(x_dot + y_dot)*y/sqrt((H - x)**2 + y**2) + g*m - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*y/sqrt(x**2 + y**2) - 1.0*k*(-L_2_init + sqrt((H - x)**2 + y**2))*y/sqrt((H - x)**2 + y**2))*sin(beta)/2 - c_beta*beta_dot - 1.0*k_beta*beta - m*(-D*(-sin(beta)*beta_dot*x_dot + cos(beta)*beta_dot*y_dot)/2 + D*sin(beta)*beta_dot*x_dot/2 - D*cos(beta)*beta_dot*y_dot/2)/2 + m*(-D*(-sin(beta)*x_dot + cos(beta)*y_dot)*beta_dot/2 + D*sin(beta)*beta_dot*x_dot/2 - D*cos(beta)*beta_dot*y_dot/2)/2)*cos(beta)/(2*(-D**2*m*sin(beta)**2/4 - D**2*m*cos(beta)**2/4 + D**2*m/4 + Izz)) + c*(H - x)*(x_dot + y_dot)/sqrt((H - x)**2 + y**2) - c*(x_dot + y_dot)*x/sqrt(x**2 + y**2) - 1.0*k*(-H + x)*(-L_2_init + sqrt((H - x)**2 + y**2))/sqrt((H - x)**2 + y**2) - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*x/sqrt(x**2 + y**2))/m,\n",
    "              (D*m*cos(beta)*beta_dot**2/2 + D*m*(-D*g*m*sin(beta)/2 + D*(-D*m*sin(beta)*beta_dot**2/2 + c*(H - x)*(x_dot + y_dot)/sqrt((H - x)**2 + y**2) - c*(x_dot + y_dot)*x/sqrt(x**2 + y**2) - 1.0*k*(-H + x)*(-L_2_init + sqrt((H - x)**2 + y**2))/sqrt((H - x)**2 + y**2) - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*x/sqrt(x**2 + y**2))*cos(beta)/2 + D*(D*m*cos(beta)*beta_dot**2/2 - c*(x_dot + y_dot)*y/sqrt(x**2 + y**2) - c*(x_dot + y_dot)*y/sqrt((H - x)**2 + y**2) + g*m - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*y/sqrt(x**2 + y**2) - 1.0*k*(-L_2_init + sqrt((H - x)**2 + y**2))*y/sqrt((H - x)**2 + y**2))*sin(beta)/2 - c_beta*beta_dot - 1.0*k_beta*beta - m*(-D*(-sin(beta)*beta_dot*x_dot + cos(beta)*beta_dot*y_dot)/2 + D*sin(beta)*beta_dot*x_dot/2 - D*cos(beta)*beta_dot*y_dot/2)/2 + m*(-D*(-sin(beta)*x_dot + cos(beta)*y_dot)*beta_dot/2 + D*sin(beta)*beta_dot*x_dot/2 - D*cos(beta)*beta_dot*y_dot/2)/2)*sin(beta)/(2*(-D**2*m*sin(beta)**2/4 - D**2*m*cos(beta)**2/4 + D**2*m/4 + Izz)) - c*(x_dot + y_dot)*y/sqrt(x**2 + y**2) - c*(x_dot + y_dot)*y/sqrt((H - x)**2 + y**2) + g*m - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*y/sqrt(x**2 + y**2) - 1.0*k*(-L_2_init + sqrt((H - x)**2 + y**2))*y/sqrt((H - x)**2 + y**2))/m,\n",
    "              (-D*g*m*sin(beta)/2 + D*(-D*m*sin(beta)*beta_dot**2/2 + c*(H - x)*(x_dot + y_dot)/sqrt((H - x)**2 + y**2) - c*(x_dot + y_dot)*x/sqrt(x**2 + y**2) - 1.0*k*(-H + x)*(-L_2_init + sqrt((H - x)**2 + y**2))/sqrt((H - x)**2 + y**2) - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*x/sqrt(x**2 + y**2))*cos(beta)/2 + D*(D*m*cos(beta)*beta_dot**2/2 - c*(x_dot + y_dot)*y/sqrt(x**2 + y**2) - c*(x_dot + y_dot)*y/sqrt((H - x)**2 + y**2) + g*m - 1.0*k*(-L_1_init + sqrt(x**2 + y**2))*y/sqrt(x**2 + y**2) - 1.0*k*(-L_2_init + sqrt((H - x)**2 + y**2))*y/sqrt((H - x)**2 + y**2))*sin(beta)/2 - c_beta*beta_dot - 1.0*k_beta*beta - m*(-D*(-sin(beta)*beta_dot*x_dot + cos(beta)*beta_dot*y_dot)/2 + D*sin(beta)*beta_dot*x_dot/2 - D*cos(beta)*beta_dot*y_dot/2)/2 + m*(-D*(-sin(beta)*x_dot + cos(beta)*y_dot)*beta_dot/2 + D*sin(beta)*beta_dot*x_dot/2 - D*cos(beta)*beta_dot*y_dot/2)/2)/(-D**2*m*sin(beta)**2/4 - D**2*m*cos(beta)**2/4 + D**2*m/4 + Izz)\n",
    "             ]\n",
    "    return sysODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint\n",
    "import numpy as np\n",
    "from numpy import sin, cos, sqrt\n",
    "import seaborn as sns\n",
    "sns.set_context(\"notebook\", font_scale=1.5, rc={\"lines.linewidth\": 2.5})\n",
    "import matplotlib.pyplot as plt\n",
    "# %matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Set up simulation parameters \n",
    "m = 1.0\n",
    "k = 10.0 \n",
    "# L = 1.0 \n",
    "g = 9.81 \n",
    "H = 20.0 \n",
    "c = 0.1 \n",
    "D = 1.0 \n",
    "Izz = 0.3333\n",
    "k_beta = 1.0\n",
    "c_beta = 1.0\n",
    "L_1_init = 7.34720397  \n",
    "L_2_init = 14.28220593\n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 25.0\n",
    "numpoints = 1000\n",
    "\n",
    "# Create the time samples for the output of the ODE solver\n",
    "t = np.linspace(0.0, stoptime, numpoints)\n",
    "\n",
    "# Initial conditions\n",
    "x_init = -3.75                             # initial position\n",
    "x_dot_init = 0.0                    # initial velocity\n",
    "y_init = 3.8625                    # initial angle\n",
    "y_dot_init = 0.0                # initial angular velocity\n",
    "beta_init = 0.0                        # initial position\n",
    "beta_dot_init = 0.0 \n",
    "\n",
    "# wf = np.np.sqrt(k / m1)                # forcing function frequency\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m, k, L, g, H, c, D, t, Izz, k_beta, c_beta, L_1_init, L_2_init]\n",
    "x0 = [x_init, y_init, beta_init, x_dot_init, y_dot_init, beta_dot_init]\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10d33a090>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DFF2LJSHjQl2VQEmm/80jFEge1fatgL3Bg0nqLKgUjm0xFWHtwHKxrJiEntGq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10de796d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(6)\n",
    "# plt.subplot(211)\n",
    "plt.plot(t, np.degrees(resp[:,2]))\n",
    "# plt.plot(t,resp[:,0])\n",
    "plt.title('Beta Motion')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('Degrees')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def CRAWLAB_fft(data,time,plotflag):\n",
    "    ''' Function to get the FFT for a response\n",
    "    #\n",
    "    # Inputs:\n",
    "    #   time = time array corresponding to the data\n",
    "    #   data = the response data array (only pass a single dimension/state at at time)\n",
    "    #   plotflag = will plot the FFT if nonzero\n",
    "    #   \n",
    "    # Output:\n",
    "    #   fft_freq = an array of the freqs used in the FFT\n",
    "    #   fft_mag = an array of the amplitude of the FFT at each freq in fft_freq\n",
    "    #\n",
    "    # Created: 03/28/14\n",
    "    #   - Joshua Vaughan\n",
    "    #   - joshua.vaughan@louisiana.edu\n",
    "    #   - http://www.ucs.louisiana.edu/~jev9637\n",
    "    ######################################################################################\n",
    "    '''\n",
    "    \n",
    "    from scipy.fftpack import fft\n",
    "    \n",
    "    # correct for any DC offset\n",
    "    offset = np.mean(data) \n",
    "\n",
    "    # Get the natural frequency\n",
    "    sample_time = time[1] - time[0]\n",
    "    n = len(data)\n",
    "\n",
    "    fft_mag = fft((data - offset)*np.hanning(len(data)))\n",
    "    fft_freq = np.linspace(0.0, 1.0/(2.0*sample_time), n/2)\n",
    "    \n",
    "    # Only return the \"useful\" part of the fft\n",
    "    fft_mag = 2.0/n * np.abs(fft_mag[0:n/2])\n",
    "    \n",
    "    if plotflag:\n",
    "        # Plot the relationshiop\n",
    "        #   Many of these setting could also be made default by the .matplotlibrc file\n",
    "        fig = plt.figure(figsize=(6,4))\n",
    "        ax = plt.gca()\n",
    "        plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "        plt.setp(ax.get_ymajorticklabels(),fontsize=18)\n",
    "        plt.setp(ax.get_xmajorticklabels(),fontsize=18)\n",
    "        ax.spines['right'].set_color('none')\n",
    "        ax.spines['top'].set_color('none')\n",
    "        ax.xaxis.set_ticks_position('bottom')\n",
    "        ax.yaxis.set_ticks_position('left')\n",
    "        ax.grid(True,linestyle=':',color='0.75')\n",
    "        ax.set_axisbelow(True)\n",
    "\n",
    "        plt.xlabel('Frequency (Hz)',fontsize=22,labelpad=8)\n",
    "        plt.ylabel('FFT magnitude',fontsize=22,labelpad=10)\n",
    "    \n",
    "        plt.plot(fft_freq, fft_mag, linewidth=2, linestyle='-')\n",
    "        \n",
    "        # Adjust the page layout filling the page using the new tight_layout command\n",
    "        plt.tight_layout(pad=0.5)\n",
    "        plt.show()\n",
    "    \n",
    "    return fft_freq, fft_mag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "freq, mag = CRAWLAB_fft(resp[:,2][800:], t[800:],False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(7)\n",
    "plt.plot(freq, mag)\n",
    "plt.title('FFT')\n",
    "plt.xlabel('frequency')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.xlim(0, 5)\n",
    "freq_index = np.argmax(mag)\n",
    "print freq[freq_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.size(response[:,2][400:])\n",
    "np.size(sim_time[400:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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