{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7f9508e6",
   "metadata": {},
   "source": [
    "# Exercise: Derivatives\n",
    "\n",
    "- by Börge Göbel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "04fafd2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d7d137f",
   "metadata": {},
   "source": [
    "### Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eeb0d15b",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt(\"04b_Exercise_velocity_acceleration_data_file.dat\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c635be8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.        ,   1.        ],\n",
       "       [  0.1       ,   1.01980001],\n",
       "       [  0.2       ,   1.03920011],\n",
       "       ...,\n",
       "       [ 99.8       ,  15.25565932],\n",
       "       [ 99.9       ,  15.33160759],\n",
       "       [100.        ,  15.40808206]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dc649d6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x20632563880>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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za0/eeg5+SVOAW5r74xbCwT84eu3JdmsQvwH0ErpTBBe+s/890m7/nQYx/NP8lFPl3j5MHPyJQ9kR8QywTVJ9Jrla10a2jDK0+upcQh+eXYpg7Ujn2RplsfzC67sO/WUL5vCTj67IJJg2rVne1SDwZRvvG5i/65ak2v6yBXMqHfqdpK3xfxd4DfB94HfTDyLiqOya9iz3+MstrweOJlL2WnS3ves876fbn0IGpeef5mtyx/krcmpNcSbq8aed1XNun9tjFVGG+edlfQK1l9JOv2r5aX3kmFcy/KI5qQd+L9t4H8MvKndPeWTLaGLoV32jlSTdDO7Oo9HrB/h+ROzKrFXjuMdfTr2G/kT1+X4NCucdnu308ndTdG+6m59MylwbX7T2m4lr8pS5/f00qVk9kt4JrKPxtK6A1wJnRsSX+tzOthz85dNtsHU7SNmPbwJFBOmgT5vsJvyL/kbVTpq//0GcGNCryQb/NmB5q5ff3Hz9XyLi4B4bsw/waeAgGj+pvzsibprofAd/uXRb059sQEymnLT3HlNzexCpl7GOebNnsGnN8oxa1JtBDv+XfOgannpm4kybAvykBrX9lp5n9bTOG1fa+XkXn9vOJ4BrI+JlwMHA7ZN4L8vR2pHtqcNt3uwZ7Dh/xaSDYcPpR3DRcUt6+oJ75PGnGVp9NYvWfjNxg+1etWY0dRv6yxbMKV3oQ2PGz8L9ZqU697KN92X299qtEy++qWPoA1x43JJ8GlNyaXv864DFNJ7cBTiOxtz+rjdgl7Q3sA14caQcYHCPvxy6Kb9kVWef7AqW/e5h9/LcQplKO510c29Fz5BJ83UxfQrc9Xf16e1Df57cfRvwJzS+bnt+clfSEmA98CMavf2bgVMjYsKf5R38xesm9POooRY5BjCyZZQzv7iVJzuPH7ZVxtJOJ2mfMi76m1lSiQfqM6A7Vj+Cfx7wxzRq8j3P6pE0DGwElkXEJkmfAB6JiL8ad94qYBXA/PnzX33vvff2cjnrg2562XnXfPvxDEGnBc/6ea1BHVQs+2wfbzo/sdLM6pH0R8DGiBhqfvxaYHVETPgzmHv8xUrTm4Li/nONbBnl9Cu30kMHPBdF94b7oZsB9jzLPmk6JXUb0B1rsoO7a4DXRMRJEfEXNHr+f5XwOW1FxM+A+yUtah56I42yj5VQmgEzaNT0i+pRHXPI/vzk/BVcVMKBu4X7zeKe87NZdiFPG04/gnmzZ6Q698DVV+c24Hv6F7YmnuMB3T9U1Kye9wKXS7oFWAL83STeyzKS5glIKMcDU9D4BjDZjUj6ZYoaZY8y/L30y6Y1y9l7j6mJ57WepM56bZ/F51xLUp+kzuvxdDKZWT3bI+KDGbbtd1zqKcaLz7468T9WWUK/nSyXh+6kbHPb+62bZaWz+rtIO+5Q9GyjopVmVk8vHPz5S1PTHZTaaV6LyNVpALGb8O/330va8YaqfwNOo6fgl/QSYF5E3Dju+OuA0Yi4u+8tbcPBn6+0s3gGbXpcVj8B1Cnwx+om/Ps1jTVtT7/MP4nmqdfg/wbwoYi4ZdzxYeCciPizvre0DQd/vtKUeAa9NzXZbwJ1Dfvxugn/yc5uetmaa/jt08kVikF7ViJLvQb/rRPtvCVpe0Tk8j/fwZ+fND0qh56N1e3Ty932xrt9Wrvudf2xep3OuWeH12ZOrklWNidefFOq/8AOfRtr05rlqad6Aty169epd0879LwNXYV+Gaf0llFS8P9A0injD0o6mcZSC1YRaadu+j+WtdNt+ENjgbeh1Vfzkg9d83vz/teObGdo9dVdb+W5cun8gRpzKlJSqWce8BXgCZ4N+mFgBvDnzYexMudST/bSbF7hEo8lKWobzkEfc8pKT6WeiHgwIg6nsfXijuavcyPisLxC37I3smU0MfTnzZ7h0LdEl59yGCuXzs/1mhcdt8Sh36VUe+5GxHXAdRm3xQpyxhe3JZ7jWRKWVrf7+PZqz6nijvPekuk1qmoyyy5YBaRZi8d1fetWa/mMrHr/82bPcOhPgoO/xtIM6E6fggfMrGcfOeaV7Dh/RdcDv52sXDrfP4FOUqpSj1XTWV++JfGcdccuyb4hVnmb1iyf1AY24MkF/eTgr6k0A7pe2dD66ZhD9v/d11PaJ6enTREXHHuwvw77LPUibUXydM7+S9pcZVAWYDOziU12IxarkDQDut68wqy6HPw14wFdM3Pw10yaOfse0DWrNgd/jawd2Z5Y4vGArln1OfhrJGkWxRS88qZZHRQW/JKmStrS3OzFMnbixTclnuMBXbN6KLLHfypwe4HXr400A7ou8ZjVRyHBL+kAYAXw6SKuXzdpBnRd4jGrj6J6/BcBHwR6fHjb0kozZz/vZXTNrFi5B7+ktwK7IqLjDl6SVknaLGnz7t27c2pdtaQp8UwBr2VuVjNF9PiXAUdJ2gF8HniDpMvGnxQR6yNiOCKG586dm3cbKyFNiccDumb1k3vwR8TZEXFARAwBxwPfjYiVebej6tKUeDyga1ZPnsdfQWk3TveArlk9Fbosc0RcD1xfZBuqKE2JxwO6ZvXlHn/FpFmWYeF+szyga1ZjDv6KSbMsw4bTj8ilLWZWTg7+CvGyDGaWhoO/ItaObPeyDGaWioO/Aka2jKbav9SzeMwMHPyVcNaXb0k8x7N4zKzFwT/g1o5s5/GnOi955GUZzGwsB/8AS1vi8YCumY3l4B9gp39ha+I5HtA1s/Ec/APq0PM2kPCclrdSNLO2HPwD6MSLb+LBR59IPM8lHjNrx8E/YNLM1weXeMxsYg7+AZJ2MHfhfrNc4jGzCTn4B0iawdx5s2d4LR4z68jBPyDSDOYCbFqzPPvGmNlAc/APgEPP25BqMNdP55pZGoVuxGLJFp9zLY88/nTieV5j38zScvCX2MvWXMNvn06u7yzcb5br+maWWu6lHkkvlHSdpNsl3Sbp1LzbUHYjW0YZWn11qtAHb6xiZt0posf/FPCBiPihpNnAzZI2RMSPCmhL6Zx48U2p5um3XOSHtMysS7kHf0Q8ADzQ/POjkm4H9gdqH/xpB3FbVi6d74e0zKxrhdb4JQ0BhwCbimxH0daObE/1YFaLgI8ft8Shb2Y9KSz4JT0H+DJwWkQ80ub1VcAqgPnzqzlNcWTLKKddubWrz9lzqrjjvLdk0yAzq4VCgl/SdBqhf3lEXNXunIhYD6wHGB4eTjfKOSC6reO3OPTNrB9yD35JAj4D3B4RF+Z9/SL0GvRjzZs9w0/lmllfFNHjXwb8V2C7pK3NYx+KiGsKaMuE+hHW/eJ5+mbWT0XM6vm/NMYnS6PbwdU8rVw630/kmllf1fbJ3ZEto5z5xa082Xmf8sK4l29mWall8Hc7Xz5PnqppZlmrVfCXqW7fjss6ZpaHWgR/L/Pl87LHtCl87O2L3cM3s9xUPvjL1st30JtZ0Sod/P2q5S9bMMd72JpZZVQ2+CcT+q61m1mVVTL4145s7zr0HfZmVheVDP4rNt2f+lyXccysbioZ/E9H8ppue+8xlVvOPTKH1piZlUvuWy/mYao6rwixbMEch76Z1VYlg/+EQ1/Y9vgUNbYqdGnHzOqskqWe1iDtFZvu5+kIpkqccOgLPXhrZgYoUtTDizY8PBybN28uuhlmZgNF0s0RMTz+eCVLPWZmNjEHv5lZzTj4zcxqxsFvZlYzDn4zs5oZiFk9knYD9/b46fsCD/WxOYPA91wPvud6mMw9vygi5o4/OBDBPxmSNrebzlRlvud68D3XQxb37FKPmVnNOPjNzGqmDsG/vugGFMD3XA++53ro+z1XvsZvZma/rw49fjMzG6PSwS/pSEl3SvqxpNVFt6ffJL1Q0nWSbpd0m6RTm8fnSNog6a7m788tuq39JmmqpC2SvtH8uNL3LGkfSV+SdEfz3/uwGtzz+5tf17dKukLSnlW7Z0mXSNol6dYxxya8R0lnN/PsTklv6vW6lQ1+SVOBfwTeDLwcOEHSy4ttVd89BXwgIv4jsBT4y+Y9rga+ExELge80P66aU4Hbx3xc9Xv+BHBtRLwMOJjGvVf2niXtD7wPGI6Ig4CpwPFU754vBcbvCtX2Hpv/t48HXtH8nE81c65rlQ1+4I+BH0fETyLiCeDzwNEFt6mvIuKBiPhh88+P0giD/Wnc52ebp30WOKaQBmZE0gHACuDTYw5X9p4l7Q28DvgMQEQ8ERG/oML33DQNmClpGrAX8FMqds8RcQPw8LjDE93j0cDnI+LxiLgH+DGNnOtalYN/f2Dsrus7m8cqSdIQcAiwCZgXEQ9A45sDsF+BTcvCRcAHgWfGHKvyPb8Y2A3872Z569OSZlHhe46IUeAC4D7gAeCXEfFtKnzPY0x0j33LtCoHf7uNdys5hUnSc4AvA6dFxCNFtydLkt4K7IqIm4tuS46mAa8C/ikiDgF+zeCXODpq1rWPBg4EXgDMkrSy2FYVrm+ZVuXg3wmM3Xz3ABo/KlaKpOk0Qv/yiLiqefhBSc9vvv58YFdR7cvAMuAoSTtolO/eIOkyqn3PO4GdEbGp+fGXaHwjqPI9/ylwT0TsjogngauAw6n2PbdMdI99y7QqB/8PgIWSDpQ0g8agyNcKblNfSRKNuu/tEXHhmJe+BpzU/PNJwFfzbltWIuLsiDggIoZo/Jt+NyJWUu17/hlwv6RFzUNvBH5Ehe+ZRolnqaS9ml/nb6QxhlXle26Z6B6/BhwvaQ9JBwILge/3dIWIqOwv4C3AvwF3A2uKbk8G9/cnNH7UuwXY2vz1FuB5NGYD3NX8fU7Rbc3o/o8AvtH8c6XvGVgCbG7+W48Az63BPZ8L3AHcCnwO2KNq9wxcQWMM40kaPfqTO90jsKaZZ3cCb+71un5y18ysZqpc6jEzszYc/GZmNePgNzOrGQe/mVnNOPjNzGrGwW9mVjMOfqs0Sc+TtLX562eSRpt//pWkT2VwvWMmWgVW0qWS7pH0ng6f/1pJPxq7TK9Zv3kev9WGpA8Dv4qICzK8xqU0Hir7UjevjTtvqHneQVm00cw9fqslSUeM2cTlw5I+K+nbknZIepukv5e0XdK1zfWQkPRqSd+TdLOkb7XWUxnznocDRwHrmj9VLEhow7HNTUa2Sbohq3s1G8/Bb9awgMYa/0cDlwHXRcQrgceAFc3w/wfgHRHxauAS4LyxbxAR/4/GeipnRsSSiLg74Zp/DbwpIg6m8Q3DLBfTim6AWUl8MyKelLSdxm5P1zaPbweGgEXAQcCGxpphTKWxxspk3AhcKukLNFafNMuFg9+s4XGAiHhG0pPx7ODXMzT+nwi4LSIO69cFI+I9kg6l8ZPGVklLIuLn/Xp/s4m41GOWzp3AXEmHQWMfBEmvaHPeo8DsNG8oaUFEbIqIvwYe4vfXWjfLjIPfLIVo7Nv8DuBjkrbRWAL78Danfh44s7lFYsfBXRqDwNubUzdvALb1s81mE/F0TrOceDqnlYV7/Gb5+SXwt0kPcAFfp1H6McuEe/xmZjXjHr+ZWc04+M3MasbBb2ZWMw5+M7OacfCbmdXM/wdRlttBtlKXCgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Coordinate x [m]')\n",
    "plt.scatter(data[:,0],data[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb7db420",
   "metadata": {},
   "source": [
    "### Task"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96ae330b",
   "metadata": {},
   "source": [
    "Calculate the velocity \\\\(v(t)=\\dot{x}(t)\\\\) and the acceleration \\\\(a(t)=\\ddot{x}(t)\\\\) for the loaded data set that describes a set of points \\\\((t_i,x_i)\\\\) for \\\\(i=0,\\dots,1000\\\\).\n",
    "\n",
    "1. Calculate \\\\(v_i\\\\) and \\\\(a_i\\\\) using the forward-differences, central-differences and Richardson methods\n",
    "2. Determine the maximum value of the acceleration and the corresponding time.\n",
    "\n",
    "Be careful, now we do not know the function \\\\(x(t)\\\\) but only its values for specific points. You have to define the functions for the derivativesa bit differently."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9c52bff",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "79f5edae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0. ,   0.1,   0.2, ...,  99.8,  99.9, 100. ])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "249408a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward(data):\n",
    "    derive = np.zeros(len(data[:,1]))\n",
    "    # for equidistant data\n",
    "    # h = (data[1,0]-data[0,0])\n",
    "    # velocity[:-1] = (data[1:,1]-data[:-1,1]) / h\n",
    "    # general\n",
    "    derive[:-1] = (data[1:,1]-data[:-1,1]) / (data[1:,0]-data[:-1,0])\n",
    "    # last value use backwards method (or just set to second-last value)\n",
    "    derive[-1] = (data[-1,1]-data[-2,1]) / (data[-1,0]-data[-2,0])\n",
    "    return np.transpose([data[:,0],derive])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "96f3fe3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "velocityForward = forward(data)\n",
    "accelerationForward = forward(forward(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "111e6b18",
   "metadata": {},
   "outputs": [],
   "source": [
    "def central(data):\n",
    "    derive = np.zeros(len(data[:,1]))\n",
    "    derive[1:-1] = (data[2:,1]-data[:-2,1]) / (data[2:,0]-data[:-2,0])\n",
    "    # first value use forward method (or just set to second value)\n",
    "    derive[0] = (data[1,1]-data[0,1]) / (data[1,0]-data[0,0])\n",
    "    # last value use backward method (or just set to second-last value)\n",
    "    derive[-1] = (data[-1,1]-data[-2,1]) / (data[-1,0]-data[-2,0])\n",
    "    return np.transpose([data[:,0],derive])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7160272e",
   "metadata": {},
   "outputs": [],
   "source": [
    "velocityCentral = central(data)\n",
    "accelerationCentral = central(central(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "99c0a289",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Richardson(data):\n",
    "    derive = np.zeros(len(data[:,1]))\n",
    "    derive[2:-2] = (-data[4:,1]+8*data[3:-1,1]-8*data[1:-3,1]+data[:-4,1]) / (12*(data[3:-1,0]-data[2:-2,0]))\n",
    "    # first values \n",
    "    derive[0] = (data[1,1]-data[0,1]) / (data[1,0]-data[0,0])\n",
    "    derive[1] = (data[2,1]-data[0,1]) / (data[2,0]-data[0,0])\n",
    "    # last values \n",
    "    derive[-2] = (data[-1,1]-data[-3,1]) / (data[-1,0]-data[-3,0])\n",
    "    derive[-1] = (data[-1,1]-data[-2,1]) / (data[-1,0]-data[-2,0])\n",
    "    return np.transpose([data[:,0],derive])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "de934efa",
   "metadata": {},
   "outputs": [],
   "source": [
    "velocityRichardson = Richardson(data)\n",
    "accelerationRichardson = Richardson(Richardson(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a88a9a53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Velocity v [m/s]')\n",
    "plt.scatter(velocityForward[:,0],velocityForward[:,1])\n",
    "plt.scatter(velocityCentral[:,0],velocityCentral[:,1])\n",
    "plt.scatter(velocityRichardson[:,0],velocityRichardson[:,1])\n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Acceleration a [m/s$^2$]')\n",
    "plt.scatter(accelerationForward[:,0],accelerationForward[:,1])\n",
    "plt.scatter(accelerationCentral[:,0],accelerationCentral[:,1])\n",
    "plt.scatter(accelerationRichardson[:,0],accelerationRichardson[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0cdf237",
   "metadata": {},
   "source": [
    "_- Without the inaccurate points_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7b79d2be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Velocity v [m/s]')\n",
    "plt.scatter(velocityForward[2:-2,0],velocityForward[2:-2,1])\n",
    "plt.scatter(velocityCentral[2:-2,0],velocityCentral[2:-2,1])\n",
    "plt.scatter(velocityRichardson[2:-2,0],velocityRichardson[2:-2,1])\n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Acceleration a [m/s$^2$]')\n",
    "plt.scatter(accelerationForward[4:-4,0],accelerationForward[4:-4,1])\n",
    "plt.scatter(accelerationCentral[4:-4,0],accelerationCentral[4:-4,1])\n",
    "plt.scatter(accelerationRichardson[4:-4,0],accelerationRichardson[4:-4,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47362f76",
   "metadata": {},
   "source": [
    "### How the data was generated"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "144954b1",
   "metadata": {},
   "source": [
    "- Position\n",
    "\\\\(\n",
    "x(t) = \\cos(at)+bt^5+ct^4+dt\n",
    "\\\\)\n",
    "\n",
    "\n",
    "- Parameters\n",
    "\\\\(\n",
    "a = 0.2\\,\\frac{1}{\\mathrm{s}}\\\\\n",
    "b = 0.95\\times 10^{-8}\\,\\mathrm{m}\\\\\n",
    "c = -10^{-6}\\,\\mathrm{m}\\\\\n",
    "d = 0.2\\,\\mathrm{m}\n",
    "\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1af30137",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2063287a340>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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za0/eeg5+SVOAW5r74xbCwT84eu3JdmsQvwH0ErpTBBe+s/890m7/nQYx/NP8lFPl3j5MHPyJQ9kR8QywTVJ9Jrla10a2jDK0+upcQh+eXYpg7Ujn2RplsfzC67sO/WUL5vCTj67IJJg2rVne1SDwZRvvG5i/65ak2v6yBXMqHfqdpK3xfxd4DfB94HfTDyLiqOya9iz3+MstrweOJlL2WnS3ves876fbn0IGpeef5mtyx/krcmpNcSbq8aed1XNun9tjFVGG+edlfQK1l9JOv2r5aX3kmFcy/KI5qQd+L9t4H8MvKndPeWTLaGLoV32jlSTdDO7Oo9HrB/h+ROzKrFXjuMdfTr2G/kT1+X4NCucdnu308ndTdG+6m59MylwbX7T2m4lr8pS5/f00qVk9kt4JrKPxtK6A1wJnRsSX+tzOthz85dNtsHU7SNmPbwJFBOmgT5vsJvyL/kbVTpq//0GcGNCryQb/NmB5q5ff3Hz9XyLi4B4bsw/waeAgGj+pvzsibprofAd/uXRb059sQEymnLT3HlNzexCpl7GOebNnsGnN8oxa1JtBDv+XfOgannpm4kybAvykBrX9lp5n9bTOG1fa+XkXn9vOJ4BrI+JlwMHA7ZN4L8vR2pHtqcNt3uwZ7Dh/xaSDYcPpR3DRcUt6+oJ75PGnGVp9NYvWfjNxg+1etWY0dRv6yxbMKV3oQ2PGz8L9ZqU697KN92X299qtEy++qWPoA1x43JJ8GlNyaXv864DFNJ7cBTiOxtz+rjdgl7Q3sA14caQcYHCPvxy6Kb9kVWef7AqW/e5h9/LcQplKO510c29Fz5BJ83UxfQrc9Xf16e1Df57cfRvwJzS+bnt+clfSEmA98CMavf2bgVMjYsKf5R38xesm9POooRY5BjCyZZQzv7iVJzuPH7ZVxtJOJ2mfMi76m1lSiQfqM6A7Vj+Cfx7wxzRq8j3P6pE0DGwElkXEJkmfAB6JiL8ad94qYBXA/PnzX33vvff2cjnrg2562XnXfPvxDEGnBc/6ea1BHVQs+2wfbzo/sdLM6pH0R8DGiBhqfvxaYHVETPgzmHv8xUrTm4Li/nONbBnl9Cu30kMHPBdF94b7oZsB9jzLPmk6JXUb0B1rsoO7a4DXRMRJEfEXNHr+f5XwOW1FxM+A+yUtah56I42yj5VQmgEzaNT0i+pRHXPI/vzk/BVcVMKBu4X7zeKe87NZdiFPG04/gnmzZ6Q698DVV+c24Hv6F7YmnuMB3T9U1Kye9wKXS7oFWAL83STeyzKS5glIKMcDU9D4BjDZjUj6ZYoaZY8y/L30y6Y1y9l7j6mJ57WepM56bZ/F51xLUp+kzuvxdDKZWT3bI+KDGbbtd1zqKcaLz7468T9WWUK/nSyXh+6kbHPb+62bZaWz+rtIO+5Q9GyjopVmVk8vHPz5S1PTHZTaaV6LyNVpALGb8O/330va8YaqfwNOo6fgl/QSYF5E3Dju+OuA0Yi4u+8tbcPBn6+0s3gGbXpcVj8B1Cnwx+om/Ps1jTVtT7/MP4nmqdfg/wbwoYi4ZdzxYeCciPizvre0DQd/vtKUeAa9NzXZbwJ1Dfvxugn/yc5uetmaa/jt08kVikF7ViJLvQb/rRPtvCVpe0Tk8j/fwZ+fND0qh56N1e3Ty932xrt9Wrvudf2xep3OuWeH12ZOrklWNidefFOq/8AOfRtr05rlqad6Aty169epd0879LwNXYV+Gaf0llFS8P9A0injD0o6mcZSC1YRaadu+j+WtdNt+ENjgbeh1Vfzkg9d83vz/teObGdo9dVdb+W5cun8gRpzKlJSqWce8BXgCZ4N+mFgBvDnzYexMudST/bSbF7hEo8lKWobzkEfc8pKT6WeiHgwIg6nsfXijuavcyPisLxC37I3smU0MfTnzZ7h0LdEl59yGCuXzs/1mhcdt8Sh36VUe+5GxHXAdRm3xQpyxhe3JZ7jWRKWVrf7+PZqz6nijvPekuk1qmoyyy5YBaRZi8d1fetWa/mMrHr/82bPcOhPgoO/xtIM6E6fggfMrGcfOeaV7Dh/RdcDv52sXDrfP4FOUqpSj1XTWV++JfGcdccuyb4hVnmb1iyf1AY24MkF/eTgr6k0A7pe2dD66ZhD9v/d11PaJ6enTREXHHuwvw77LPUibUXydM7+S9pcZVAWYDOziU12IxarkDQDut68wqy6HPw14wFdM3Pw10yaOfse0DWrNgd/jawd2Z5Y4vGArln1OfhrJGkWxRS88qZZHRQW/JKmStrS3OzFMnbixTclnuMBXbN6KLLHfypwe4HXr400A7ou8ZjVRyHBL+kAYAXw6SKuXzdpBnRd4jGrj6J6/BcBHwR6fHjb0kozZz/vZXTNrFi5B7+ktwK7IqLjDl6SVknaLGnz7t27c2pdtaQp8UwBr2VuVjNF9PiXAUdJ2gF8HniDpMvGnxQR6yNiOCKG586dm3cbKyFNiccDumb1k3vwR8TZEXFARAwBxwPfjYiVebej6tKUeDyga1ZPnsdfQWk3TveArlk9Fbosc0RcD1xfZBuqKE2JxwO6ZvXlHn/FpFmWYeF+szyga1ZjDv6KSbMsw4bTj8ilLWZWTg7+CvGyDGaWhoO/ItaObPeyDGaWioO/Aka2jKbav9SzeMwMHPyVcNaXb0k8x7N4zKzFwT/g1o5s5/GnOi955GUZzGwsB/8AS1vi8YCumY3l4B9gp39ha+I5HtA1s/Ec/APq0PM2kPCclrdSNLO2HPwD6MSLb+LBR59IPM8lHjNrx8E/YNLM1weXeMxsYg7+AZJ2MHfhfrNc4jGzCTn4B0iawdx5s2d4LR4z68jBPyDSDOYCbFqzPPvGmNlAc/APgEPP25BqMNdP55pZGoVuxGLJFp9zLY88/nTieV5j38zScvCX2MvWXMNvn06u7yzcb5br+maWWu6lHkkvlHSdpNsl3Sbp1LzbUHYjW0YZWn11qtAHb6xiZt0posf/FPCBiPihpNnAzZI2RMSPCmhL6Zx48U2p5um3XOSHtMysS7kHf0Q8ADzQ/POjkm4H9gdqH/xpB3FbVi6d74e0zKxrhdb4JQ0BhwCbimxH0daObE/1YFaLgI8ft8Shb2Y9KSz4JT0H+DJwWkQ80ub1VcAqgPnzqzlNcWTLKKddubWrz9lzqrjjvLdk0yAzq4VCgl/SdBqhf3lEXNXunIhYD6wHGB4eTjfKOSC6reO3OPTNrB9yD35JAj4D3B4RF+Z9/SL0GvRjzZs9w0/lmllfFNHjXwb8V2C7pK3NYx+KiGsKaMuE+hHW/eJ5+mbWT0XM6vm/NMYnS6PbwdU8rVw630/kmllf1fbJ3ZEto5z5xa082Xmf8sK4l29mWall8Hc7Xz5PnqppZlmrVfCXqW7fjss6ZpaHWgR/L/Pl87LHtCl87O2L3cM3s9xUPvjL1st30JtZ0Sod/P2q5S9bMMd72JpZZVQ2+CcT+q61m1mVVTL4145s7zr0HfZmVheVDP4rNt2f+lyXccysbioZ/E9H8ppue+8xlVvOPTKH1piZlUvuWy/mYao6rwixbMEch76Z1VYlg/+EQ1/Y9vgUNbYqdGnHzOqskqWe1iDtFZvu5+kIpkqccOgLPXhrZgYoUtTDizY8PBybN28uuhlmZgNF0s0RMTz+eCVLPWZmNjEHv5lZzTj4zcxqxsFvZlYzDn4zs5oZiFk9knYD9/b46fsCD/WxOYPA91wPvud6mMw9vygi5o4/OBDBPxmSNrebzlRlvud68D3XQxb37FKPmVnNOPjNzGqmDsG/vugGFMD3XA++53ro+z1XvsZvZma/rw49fjMzG6PSwS/pSEl3SvqxpNVFt6ffJL1Q0nWSbpd0m6RTm8fnSNog6a7m788tuq39JmmqpC2SvtH8uNL3LGkfSV+SdEfz3/uwGtzz+5tf17dKukLSnlW7Z0mXSNol6dYxxya8R0lnN/PsTklv6vW6lQ1+SVOBfwTeDLwcOEHSy4ttVd89BXwgIv4jsBT4y+Y9rga+ExELge80P66aU4Hbx3xc9Xv+BHBtRLwMOJjGvVf2niXtD7wPGI6Ig4CpwPFU754vBcbvCtX2Hpv/t48HXtH8nE81c65rlQ1+4I+BH0fETyLiCeDzwNEFt6mvIuKBiPhh88+P0giD/Wnc52ebp30WOKaQBmZE0gHACuDTYw5X9p4l7Q28DvgMQEQ8ERG/oML33DQNmClpGrAX8FMqds8RcQPw8LjDE93j0cDnI+LxiLgH+DGNnOtalYN/f2Dsrus7m8cqSdIQcAiwCZgXEQ9A45sDsF+BTcvCRcAHgWfGHKvyPb8Y2A3872Z569OSZlHhe46IUeAC4D7gAeCXEfFtKnzPY0x0j33LtCoHf7uNdys5hUnSc4AvA6dFxCNFtydLkt4K7IqIm4tuS46mAa8C/ikiDgF+zeCXODpq1rWPBg4EXgDMkrSy2FYVrm+ZVuXg3wmM3Xz3ABo/KlaKpOk0Qv/yiLiqefhBSc9vvv58YFdR7cvAMuAoSTtolO/eIOkyqn3PO4GdEbGp+fGXaHwjqPI9/ylwT0TsjogngauAw6n2PbdMdI99y7QqB/8PgIWSDpQ0g8agyNcKblNfSRKNuu/tEXHhmJe+BpzU/PNJwFfzbltWIuLsiDggIoZo/Jt+NyJWUu17/hlwv6RFzUNvBH5Ehe+ZRolnqaS9ml/nb6QxhlXle26Z6B6/BhwvaQ9JBwILge/3dIWIqOwv4C3AvwF3A2uKbk8G9/cnNH7UuwXY2vz1FuB5NGYD3NX8fU7Rbc3o/o8AvtH8c6XvGVgCbG7+W48Az63BPZ8L3AHcCnwO2KNq9wxcQWMM40kaPfqTO90jsKaZZ3cCb+71un5y18ysZqpc6jEzszYc/GZmNePgNzOrGQe/mVnNOPjNzGrGwW9mVjMOfqs0Sc+TtLX562eSRpt//pWkT2VwvWMmWgVW0qWS7pH0ng6f/1pJPxq7TK9Zv3kev9WGpA8Dv4qICzK8xqU0Hir7UjevjTtvqHneQVm00cw9fqslSUeM2cTlw5I+K+nbknZIepukv5e0XdK1zfWQkPRqSd+TdLOkb7XWUxnznocDRwHrmj9VLEhow7HNTUa2Sbohq3s1G8/Bb9awgMYa/0cDlwHXRcQrgceAFc3w/wfgHRHxauAS4LyxbxAR/4/GeipnRsSSiLg74Zp/DbwpIg6m8Q3DLBfTim6AWUl8MyKelLSdxm5P1zaPbweGgEXAQcCGxpphTKWxxspk3AhcKukLNFafNMuFg9+s4XGAiHhG0pPx7ODXMzT+nwi4LSIO69cFI+I9kg6l8ZPGVklLIuLn/Xp/s4m41GOWzp3AXEmHQWMfBEmvaHPeo8DsNG8oaUFEbIqIvwYe4vfXWjfLjIPfLIVo7Nv8DuBjkrbRWAL78Danfh44s7lFYsfBXRqDwNubUzdvALb1s81mE/F0TrOceDqnlYV7/Gb5+SXwt0kPcAFfp1H6McuEe/xmZjXjHr+ZWc04+M3MasbBb2ZWMw5+M7OacfCbmdXM/wdRlttBtlKXCgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.2\n",
    "b = 0.95e-8\n",
    "c = -1e-6\n",
    "d = 0.2\n",
    "\n",
    "def position(t):\n",
    "    return np.cos(a*t) + b*t**5 + c*t**4 + d*t\n",
    "\n",
    "tList = np.linspace(0,100,1001)\n",
    "xList = position(tList)\n",
    "\n",
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Coordinate x [m]')\n",
    "plt.scatter(tList,xList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a4aca004",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.transpose([tList,xList])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5ea97250",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.        ,   1.        ],\n",
       "       [  0.1       ,   1.01980001],\n",
       "       [  0.2       ,   1.03920011],\n",
       "       ...,\n",
       "       [ 99.8       ,  15.25565932],\n",
       "       [ 99.9       ,  15.33160759],\n",
       "       [100.        ,  15.40808206]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9d5a1447",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt(\"04b_Exercise_velocity_acceleration_data_file.dat\", data, fmt=\"%s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a930e53",
   "metadata": {},
   "source": [
    "### Compare with analytical solution\n",
    "\n",
    "- velocity & acceleration\n",
    "\\\\(\n",
    "v(t)=\\dot{x}(t) = -a\\sin(at) + 5bt^4+4ct^3+d\\\\\n",
    "a(t)=\\ddot{x}(t) = -a^2\\cos(at) + 20bt^3+12ct^2\n",
    "\\\\)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bb75ef65",
   "metadata": {},
   "outputs": [],
   "source": [
    "def velocity(t):\n",
    "    return -a*np.sin(a*t) + 5*b*t**4 +4*c*t**3 + d\n",
    "\n",
    "def acceleration(t):\n",
    "    return -a**2*np.cos(a*t) + 20*b*t**3 +12*c*t**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1b1c57a0",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tList = np.linspace(0,100,1001)\n",
    "vList = velocity(tList)\n",
    "aList = acceleration(tList)\n",
    "\n",
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Velocity v [m/s]')\n",
    "plt.scatter(tList,vList)\n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('Acceleration a [m/s$^2$]')\n",
    "plt.scatter(tList,aList)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd6b3255",
   "metadata": {},
   "source": [
    "_- Error_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f243366a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('$\\Delta v$ [m/s]')\n",
    "plt.plot(tList[2:-2],velocityForward[2:-2,1]-vList[2:-2],'blue')\n",
    "plt.plot(tList[2:-2],velocityCentral[2:-2,1]-vList[2:-2],'red')\n",
    "plt.plot(tList[2:-2],velocityRichardson[2:-2,1]-vList[2:-2],'green')\n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Time t [s]')\n",
    "plt.ylabel('$\\Delta a$ [m/s$^2$]')\n",
    "plt.plot(tList[4:-4],accelerationForward[4:-4,1]-aList[4:-4],'blue')\n",
    "plt.plot(tList[4:-4],accelerationCentral[4:-4,1]-aList[4:-4],'red')\n",
    "plt.plot(tList[4:-4],accelerationRichardson[4:-4,1]-aList[4:-4],'green')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d11c4a87",
   "metadata": {},
   "source": [
    "_- Total error_\n",
    "\\\\( \\sum_i (v_n(t_i)-v_a(t_i))^2 \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5251bc1c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.002427824988964186\n",
      "8.903209968415735e-08\n",
      "5.566204890981249e-16\n"
     ]
    }
   ],
   "source": [
    "print( sum((velocityForward[2:-2,1]-vList[2:-2])**2) )\n",
    "print( sum((velocityCentral[2:-2,1]-vList[2:-2])**2) )\n",
    "print( sum((velocityRichardson[2:-2,1]-vList[2:-2])**2) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f539f08",
   "metadata": {},
   "source": [
    "_- Total error_\n",
    "\\\\( \\sum_i (a_n(t_i)-a_a(t_i))^2 \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "69dec4e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00031896113294448787\n",
      "1.4528874612961403e-08\n",
      "9.195018806923526e-17\n"
     ]
    }
   ],
   "source": [
    "print( sum((accelerationForward[4:-4,1]-aList[4:-4])**2) )\n",
    "print( sum((accelerationCentral[4:-4,1]-aList[4:-4])**2) )\n",
    "print( sum((accelerationRichardson[4:-4,1]-aList[4:-4])**2) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7534a47d",
   "metadata": {},
   "source": [
    "### Determine maximum acceleration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9c535653",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00, -1.99954035e-02],\n",
       "       [ 1.00000000e-01, -2.99898219e-02],\n",
       "       [ 2.00000000e-01, -4.16368452e-02],\n",
       "       ...,\n",
       "       [ 9.98000000e+01,  5.39100475e-02],\n",
       "       [ 9.99000000e+01,  3.92904337e-02],\n",
       "       [ 1.00000000e+02,  2.63103838e-02]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accelerationRichardson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fad17ccf",
   "metadata": {},
   "outputs": [],
   "source": [
    "accelerationMax = max( accelerationRichardson[:,1] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "cb2d6d01",
   "metadata": {},
   "outputs": [],
   "source": [
    "indexAccelerationMax = np.argmax( accelerationRichardson[:,1] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4e51a6a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "timeAccelerationMax = accelerationRichardson[indexAccelerationMax,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "aca9cf3c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.058898335802765\n",
      "796\n",
      "79.60000000000001\n"
     ]
    }
   ],
   "source": [
    "print(accelerationMax)\n",
    "print(indexAccelerationMax)\n",
    "print(timeAccelerationMax)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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",
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