Initial commit

2019-05-11 15:18:34 +02:00 · 2019-05-11 15:18:34 +02:00 · 283093ef2f
commit 283093ef2f
22 changed files with 42298 additions and 0 deletions
--- a/.ipynb_checkpoints/Duffing-checkpoint.ipynb
+++ b/.ipynb_checkpoints/Duffing-checkpoint.ipynb
--- a/.ipynb_checkpoints/duffing-estimation-checkpoint.ipynb
+++ b/.ipynb_checkpoints/duffing-estimation-checkpoint.ipynb
--- a/.ipynb_checkpoints/duffing-stuffing-checkpoint.ipynb
+++ b/.ipynb_checkpoints/duffing-stuffing-checkpoint.ipynb
@ -0,0 +1,222 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib notebook\n",
+    "\n",
+    "import numpy as np\n",
+    "from scipy.integrate import odeint\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib import animation\n",
+    "plt.rcParams[\"animation.html\"] = \"jshtml\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m1 = 1\n",
+    "m2 = 1\n",
+    "c1 = 0.1\n",
+    "c2 = 0.1\n",
+    "c3 = 0.1\n",
+    "a1 = 0.1\n",
+    "a2 = 0.1\n",
+    "a3 = 0.1\n",
+    "k1 = 0.05\n",
+    "k2 = 0.21\n",
+    "k3 = 0.11\n",
+    "C1 = 0.15\n",
+    "C2 = 0.30\n",
+    "omega = 0.1\n",
+    "\n",
+    "f1 = lambda t: C1*np.cos(omega*t)\n",
+    "f2 = lambda t: C2*np.cos(omega*t)\n",
+    "\n",
+    "def deriv(X, t):\n",
+    "    \"\"\"Return the derivatives dx/dt and d2x/dt2.\"\"\"\n",
+    "    x1, x2, xd1, xd2 = X\n",
+    "    F1 = f1(t)\n",
+    "    F2 = f2(t)\n",
+    "    xdd1 = F1 - xd1*(c1 + c2) + xd2*c2 - x1*(k1 + k2) + x2*k2 - a1*x1**3 + a2*(x2 - x1)**3\n",
+    "    xdd2 = F2 - xd2*(c2 + c3) + xd1*c1 - x2*(k2 + k3) + x1*k2 - a3*x2**3 + a2*(x2 - x1)**3\n",
+    "    return xd1, xd2, xdd1/m1, xdd2/m2\n",
+    "\n",
+    "\n",
+    "def solve_duffing(tmax, dt_per_period, t_trans, x0, v0):\n",
+    "    \"\"\"Solve the Duffing equation with the standard odeint solver.\n",
+    "    \n",
+    "    Find the numerical solution to the Duffing equation using a suitable\n",
+    "    time grid: tmax is the maximum time (s) to integrate to; t_trans is\n",
+    "    the initial time period of transient behaviour until the solution\n",
+    "    settles down (if it does) to some kind of periodic motion (these data\n",
+    "    points are dropped) and dt_per_period is the number of time samples\n",
+    "    (of duration dt) to include per period of the driving motion (frequency\n",
+    "    omega).\n",
+    "    \n",
+    "    Returns the time grid, t (after t_trans), position, x, and velocity,\n",
+    "    xdot, dt, and step, the number of array points per period of the driving\n",
+    "    motion.\n",
+    "    \n",
+    "    \"\"\"\n",
+    "    # Time point spacings and the time grid\n",
+    "\n",
+    "    period = 2*np.pi/omega\n",
+    "    dt = 2*np.pi/omega / dt_per_period\n",
+    "    step = int(period / dt)\n",
+    "    t = np.arange(0, tmax, dt)\n",
+    "    # Initial conditions: x, xdot\n",
+    "    X0 = x0 + v0\n",
+    "    X = odeint(deriv, X0, t)\n",
+    "    idx = int(t_trans / dt)\n",
+    "    return t[idx:], X[idx:], dt, step"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set up the motion for a oscillator with initial positions and velocities\n",
+    "x0, v0 = (0.5, -0.5), (0.5, -0.1)\n",
+    "tmax, t_trans = 150, 0\n",
+    "dt_per_period = 100"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solve the equation of motion.\n",
+    "t, X, dt, pstep = solve_duffing(tmax, dt_per_period, t_trans, x0, v0)\n",
+    "print(\"# samples: %d\" % len(t))\n",
+    "print(\"dt: %.4f\" % dt)\n",
+    "print(\"Steps per period: %d\" % pstep)\n",
+    "x1, x2, xd1, xd2 = X.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig1, ((ax11, ax12), (ax21, ax22)) = plt.subplots(nrows=2, ncols=2)\n",
+    "\n",
+    "ax11.plot(t, x1)\n",
+    "ax11.set_xlabel(r'$x_1$')\n",
+    "ax12.plot(t, x2)\n",
+    "ax12.set_xlabel(r'$x_2$')\n",
+    "ax21.plot(t, xd1)\n",
+    "ax21.set_xlabel(r'$v_1$')\n",
+    "ax22.plot(t, xd2)\n",
+    "ax22.set_xlabel(r'$v_2$')\n",
+    "plt.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [],
+   "source": [
+    "%%capture\n",
+    "fig2, ((ax11, ax12), (ax21, ax22)) = plt.subplots(nrows=2, ncols=2)\n",
+    "\n",
+    "# Positions\n",
+    "ax11.set_xlabel(r'$x_1$')\n",
+    "ax11.set_ylabel(r'$x_2$')\n",
+    "ln11, = ax11.plot([], [])\n",
+    "ax11.set_xlim([np.min(x1), np.max(x1)])\n",
+    "ax11.set_ylim([np.min(x2), np.max(x2)])\n",
+    "\n",
+    "# Velocities\n",
+    "ax12.set_xlabel(r'$v_1$')\n",
+    "ax12.set_ylabel(r'$v_2$')\n",
+    "ln12, = ax12.plot([], [])\n",
+    "ax12.set_xlim([np.min(xd1), np.max(xd1)])\n",
+    "ax12.set_ylim([np.min(xd2), np.max(xd2)])\n",
+    "\n",
+    "# Phase spaces\n",
+    "ax21.set_xlabel(r'$\\mathbf{x}$')\n",
+    "ax21.set_ylabel(r'$\\mathbf{v}$')\n",
+    "ln21a, = ax21.plot([], [])\n",
+    "ln21b, = ax21.plot([], [])\n",
+    "ax21.set_xlim([min(np.min(x1), np.min(x2)), max(np.max(x1), np.max(x2))])\n",
+    "ax21.set_ylim([min(np.min(xd1), np.min(xd2)), max(np.max(xd1), np.max(xd2))])\n",
+    "\n",
+    "# F(t)\n",
+    "F1 = f1(t)\n",
+    "F2 = f2(t)\n",
+    "ax22.set_xlabel(r'$t$')\n",
+    "ax22.set_ylabel(r'$\\mathbf{F}(t)$')\n",
+    "ln22a, = ax22.plot([], [])\n",
+    "ln22b, = ax22.plot([], [])\n",
+    "ax22.set_xlim([t[0], t[-1]])\n",
+    "ax21.set_ylim([min(np.min(F1), np.min(F2)), max(np.max(F1), np.max(F2))])\n",
+    "\n",
+    "plt.tight_layout()\n",
+    "\n",
+    "def animate(i):\n",
+    "    ln11.set_data(x1[:i], x2[:i])\n",
+    "    ln12.set_data(xd1[:i], xd2[:i])\n",
+    "    ln21a.set_data(x1[:i], xd1[:i])\n",
+    "    ln21b.set_data(x2[:i], xd2[:i])\n",
+    "    ln22a.set_data(t[:i], F1[:i])\n",
+    "    ln22b.set_data(t[:i], F2[:i])\n",
+    "    \n",
+    "\n",
+    "anim = animation.FuncAnimation(fig2, animate, frames=len(t), interval=100, repeat_delay=1000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "anim"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
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+      >0</text
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+      >Frequency [kHz]</text
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+    ><text x="-12" xml:space="preserve" y="8" style="stroke:none;"
+      >0</text
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+    ><g transform="translate(97.3333,387.875)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >10</text
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >20</text
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >30</text
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >40</text
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >50</text
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >60</text
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+    ><g transform="translate(97.3333,87.125)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >70</text
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+    ><g transform="translate(97.3333,37)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >80</text
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+    ><g transform="translate(70.3333,237.4998) rotate(-90)" style="font-size:22px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-56" xml:space="preserve" y="-5" style="stroke:none;"
+      >Angle [deg]</text
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+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
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+      >Frequency [kHz]</text
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+    ><text x="-12" xml:space="preserve" y="8" style="stroke:none;"
+      >0</text
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+    ><g transform="translate(97.3333,387.875)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >20</text
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+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >30</text
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+    ><g transform="translate(97.3333,237.5)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >40</text
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+    ><g transform="translate(97.3333,187.375)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >50</text
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+    ><g transform="translate(97.3333,137.25)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >60</text
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+    ><g transform="translate(97.3333,87.125)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >70</text
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+    ><g transform="translate(97.3333,37)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >80</text
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+    ><text x="-56" xml:space="preserve" y="-5" style="stroke:none;"
+      >Angle [deg]</text
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+    ><g style="fill:white; text-rendering:optimizeSpeed; color-rendering:optimizeSpeed; image-rendering:optimizeSpeed; shape-rendering:crispEdges; stroke:white; color-interpolation:sRGB;"
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+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
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+    ><g style="stroke-linecap:butt; fill:rgb(0,114,189); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(0,114,189); color-interpolation:linearRGB; stroke-width:4;"
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+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
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+    ><g style="stroke-linecap:butt; fill:rgb(217,83,25); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(217,83,25); color-interpolation:linearRGB; stroke-width:4;"
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+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
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+    ><g style="stroke-linecap:butt; fill:rgb(237,177,32); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(237,177,32); color-interpolation:linearRGB; stroke-width:4;"
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+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
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+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
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+    ><g style="stroke-linecap:butt; fill:rgb(77,190,238); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(77,190,238); color-interpolation:linearRGB; stroke-width:4;"
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+    ><g style="stroke-linecap:butt; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB; stroke-width:0.6667;"
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+>
--- a/data/XYPost.mat
+++ b/data/XYPost.mat
--- a/data/XY_ampl_ex.svg
+++ b/data/XY_ampl_ex.svg
@ -0,0 +1,188 @@
+<?xml version="1.0"?>
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+    ><line y2="438" style="fill:none;" x1="104" x2="724" y1="438"
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+    ><g transform="translate(104,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
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+      >0</text
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+    ><g transform="translate(228,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >2000</text
+    ></g
+    ><g transform="translate(352,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >4000</text
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+    ><g transform="translate(476,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >6000</text
+    ></g
+    ><g transform="translate(600,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >8000</text
+    ></g
+    ><g transform="translate(724,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-28" xml:space="preserve" y="21" style="stroke:none;"
+      >10000</text
+    ></g
+    ><g transform="translate(414.0003,472)" style="font-size:22px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-75" xml:space="preserve" y="23" style="stroke:none;"
+      >Frequency [Hz]</text
+    ></g
+    ><g style="text-rendering:geometricPrecision; stroke-width:0.6667; color-interpolation:linearRGB; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke-linejoin:round;"
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+      /><line y2="387.875" style="fill:none;" x1="104" x2="110.2" y1="387.875"
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+      /><line y2="287.625" style="fill:none;" x1="104" x2="110.2" y1="287.625"
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+      /><line y2="137.25" style="fill:none;" x1="104" x2="110.2" y1="137.25"
+      /><line y2="87.125" style="fill:none;" x1="104" x2="110.2" y1="87.125"
+      /><line y2="37" style="fill:none;" x1="104" x2="110.2" y1="37"
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+      /><line y2="287.625" style="fill:none;" x1="724" x2="717.8" y1="287.625"
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+      /><line y2="187.375" style="fill:none;" x1="724" x2="717.8" y1="187.375"
+      /><line y2="137.25" style="fill:none;" x1="724" x2="717.8" y1="137.25"
+      /><line y2="87.125" style="fill:none;" x1="724" x2="717.8" y1="87.125"
+      /><line y2="37" style="fill:none;" x1="724" x2="717.8" y1="37"
+    /></g
+    ><g transform="translate(97.3333,438)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-12" xml:space="preserve" y="8" style="stroke:none;"
+      >0</text
+    ></g
+    ><g transform="translate(97.3333,387.875)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >10</text
+    ></g
+    ><g transform="translate(97.3333,337.75)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >20</text
+    ></g
+    ><g transform="translate(97.3333,287.625)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >30</text
+    ></g
+    ><g transform="translate(97.3333,237.5)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >40</text
+    ></g
+    ><g transform="translate(97.3333,187.375)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >50</text
+    ></g
+    ><g transform="translate(97.3333,137.25)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >60</text
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+    ><g transform="translate(97.3333,87.125)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >70</text
+    ></g
+    ><g transform="translate(97.3333,37)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >80</text
+    ></g
+    ><g transform="translate(70.3333,237.4998) rotate(-90)" style="font-size:22px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-49" xml:space="preserve" y="-5" style="stroke:none;"
+      >Amplitude</text
+    ></g
+    ><g style="stroke-linecap:butt; fill:red; text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:red; color-interpolation:linearRGB; stroke-width:4;"
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+    /></g
+    ><g style="fill:white; text-rendering:optimizeSpeed; color-rendering:optimizeSpeed; image-rendering:optimizeSpeed; shape-rendering:crispEdges; stroke:white; color-interpolation:sRGB;"
+    ><path style="stroke:none;" d="M263 98 L263 48 L115 48 L115 98 Z"
+    /></g
+    ><g transform="translate(162,61.3663)" style="font-size:18px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
+      >X-amplitude</text
+    ></g
+    ><g style="stroke-linecap:butt; fill:red; text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:red; color-interpolation:linearRGB; stroke-width:4;"
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+    ><g style="stroke-linecap:butt; fill:blue; text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:blue; color-interpolation:linearRGB; stroke-width:4;"
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+    ><g style="fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(38,38,38); color-interpolation:linearRGB; stroke-width:0.6667;"
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+    ><g transform="translate(104,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-6" xml:space="preserve" y="21" style="stroke:none;"
+      >0</text
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+    ><g transform="translate(228,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >2000</text
+    ></g
+    ><g transform="translate(352,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >4000</text
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+    ><g transform="translate(476,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >6000</text
+    ></g
+    ><g transform="translate(600,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-22.5" xml:space="preserve" y="21" style="stroke:none;"
+      >8000</text
+    ></g
+    ><g transform="translate(724,444.6667)" style="font-size:20px; fill:rgb(38,38,38); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; font-family:'SansSerif'; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+    ><text x="-28" xml:space="preserve" y="21" style="stroke:none;"
+      >10000</text
+    ></g
+    ><g transform="translate(414.0003,472)" style="font-size:22px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-75" xml:space="preserve" y="23" style="stroke:none;"
+      >Frequency [Hz]</text
+    ></g
+    ><g style="text-rendering:geometricPrecision; stroke-width:0.6667; color-interpolation:linearRGB; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke-linejoin:round;"
+    ><line y2="37" style="fill:none;" x1="104" x2="104" y1="438"
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+      /><line y2="387.875" style="fill:none;" x1="104" x2="110.2" y1="387.875"
+      /><line y2="337.75" style="fill:none;" x1="104" x2="110.2" y1="337.75"
+      /><line y2="287.625" style="fill:none;" x1="104" x2="110.2" y1="287.625"
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+      /><line y2="187.375" style="fill:none;" x1="104" x2="110.2" y1="187.375"
+      /><line y2="137.25" style="fill:none;" x1="104" x2="110.2" y1="137.25"
+      /><line y2="87.125" style="fill:none;" x1="104" x2="110.2" y1="87.125"
+      /><line y2="37" style="fill:none;" x1="104" x2="110.2" y1="37"
+      /><line y2="438" style="fill:none;" x1="724" x2="717.8" y1="438"
+      /><line y2="387.875" style="fill:none;" x1="724" x2="717.8" y1="387.875"
+      /><line y2="337.75" style="fill:none;" x1="724" x2="717.8" y1="337.75"
+      /><line y2="287.625" style="fill:none;" x1="724" x2="717.8" y1="287.625"
+      /><line y2="237.5" style="fill:none;" x1="724" x2="717.8" y1="237.5"
+      /><line y2="187.375" style="fill:none;" x1="724" x2="717.8" y1="187.375"
+      /><line y2="137.25" style="fill:none;" x1="724" x2="717.8" y1="137.25"
+      /><line y2="87.125" style="fill:none;" x1="724" x2="717.8" y1="87.125"
+      /><line y2="37" style="fill:none;" x1="724" x2="717.8" y1="37"
+    /></g
+    ><g transform="translate(97.3333,438)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-12" xml:space="preserve" y="8" style="stroke:none;"
+      >0</text
+    ></g
+    ><g transform="translate(97.3333,387.875)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >10</text
+    ></g
+    ><g transform="translate(97.3333,337.75)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >20</text
+    ></g
+    ><g transform="translate(97.3333,287.625)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >30</text
+    ></g
+    ><g transform="translate(97.3333,237.5)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >40</text
+    ></g
+    ><g transform="translate(97.3333,187.375)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >50</text
+    ></g
+    ><g transform="translate(97.3333,137.25)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >60</text
+    ></g
+    ><g transform="translate(97.3333,87.125)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >70</text
+    ></g
+    ><g transform="translate(97.3333,37)" style="font-size:20px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-23" xml:space="preserve" y="8" style="stroke:none;"
+      >80</text
+    ></g
+    ><g transform="translate(70.3333,237.4998) rotate(-90)" style="font-size:22px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="-49" xml:space="preserve" y="-5" style="stroke:none;"
+      >Amplitude</text
+    ></g
+    ><g style="stroke-linecap:butt; fill:red; text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:red; color-interpolation:linearRGB; stroke-width:4;"
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+    ><g style="fill:white; text-rendering:optimizeSpeed; color-rendering:optimizeSpeed; image-rendering:optimizeSpeed; shape-rendering:crispEdges; stroke:white; color-interpolation:sRGB;"
+    ><path style="stroke:none;" d="M263 98 L263 48 L115 48 L115 98 Z"
+    /></g
+    ><g transform="translate(162,61.3663)" style="font-size:18px; text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; font-family:'SansSerif'; color-interpolation:linearRGB;"
+    ><text x="0" xml:space="preserve" y="7.5" style="stroke:none;"
+      >X-amplitude</text
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+    ><g style="stroke-linecap:butt; fill:red; text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:red; color-interpolation:linearRGB; stroke-width:4;"
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+    ><g style="stroke-linecap:butt; fill:blue; text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:blue; color-interpolation:linearRGB; stroke-width:4;"
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+    /></g
+  ></g
+></svg
+>
--- a/duffing-estimation.ipynb
+++ b/duffing-estimation.ipynb
--- a/duffing-stuffing.ipynb
+++ b/duffing-stuffing.ipynb
@ -0,0 +1,222 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib notebook\n",
+    "\n",
+    "import numpy as np\n",
+    "from scipy.integrate import odeint\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib import animation\n",
+    "plt.rcParams[\"animation.html\"] = \"jshtml\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m1 = 1\n",
+    "m2 = 1\n",
+    "c1 = 0.1\n",
+    "c2 = 0.1\n",
+    "c3 = 0.1\n",
+    "a1 = 0.1\n",
+    "a2 = 0.1\n",
+    "a3 = 0.1\n",
+    "k1 = 0.05\n",
+    "k2 = 0.21\n",
+    "k3 = 0.11\n",
+    "C1 = 0.15\n",
+    "C2 = 0.30\n",
+    "omega = 0.1\n",
+    "\n",
+    "f1 = lambda t: C1*np.cos(omega*t)\n",
+    "f2 = lambda t: C2*np.cos(omega*t)\n",
+    "\n",
+    "def deriv(X, t):\n",
+    "    \"\"\"Return the derivatives dx/dt and d2x/dt2.\"\"\"\n",
+    "    x1, x2, xd1, xd2 = X\n",
+    "    F1 = f1(t)\n",
+    "    F2 = f2(t)\n",
+    "    xdd1 = F1 - xd1*(c1 + c2) + xd2*c2 - x1*(k1 + k2) + x2*k2 - a1*x1**3 + a2*(x2 - x1)**3\n",
+    "    xdd2 = F2 - xd2*(c2 + c3) + xd1*c1 - x2*(k2 + k3) + x1*k2 - a3*x2**3 + a2*(x2 - x1)**3\n",
+    "    return xd1, xd2, xdd1/m1, xdd2/m2\n",
+    "\n",
+    "\n",
+    "def solve_duffing(tmax, dt_per_period, t_trans, x0, v0):\n",
+    "    \"\"\"Solve the Duffing equation with the standard odeint solver.\n",
+    "    \n",
+    "    Find the numerical solution to the Duffing equation using a suitable\n",
+    "    time grid: tmax is the maximum time (s) to integrate to; t_trans is\n",
+    "    the initial time period of transient behaviour until the solution\n",
+    "    settles down (if it does) to some kind of periodic motion (these data\n",
+    "    points are dropped) and dt_per_period is the number of time samples\n",
+    "    (of duration dt) to include per period of the driving motion (frequency\n",
+    "    omega).\n",
+    "    \n",
+    "    Returns the time grid, t (after t_trans), position, x, and velocity,\n",
+    "    xdot, dt, and step, the number of array points per period of the driving\n",
+    "    motion.\n",
+    "    \n",
+    "    \"\"\"\n",
+    "    # Time point spacings and the time grid\n",
+    "\n",
+    "    period = 2*np.pi/omega\n",
+    "    dt = 2*np.pi/omega / dt_per_period\n",
+    "    step = int(period / dt)\n",
+    "    t = np.arange(0, tmax, dt)\n",
+    "    # Initial conditions: x, xdot\n",
+    "    X0 = x0 + v0\n",
+    "    X = odeint(deriv, X0, t)\n",
+    "    idx = int(t_trans / dt)\n",
+    "    return t[idx:], X[idx:], dt, step"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set up the motion for a oscillator with initial positions and velocities\n",
+    "x0, v0 = (0.5, -0.5), (0.5, -0.1)\n",
+    "tmax, t_trans = 150, 0\n",
+    "dt_per_period = 100"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solve the equation of motion.\n",
+    "t, X, dt, pstep = solve_duffing(tmax, dt_per_period, t_trans, x0, v0)\n",
+    "print(\"# samples: %d\" % len(t))\n",
+    "print(\"dt: %.4f\" % dt)\n",
+    "print(\"Steps per period: %d\" % pstep)\n",
+    "x1, x2, xd1, xd2 = X.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig1, ((ax11, ax12), (ax21, ax22)) = plt.subplots(nrows=2, ncols=2)\n",
+    "\n",
+    "ax11.plot(t, x1)\n",
+    "ax11.set_xlabel(r'$x_1$')\n",
+    "ax12.plot(t, x2)\n",
+    "ax12.set_xlabel(r'$x_2$')\n",
+    "ax21.plot(t, xd1)\n",
+    "ax21.set_xlabel(r'$v_1$')\n",
+    "ax22.plot(t, xd2)\n",
+    "ax22.set_xlabel(r'$v_2$')\n",
+    "plt.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [],
+   "source": [
+    "%%capture\n",
+    "fig2, ((ax11, ax12), (ax21, ax22)) = plt.subplots(nrows=2, ncols=2)\n",
+    "\n",
+    "# Positions\n",
+    "ax11.set_xlabel(r'$x_1$')\n",
+    "ax11.set_ylabel(r'$x_2$')\n",
+    "ln11, = ax11.plot([], [])\n",
+    "ax11.set_xlim([np.min(x1), np.max(x1)])\n",
+    "ax11.set_ylim([np.min(x2), np.max(x2)])\n",
+    "\n",
+    "# Velocities\n",
+    "ax12.set_xlabel(r'$v_1$')\n",
+    "ax12.set_ylabel(r'$v_2$')\n",
+    "ln12, = ax12.plot([], [])\n",
+    "ax12.set_xlim([np.min(xd1), np.max(xd1)])\n",
+    "ax12.set_ylim([np.min(xd2), np.max(xd2)])\n",
+    "\n",
+    "# Phase spaces\n",
+    "ax21.set_xlabel(r'$\\mathbf{x}$')\n",
+    "ax21.set_ylabel(r'$\\mathbf{v}$')\n",
+    "ln21a, = ax21.plot([], [])\n",
+    "ln21b, = ax21.plot([], [])\n",
+    "ax21.set_xlim([min(np.min(x1), np.min(x2)), max(np.max(x1), np.max(x2))])\n",
+    "ax21.set_ylim([min(np.min(xd1), np.min(xd2)), max(np.max(xd1), np.max(xd2))])\n",
+    "\n",
+    "# F(t)\n",
+    "F1 = f1(t)\n",
+    "F2 = f2(t)\n",
+    "ax22.set_xlabel(r'$t$')\n",
+    "ax22.set_ylabel(r'$\\mathbf{F}(t)$')\n",
+    "ln22a, = ax22.plot([], [])\n",
+    "ln22b, = ax22.plot([], [])\n",
+    "ax22.set_xlim([t[0], t[-1]])\n",
+    "ax21.set_ylim([min(np.min(F1), np.min(F2)), max(np.max(F1), np.max(F2))])\n",
+    "\n",
+    "plt.tight_layout()\n",
+    "\n",
+    "def animate(i):\n",
+    "    ln11.set_data(x1[:i], x2[:i])\n",
+    "    ln12.set_data(xd1[:i], xd2[:i])\n",
+    "    ln21a.set_data(x1[:i], xd1[:i])\n",
+    "    ln21b.set_data(x2[:i], xd2[:i])\n",
+    "    ln22a.set_data(t[:i], F1[:i])\n",
+    "    ln22b.set_data(t[:i], F2[:i])\n",
+    "    \n",
+    "\n",
+    "anim = animation.FuncAnimation(fig2, animate, frames=len(t), interval=100, repeat_delay=1000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "anim"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
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+}