{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">Two Mass-Spring-Damper <br> Modal Damping Approximation</h1>\n",
    "<h3 style=\"text-align:center\">MCHE 485: Mechanical Vibrations</h3> \n",
    "<p style=\"text-align:center\">Dr. Joshua Vaughan <br>\n",
    "<a href=\"mailto:joshua.vaughan@louisiana.edu\">joshua.vaughan@louisiana.edu</a><br>\n",
    "http://www.ucs.louisiana.edu/~jev9637/   </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "\t<img src=\"http://shared.crawlab.org/TwoMass_3spring_Damped.png\" alt=\"A Two-Mass-Spring-Damper System\" width=50%/></a><br>\n",
    "    <strong> Figure 1: A Two-Mass-Spring-Damper System</strong>\n",
    "</p>\n",
    "\n",
    "This notebook demonstrates investigates the modal damping of a two-mass-spring-damper system shown in Figure 1. We'll first simluate the \"full\" system, then simluate the decoupled equations of motion generated using an approximation to allow the decoupling. For light damping, we'll see that this approximation works reasonably well.\n",
    "\n",
    "We'll just look at one example set of parameters. The same techniques apply for other parameters and for larger matrices. \n",
    "\n",
    "The equations of motion for the system are:\n",
    "\n",
    "$ \\quad m_1 \\ddot{x}_1 + (c_1+c_2)\\dot{x}_1 - c_2\\dot{x}_2 + (k_1+k_2)x_1 - k_2 x_2 = 0 $\n",
    "\n",
    "$ \\quad m_2 \\ddot{x}_2 - c_2\\dot{x}_1 + (c_2 + c_3)\\dot{x}_2 - k_2 x_1 + (k_2 + k_3)x_2 = 0 $\n",
    "\n",
    "We could also write these equations in matrix form:\n",
    "\n",
    "$ \\quad \\begin{bmatrix}m_1 & 0 \\\\ 0 & m_2\\end{bmatrix}\\begin{bmatrix}\\ddot{x}_1 \\\\ \\ddot{x}_2\\end{bmatrix} + \\begin{bmatrix}c_1 + c_2 & -c_2 \\\\ -c_2 & c_2 + c_3\\end{bmatrix}\\begin{bmatrix}\\dot{x}_1 \\\\ \\dot{x}_2\\end{bmatrix} + \\begin{bmatrix}k_1 + k_2 & -k_2 \\\\ -k_2 & k_2 + k_3\\end{bmatrix}\\begin{bmatrix}x_1 \\\\ x_2\\end{bmatrix} = \\begin{bmatrix}0 \\\\ 0\\end{bmatrix}$\n",
    "\n",
    "Define\n",
    "\n",
    "$ \\quad M = \\begin{bmatrix}m_1 & 0 \\\\ 0 & m_2\\end{bmatrix} $\n",
    "\n",
    "$ \\quad C = \\begin{bmatrix}c_1 + c_2 & -c_2 \\\\ -c_2 & c_2 + c_3\\end{bmatrix} $\n",
    "\n",
    "and \n",
    "\n",
    "$ \\quad K = \\begin{bmatrix}k_1 + k_2 & -k_2 \\\\ -k_2 & k_2 + k_3\\end{bmatrix} $\n",
    "\n",
    "For information on how to obtain these equations, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html).\n",
    "\n",
    "We'll use the [Scipy version of the linear algebra module](http://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.linalg.eigh.html). It allows us to solve the \"general\" eignevalue problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np                        # Grab all of the NumPy functions with nickname np\n",
    "\n",
    "from scipy.integrate import odeint        # We also need to import odeint for the simluations\n",
    "from scipy import linalg                  # We'll use linalg for the eigenvalue problems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# We want our plots to be displayed inline, not in a separate window\n",
    "%matplotlib inline \n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the system as a series of 1st order ODEs (beginnings of state-space form)\n",
    "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 = [x1, x1_dot, x2, x2_dot]\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "                  p = [m1, m2, k1, k2, k3, c1, c2, c3]\n",
    "    \"\"\"\n",
    "    x1, x1_dot, x2, x2_dot = w\n",
    "    m1, m2, k1, k2, k3, c1, c2, c3 = p\n",
    "\n",
    "    # Create sysODE = (x1', x1_dot', x2', x2_dot'):\n",
    "    sysODE = [x1_dot,\n",
    "             (-(k1 + k2) * x1 - (c1 + c2) * x1_dot + k2 * x2 + c2 * x2_dot) / m1,\n",
    "             x2_dot,\n",
    "             (k2 * x1 + c2 * x1_dot - (k2 + k3) * x2 - (c2 + c3) * x2_dot) / m2]\n",
    "              \n",
    "    return sysODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the system parameters\n",
    "m1 = 1.0                # kg\n",
    "m2 = 2.0                # kg\n",
    "k1 = 100.0              # N/m\n",
    "k2 = 50.0               # N/m\n",
    "k3 = 250.0              # N/m\n",
    "c1 = 0.8                # Ns/m\n",
    "c2 = 0.4                # Ns/m\n",
    "c3 = 0.6                # Ns/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set up simulation parameters \n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 10.0\n",
    "numpoints = 10001\n",
    "\n",
    "# Create the time samples for the output of the ODE solver\n",
    "t = np.linspace(0.0, stoptime, numpoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Now, set up the intial conditions and call the ODE solver\n",
    "\n",
    "# Initial conditions\n",
    "x1_init = 0.5                       # initial x1 position\n",
    "x1_dot_init = 0.0                   # initial x1 velocity\n",
    "x2_init = -0.5                      # initial x2 position\n",
    "x2_dot_init = 0.0                   # initial x2 velocity\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m1, m2, k1, k2, k3, c1, c2, c3]\n",
    "x0 = [x1_init, x1_dot_init, x2_init, x2_dot_init]\n",
    "\n",
    "# Call the ODE solver.\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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sKMDuVCLHjsV/3XEs6XVvN1paWkRvoagh/cVC+ouF9BeHWbQnM2YiaufOA5A6TRkMyzja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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113953780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the plot size - 3x2 aspect ratio is best\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",
    "\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",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\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='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t,resp[:,0],linewidth=2,label=r'$x_1$')\n",
    "plt.plot(t,resp[:,2],linewidth=2,linestyle=\"--\",label=r'$x_2$')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0,5)\n",
    "plt.ylim(-0.75,0.75)\n",
    "plt.yticks([-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75], ['', '$-x_0$', '', '$0$', '', '$x_0$', ''])\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=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('MCHE485_Midterm2_Prob1ci.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Undamped problem\n",
    "Let's look first at an undamped version of this system ($c_1 = c_2 = c_3 = 0$).\n",
    "\n",
    "For the undamped proble we can use $M$ and $K$ directly to solve:\n",
    "\n",
    "$ \\quad \\left[K - \\omega^2 M\\right]\\bar{X} = 0 $ \n",
    "\n",
    "for $\\bar{X}$. This is an eigenvalue problem.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the matrices\n",
    "M = np.asarray([[m1, 0],\n",
    "                [0,  m2]])\n",
    "\n",
    "C = np.asarray([[c1 + c2, -c2],\n",
    "                [-c2,      c2 + c3]])\n",
    "\n",
    "K = np.asarray([[k1 + k2, -k2],\n",
    "                [-k2,      k2 + k3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eigenvals, eigenvects = linalg.eigh(K, M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The ```linalg.eigh``` function returns two arrays, one of the eigenvalues and one of the eigenvectors. The eigenvalues are the square of the two natural frequencies. The eigenvectors are returned in normalized form, with each 'column'' of the array representing an eigenvector.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "The resulting eigenalues are 114.64 and 185.36.\n",
      "\n",
      "\n",
      "So the two natrual frequencies are 10.71rad/s and 13.61rad/s.\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('\\n')\n",
    "print('The resulting eigenalues are {:.2f} and {:.2f}.'.format(eigenvals[0], eigenvals[1]))\n",
    "print('\\n')\n",
    "print('So the two natrual frequencies are {:.2f}rad/s and {:.2f}rad/s.'.format(np.sqrt(eigenvals[0]), np.sqrt(eigenvals[1])))\n",
    "print('\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "The first eigenvector is [-0.70710678 -0.5       ].\n",
      "\n",
      "\n",
      "The second eigenvector is [-0.70710678  0.5       ].\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('\\n')\n",
    "print('The first eigenvector is ' + str(eigenvects[:,0]) + '.')\n",
    "print('\\n')\n",
    "print('The second eigenvector is ' + str(eigenvects[:,1]) + '.')\n",
    "print('\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that these eigenvectors diagaonalize the mass and stiffness matrices, then see what happens to the damping matrix under the same transformation. The matrix returned by ```linalg.eigh``` already has the form of the $U$ matrix we use to make the decoupling transformation. So, we just need to write:\n",
    "\n",
    "$ \\quad M' = U^T M U $\n",
    "\n",
    "$ \\quad K' = U^T K U $\n",
    "\n",
    "and\n",
    "\n",
    "$ \\quad C' = U^T C U $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# The @ operator is new in Python 3 and represents matrix multiplication\n",
    "M_prime = eigenvects.T @ M @ eigenvects \n",
    "K_prime = eigenvects.T @ K @ eigenvects\n",
    "C_prime = eigenvects.T @ C @ eigenvects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make the output prettier before printing the results. We'll use the ```numpy.set_printoptions``` method. See [the help page](http://docs.scipy.org/doc/numpy/reference/generated/numpy.set_printoptions.html) for more info."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.set_printoptions(suppress=True, precision=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The M' matrix is: \n",
      "\n",
      "[[ 1.  0.]\n",
      " [ 0.  1.]]\n",
      "\n",
      "\n",
      "The K' martrix is \n",
      "\n",
      "[[ 114.6447    0.    ]\n",
      " [   0.      185.3553]]\n",
      "\n",
      "\n",
      "The C' martrix is \n",
      "\n",
      "[[ 0.5672  0.35  ]\n",
      " [ 0.35    1.1328]]\n"
     ]
    }
   ],
   "source": [
    "print('The M\\' matrix is: \\n\\n{}'.format(M_prime))\n",
    "\n",
    "print('\\n\\nThe K\\' martrix is \\n\\n{}'.format(K_prime))\n",
    "\n",
    "print('\\n\\nThe C\\' martrix is \\n\\n{}'.format(C_prime))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the $M'$ matrix is identity, as it should be, and $K'$ is a diagonal matrix with the eigenvalues on the diagonal, as it should be. The $C'$ matrix, however, has not been decoupled using this transformation.\n",
    "\n",
    "Let's look at what happens if we ignore the terms that remain coupled. The result is set of equations representing the two modes of the system:\n",
    "\n",
    "$ \\quad M' \\ddot{H} + \\tilde{C}' \\dot{H} + K' H = 0 $\n",
    "\n",
    "where \n",
    "\n",
    "$ \\quad \\tilde{C}' = \\begin{bmatrix}0.5672 & 0 \\\\ 0 & 1.1328\\end{bmatrix} $\n",
    "\n",
    "If we do this, then the result is two uncoupled equations of motion:\n",
    "\n",
    "$ \\quad \\ddot{\\eta}_1 + 2 \\zeta_1 \\omega_1 \\dot{\\eta}_1 + \\omega_1^2 \\eta_1= 0 $\n",
    "\n",
    "$ \\quad \\ddot{\\eta}_2 + 2 \\zeta_2 \\omega_2 \\dot{\\eta}_2 + \\omega_2^2 \\eta_2= 0 $\n",
    "\n",
    "where $\\omega_i$ and $\\zeta_i$ are the the $i^{th}$ mode's natural frequency and approximately modal damping ratio, respectively.\n",
    "\n",
    "We can now simluate this system decoupled by ignoring the off-diagonal terms in the $C'$ matrix and compare it to the full equation, whose response we plotted above. We'll write the system as a set of first-order different equations, then simluate and plot the response to the same initial conditions we plotted above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def modal_eq_of_motion(w, t, p):\n",
    "    \"\"\"\n",
    "    Defines the differential equations for the decoupled spring-mass system.\n",
    "\n",
    "    Arguments:\n",
    "        w :  vector of the state variables:\n",
    "                  w = [h1, h1_dot, h2, h2_dot]\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "                  p = [omega1, omega2, zeta1, zeta2]\n",
    "    \"\"\"\n",
    "    \n",
    "    h1, h1_dot, h2, h2_dot = w\n",
    "    omega1, omega2, zeta1, zeta2 = p\n",
    "    \n",
    "    sys_ODE = [h1_dot,\n",
    "               -2 * zeta1 * omega1 * h1_dot - omega1**2 * h1,\n",
    "               h2_dot,\n",
    "               -2 * zeta2 * omega2 * h2_dot - omega2**2 * h2]\n",
    "    \n",
    "    return sys_ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Now, set up the intial conditions and call the ODE solver\n",
    "\n",
    "# Translate the intial conditions of x1 and x2 into intiial conditions in the modal coordinates\n",
    "H_init = np.linalg.inv(eigenvects) @ [x1_init, x2_init]\n",
    "H_dot_init = np.linalg.inv(eigenvects) @ [x1_dot_init, x2_dot_init]\n",
    "\n",
    "# Initial conditions\n",
    "h1_init = H_init[0]                 # initial h1 position\n",
    "h1_dot_init = H_dot_init[0]         # initial h1 velocity\n",
    "h2_init = H_init[1]                 # initial h2 position\n",
    "h2_dot_init = H_dot_init[0]         # initial h2 velocity\n",
    "\n",
    "\n",
    "omega1 = np.sqrt(eigenvals[0])\n",
    "omega2 = np.sqrt(eigenvals[1])\n",
    "zeta1 = C_prime[0,0] / (2 * omega1)\n",
    "zeta2 = C_prime[1,1] / (2 * omega2)\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [omega1, omega2, zeta1, zeta2]\n",
    "x0 = [h1_init, h1_dot_init, h2_init, h2_dot_init]\n",
    "\n",
    "# Call the ODE solver.\n",
    "modal_resp = odeint(modal_eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we need to relate this modal reponse back to motion in $x_1$ and $x_2$ to allow us to compare it to the full, coupled simluation. To do this, remember that:\n",
    "\n",
    "$ \\quad X = U H $\n",
    "\n",
    "so, \n",
    "\n",
    "$ \\quad x_1 = U_{11} \\eta_1 + U_{12} \\eta_2 $ \n",
    "\n",
    "and \n",
    "\n",
    "$ \\quad x_2 = U_{21} \\eta_1 + U_{22} \\eta_2 $ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x1_decoupled = eigenvects[0,0] * modal_resp[:,0] + eigenvects[0,1] * modal_resp[:,2]\n",
    "x2_decoupled = eigenvects[1,0] * modal_resp[:,0] + eigenvects[1,1] * modal_resp[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XAkgdGTvkdMEXSN2mQtbMWGUVJC3aNjyclz2GDilmzHb2Wcr7Bw/mZV3RGGU+WaFC+ouF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BcL6S8Os2hPZsxEpJuRpTebknNu2PQ1nkM98nWTqxKvSzcOSY2MjUqaMj4yptWMmc+MmWU+WbFC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\nCiKMAQAAFPQ/rC5AiOngm/kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116345f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, let's plot the response\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\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",
    "\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",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\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='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t, x1_decoupled, linewidth=2, linestyle = '-', label=r'$x_1$')\n",
    "plt.plot(t, x2_decoupled, linewidth=2, linestyle='--', label=r'$x_2$')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0,5)\n",
    "plt.ylim(-0.75,0.75)\n",
    "plt.yticks([-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75], ['', '$-x_0$', '', '$0$', '', '$x_0$', ''])\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=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('Approx_Decoupled_Resp.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's compare the two responses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lKSmLzQAGAFzHOT+R7CDGmLrkXq0xHFo6YSiFQ8Z9YhaPOZ24yBaFPRJEjSl1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\nTz9Mje+We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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11650a7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,4))\n",
    "\n",
    "plt.subplots_adjust(bottom=0.12,left=0.17,top=0.96,right=0.96)\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax1.spines['right'].set_color('none')\n",
    "ax1.spines['top'].set_color('none')\n",
    "ax1.xaxis.set_ticks_position('bottom')\n",
    "ax1.yaxis.set_ticks_position('left')\n",
    "ax1.grid(True,linestyle=':',color='0.75')\n",
    "ax1.set_axisbelow(True)\n",
    "\n",
    "ax2.spines['right'].set_color('none')\n",
    "ax2.spines['top'].set_color('none')\n",
    "ax2.xaxis.set_ticks_position('bottom')\n",
    "ax2.yaxis.set_ticks_position('left')\n",
    "ax2.grid(True,linestyle=':',color='0.75')\n",
    "ax2.set_axisbelow(True)\n",
    "\n",
    "# x1 plot\n",
    "ax1.set_xlabel('Time (s)', family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "ax1.set_ylabel('Position (m)', family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "ax1.plot(t, resp[:,0], linewidth=2, linestyle = '-', label=r'Exact $x_1$')\n",
    "ax1.plot(t, x1_decoupled, linewidth=2, linestyle = '--', label=r'Approx. $x_1$') \n",
    "ax1.set_yticks([-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75])\n",
    "ax1.set_yticklabels(['', '$-x_0$', '', '$0$', '', '$x_0$', ''])\n",
    "\n",
    "ax1.leg = ax1.legend(loc='upper right', fancybox=True)\n",
    "ltext  = ax1.leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=16)\n",
    "\n",
    "# x2_plot\n",
    "ax2.set_xlabel('Time (s)', family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "ax2.set_ylabel('Position (m)', family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "ax2.plot(t, resp[:,2], linewidth=2, linestyle = '-', label=r'Exact $x_2$')\n",
    "ax2.plot(t, x2_decoupled, linewidth=2, linestyle = '--', label=r'Approx. $x_2$')\n",
    "# ax2.set_ylim(-0.75, 0.75)\n",
    "ax2.set_yticks([-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75])\n",
    "ax2.set_yticklabels(['', '$-x_0$', '', '$0$', '', '$x_0$', ''])\n",
    "\n",
    "ax2.leg = ax2.legend(loc='upper right', fancybox=True)\n",
    "ltext  = ax2.leg.get_texts()\n",
    "plt.setp(ltext,family='serif', fontsize=16)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5, w_pad=10)\n",
    "\n",
    "# If you want to save the figure, uncomment the commands below. \n",
    "# The figure will be saved in the same directory as your IPython notebook.\n",
    "# Save the figure as a high-res pdf in the current folder\n",
    "# plt.savefig('Comparison_of_Exact_and_Decoupled_Resps.pdf', dpi = 600)\n",
    "\n",
    "# fig.set_size_inches(18,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"border: 0px;\n",
    "        height: 1px;\n",
    "        text-align: center;\n",
    "        background: #333;\n",
    "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc);\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Licenses\n",
    "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n",
    "\n",
    "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n",
       "\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsx.otf');\n",
       "        font-weight: bold;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsi.otf');\n",
       "        font-style: oblique;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunso.otf');\n",
       "        font-weight: bold;\n",
       "        font-style: oblique;\n",
       "    }\n",
       "\n",
       "    div.cell {\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    h1 {\n",
       "        font-family: Computer Modern;\n",
       "    }\n",
       "    \n",
       "    h4 {\n",
       "        margin-top: 12px;\n",
       "        margin-bottom: 3px;\n",
       "    }\n",
       "\n",
       "    div.text_cell_render {\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width: 100%;\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    .CodeMirror {\n",
       "        font-family: \"Source Code Pro\", source-code-pro, Consolas, monospace;\n",
       "    }\n",
       "    \n",
       "    .warning {\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    }  \n",
       "  \n",
       "   \n",
       "    hr.style-end {\n",
       "        border: 0px !important;\n",
       "        height: 1px !important;\n",
       "        text-align: center !important;\n",
       "        background: #333 !important;\n",
       "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "    }\n",
       "\n",
       "    hr.style-end:after {\n",
       "        content: &#x269C !important;\n",
       "        left: 50% !important;\n",
       "        position: absolute !important;\n",
       "        /* Controls the whitespace around the symbol */\n",
       "        padding: 0px !important;\n",
       "        background: #fff !important;\n",
       "    }\n",
       "    \n",
       "/*  Center figures, etc\n",
       "    .ui-wrapper {\n",
       "        margin-left: auto !important;\n",
       "        margin-right: auto !important;\n",
       "    }\n",
       "*/\n",
       "    \n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This cell will just improve the styling of the notebook\n",
    "# You can ignore it, if you are okay with the default sytling\n",
    "from IPython.core.display import HTML\n",
    "import urllib.request\n",
    "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n",
    "HTML(response.read().decode(\"utf-8\"))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}