notebooks/Time-varying frames.ipynb

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    "# Time-varying frame\n",
    "\n",
    "> Renato Naville Watanabe, Marcos Duarte  \n",
    "> [Laboratory of Biomechanics and Motor Control](http://pesquisa.ufabc.edu.br/bmclab)  \n",
    "> Federal University of ABC, Brazil"
   ]
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   "source": [
    "<h1>Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Python-setup\" data-toc-modified-id=\"Python-setup-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Python setup</a></span></li><li><span><a href=\"#Cartesian-coordinate-system\" data-toc-modified-id=\"Cartesian-coordinate-system-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Cartesian coordinate system</a></span></li><li><span><a href=\"#Determination-of-a-coordinate-system\" data-toc-modified-id=\"Determination-of-a-coordinate-system-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Determination of a coordinate system</a></span></li><li><span><a href=\"#Time-varying-basis\" data-toc-modified-id=\"Time-varying-basis-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Time varying basis</a></span><ul class=\"toc-item\"><li><span><a href=\"#Tangential-versor\" data-toc-modified-id=\"Tangential-versor-4.1\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>Tangential versor</a></span></li><li><span><a href=\"#Normal-versor\" data-toc-modified-id=\"Normal-versor-4.2\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>Normal versor</a></span></li><li><span><a href=\"#Binormal-versor\" data-toc-modified-id=\"Binormal-versor-4.3\"><span class=\"toc-item-num\">4.3&nbsp;&nbsp;</span>Binormal versor</a></span></li></ul></li><li><span><a href=\"#Velocity-and-Acceleration-in-a-time-varying-frame\" data-toc-modified-id=\"Velocity-and-Acceleration-in-a-time-varying-frame-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Velocity and Acceleration in a time-varying frame</a></span><ul class=\"toc-item\"><li><span><a href=\"#Velocity\" data-toc-modified-id=\"Velocity-5.1\"><span class=\"toc-item-num\">5.1&nbsp;&nbsp;</span>Velocity</a></span></li><li><span><a href=\"#Acceleration\" data-toc-modified-id=\"Acceleration-5.2\"><span class=\"toc-item-num\">5.2&nbsp;&nbsp;</span>Acceleration</a></span></li></ul></li><li><span><a href=\"#Example\" data-toc-modified-id=\"Example-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Example</a></span><ul class=\"toc-item\"><li><span><a href=\"#Solving-numerically\" data-toc-modified-id=\"Solving-numerically-6.1\"><span class=\"toc-item-num\">6.1&nbsp;&nbsp;</span>Solving numerically</a></span></li><li><span><a href=\"#Symbolic-solution-(extra-reading)\" data-toc-modified-id=\"Symbolic-solution-(extra-reading)-6.2\"><span class=\"toc-item-num\">6.2&nbsp;&nbsp;</span>Symbolic solution (extra reading)</a></span></li></ul></li><li><span><a href=\"#Further-Reading\" data-toc-modified-id=\"Further-Reading-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>Further Reading</a></span></li><li><span><a href=\"#Video-lectures-on-the-Internet\" data-toc-modified-id=\"Video-lectures-on-the-Internet-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>Video lectures on the Internet</a></span></li><li><span><a href=\"#Problems\" data-toc-modified-id=\"Problems-9\"><span class=\"toc-item-num\">9&nbsp;&nbsp;</span>Problems</a></span></li><li><span><a href=\"#References\" data-toc-modified-id=\"References-10\"><span class=\"toc-item-num\">10&nbsp;&nbsp;</span>References</a></span></li></ul></div>"
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   "source": [
    "## Python setup"
   ]
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   "source": [
    "import numpy as np\n",
    "import sympy as sym\n",
    "from sympy.vector import CoordSys3D\n",
    "import matplotlib.pyplot as plt\n",
    "sym.init_printing()\n",
    "from sympy.plotting import plot_parametric\n",
    "from sympy.physics.mechanics import ReferenceFrame, Vector, dot\n",
    "from matplotlib.patches import FancyArrowPatch\n",
    "plt.rcParams.update({'figure.figsize':(8, 5), 'lines.linewidth':2})"
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    "## Cartesian coordinate system\n",
    "\n",
    "As we perceive the surrounding space as three-dimensional, a convenient coordinate system is the [Cartesian coordinate system](http://en.wikipedia.org/wiki/Cartesian_coordinate_system) in the [Euclidean space](http://en.wikipedia.org/wiki/Euclidean_space) with three orthogonal axes as shown below. The axes directions are commonly defined by the [right-hand rule](http://en.wikipedia.org/wiki/Right-hand_rule) and attributed the letters X, Y, Z. The orthogonality of the Cartesian coordinate system is convenient for its use in classical mechanics, most of the times the structure of space is assumed having the [Euclidean geometry](http://en.wikipedia.org/wiki/Euclidean_geometry) and as consequence, the motion in different directions are independent of each other.  \n",
    "<br>\n",
    "<figure><img src=\"./../images/CCS.png\" width=350/><figcaption><center><i>Figure. Representation of a point and its position vector in a Cartesian coordinate system.</i></center></figcaption></figure>  "
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    "## Determination of a coordinate system\n",
    "\n",
    "In Biomechanics, we may use different coordinate systems for convenience and refer to them as global, laboratory, local, anatomical, or technical reference frames or coordinate systems. \n",
    "\n",
    "From [linear algebra](http://en.wikipedia.org/wiki/Linear_algebra), a set of unit linearly independent vectors (orthogonal in the Euclidean space and each with norm (length) equals to one) that can represent any vector via [linear combination](http://en.wikipedia.org/wiki/Linear_combination) is called a <a href=\"http://en.wikipedia.org/wiki/Basis_(linear_algebra)\">basis</a> (or **orthonormal basis**). The figure below shows a point and its position vector in the Cartesian coordinate system and the corresponding versors (**unit vectors**) of the basis for this coordinate system. See the notebook [Scalar and vector](http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/ScalarVector.ipynb) for a description on vectors.  \n",
    "<figure><img src=\"./../images/vector3Dijk.png\" width=350/><figcaption><center><i>Figure. Representation of a point $\\mathbf{P}$ and its position vector $\\overrightarrow{\\mathbf{r}}$ in a Cartesian coordinate system. The versors <span class=\"notranslate\">$\\hat{\\mathbf{i}},\\, \\hat{\\mathbf{j}},\\, \\hat{\\mathbf{k}}\\,$ </span> form a basis for this coordinate system and are usually represented in the color sequence RGB (red, green, blue) for easier visualization.</i></center></figcaption></figure>  "
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    "One can see that the versors of the basis shown in the figure above have the following coordinates in the Cartesian coordinate system:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "\\hat{\\mathbf{i}} = \\begin{bmatrix}1\\\\0\\\\0 \\end{bmatrix}, \\quad \\hat{\\mathbf{j}} = \\begin{bmatrix}0\\\\1\\\\0 \\end{bmatrix}, \\quad \\hat{\\mathbf{k}} = \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\end{bmatrix}\n",
    "\\label{eq_1}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "Using the notation described in the figure above, the position vector $\\overrightarrow{\\mathbf{r}}$  can be expressed as:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "\\overrightarrow{\\mathbf{r}} = x\\hat{\\mathbf{i}} + y\\hat{\\mathbf{j}} + z\\hat{\\mathbf{k}}\n",
    "\\label{eq_2}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "However, to use a fixed basis can lead to very complex expressions."
   ]
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   "source": [
    "## Time varying basis"
   ]
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    "Consider that we have the position vector of a particle, moving in the path described by the parametric curve $s(t)$, described in a fixed reference frame as:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\hat{r}}(t) = {x}{\\bf\\hat{i}}+{y}{\\bf\\hat{j}} + {z}{\\bf\\hat{k}}\n",
    "\\label{eq_3}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "<figure><img src=\"./../images/velRefFrame.png\" width=500/><figcaption><center><i>Figure. Position vector of a moving particle in relation to a coordinate system.</i></center></figcaption></figure>  "
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    "### Tangential versor\n",
    "\n",
    "Often we describe all the kinematic variables in this fixed reference frame. However, it is often useful to define a time-varying basis, attached to some point of interest. In this case, what is usually done is to choose as one of the basis vector a unitary vector in the direction of the velocity of the particle. Defining this vector as:\n",
    "\n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\hat{e}_t} = \\frac{{\\bf\\vec{v}}}{\\Vert{\\bf\\vec{v}}\\Vert}\n",
    "\\label{eq_4}\n",
    "\\end{equation}\n",
    "</span>"
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     "\\bf\\vec{v": "<p><strong>SyntaxError</strong>: unexpected character after line continuation character (<ipython-input-1-59c79f8f7734>, line 1)</p>\n"
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    "### Normal versor\n",
    "\n",
    "For the second vector of the basis, we define first a vector of curvature of the path (the meaning of this curvature vector will be seeing in another notebook):\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\vec{C}} = \\frac{d{\\bf\\hat{e}_t}}{ds}\n",
    "\\label{eq_5}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "Note that $\\bf\\hat{e}_t$ is a function of the path $s(t)$. So, by the chain rule:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "\\frac{d{\\bf\\hat{e}_t}}{dt} = \\frac{d{\\bf\\hat{e}_t}}{ds}\\frac{ds}{dt} \\longrightarrow \\frac{d{\\bf\\hat{e}_t}}{ds} = \\frac{\\frac{d{\\bf\\hat{e}_t}}{dt}}{\\frac{ds}{dt}} \\longrightarrow {\\bf\\vec{C}} = \\frac{\\frac{d{\\bf\\hat{e}_t}}{dt}}{\\frac{ds}{dt}}\\longrightarrow {\\bf\\vec{C}} = \\frac{\\frac{d{\\bf\\hat{e}_t}}{dt}}{\\Vert{\\bf\\vec{v}}\\Vert}\n",
    "\\label{eq_6}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "Now we can define the second vector of the basis, ${\\bf\\hat{e}_n}$:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\hat{e}_n} = \\frac{{\\bf\\vec{C}}}{\\Vert{\\bf\\vec{C}}\\Vert}\n",
    "\\label{eq_7}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "<figure><img src=\"./../images/velRefFrameeten.png\" width=500/><figcaption><center><i>Figure. A moving particle and a corresponding time varying basis.</i></center></figcaption></figure> "
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   "source": [
    "### Binormal versor\n",
    "\n",
    "The third vector of the basis is obtained by the cross product between ${\\bf\\hat{e}_n}$ and ${\\bf\\hat{e}_t}$:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\hat{e}_b} = {\\bf\\hat{e}_t} \\times {\\bf\\hat{e}_n}\n",
    "\\label{eq_8}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "Note that the vectors <span class=\"notranslate\"> ${\\bf\\hat{e}_t}$ </span>, <span class=\"notranslate\"> ${\\bf\\hat{e}_n}$ </span> and <span class=\"notranslate\"> ${\\bf\\hat{e}_b}$ </span> vary together with the particle movement."
   ]
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   "source": [
    "## Velocity and Acceleration in a time-varying frame"
   ]
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     "d({\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t": "<p><strong>SyntaxError</strong>: unexpected character after line continuation character (<ipython-input-1-2c63c6b0c6c5>, line 1)</p>\n",
     "d\\bf\\vec{v": "<p><strong>SyntaxError</strong>: unexpected character after line continuation character (<ipython-input-1-dcdda8e1ec30>, line 1)</p>\n"
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   "source": [
    "### Velocity \n",
    "\n",
    "Given the expression of $r(t)$ in a fixed frame we can write the velocity <span class=\"notranslate\"> ${\\bf\\vec{v}(t)}$</span> as a function of the fixed frame of reference <span class=\"notranslate\"> ${\\bf\\hat{i}}$</span>, <span class=\"notranslate\"> ${\\bf\\hat{j}}$</span> and <span class=\"notranslate\"> ${\\bf\\hat{k}}$</span> (see http://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/KinematicsParticle.ipynb)).\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\vec{v}}(t) = \\dot{x}{\\bf\\hat{i}}+\\dot{y}{\\bf\\hat{j}}+\\dot{z}{\\bf\\hat{k}}\n",
    "\\label{eq_9}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "However, this can lead to very complex functions. So it is useful to use the basis find previously <span class=\"notranslate\">${\\bf\\hat{e}_t}$</span>, <span class=\"notranslate\"> ${\\bf\\hat{e}_n}$</span> and <span class=\"notranslate\">${\\bf\\hat{e}_b}$</span>.\n",
    "\n",
    "The velocity <span class=\"notranslate\"> ${\\bf\\vec{v}}$ </span> of the particle is, by the definition of <span class=\"notranslate\">${\\bf\\hat{e}_t}$</span>, in the direction of <span class=\"notranslate\">${\\bf\\hat{e}_t}$</span>:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\vec{v}}={\\Vert\\bf\\vec{v}\\Vert}.{\\bf\\hat{e}_t}\n",
    "\\label{eq_10}\n",
    "\\end{equation}\n",
    "</span>"
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     "d({\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t": "<p><strong>SyntaxError</strong>: unexpected character after line continuation character (<ipython-input-1-2c63c6b0c6c5>, line 1)</p>\n",
     "d\\bf\\vec{v": "<p><strong>SyntaxError</strong>: unexpected character after line continuation character (<ipython-input-1-dcdda8e1ec30>, line 1)</p>\n"
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   "source": [
    "### Acceleration\n",
    "\n",
    "The acceleration can be written in the fixed frame of reference as:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "{\\bf\\vec{a}}(t) = \\ddot{x}{\\bf\\hat{i}}+\\ddot{y}{\\bf\\hat{j}}+\\ddot{z}{\\bf\\hat{k}}\n",
    "\\label{eq_11}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "But for the same reasons of the velocity vector, it is useful to describe the acceleration vector in the time varying basis. We know that the acceleration is the time derivative of the velocity:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{align}\n",
    "{\\bf\\vec{a}} =& \\frac{{d\\bf\\vec{v}}}{dt}=\\\\\n",
    "    =&\\frac{{d({\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t}})}{dt}=\\\\\n",
    "    =&\\dot{\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t}+{\\Vert\\bf\\vec{v}\\Vert}\\dot{{\\bf\\hat{e}_t}}=\\\\\n",
    "    =&\\dot{\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t}+{\\Vert\\bf\\vec{v}\\Vert}\\frac{d{\\bf\\hat{e}_t}}{ds}\\frac{ds}{dt}=\\\\\n",
    "    =&\\dot{\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t}+{\\Vert\\bf\\vec{v}\\Vert}^2\\frac{d{\\bf\\hat{e}_t}}{ds}=\\\\\n",
    "    =&\\dot{\\Vert\\bf\\vec{v}\\Vert}{\\bf\\hat{e}_t}+{\\Vert\\bf\\vec{v}\\Vert}^2\\Vert{\\bf\\vec{C}} \\Vert {\\bf\\hat{e}_n}\n",
    "\\label{eq_12}\n",
    "\\end{align}\n",
    "</span>"
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   "source": [
    "## Example\n",
    "For example, consider that a particle follows the path described by the parametric curve below:\n",
    "<br>  \n",
    "<span class=\"notranslate\">\n",
    "\\begin{equation}\n",
    "\\vec{r}(t) = (10t+100){\\bf{\\hat{i}}} + \\left(-\\frac{9,81}{2}t^2+50t+100\\right){\\bf{\\hat{j}}}\n",
    "\\label{eq_13}\n",
    "\\end{equation}\n",
    "</span>\n",
    "\n",
    "This curve could be, for example, from a projectile motion. See http://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/ProjectileMotion.ipynb for an explanation on projectile motion."
   ]
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   "source": [
    "### Solving numerically\n",
    "\n",
    "Now we will obtain the time-varying basis numerically. This method is useful when it is not available a mathematical expression of the path. This often happens when you have available data collected experimentally (most of the cases in Biomechanics). \n",
    "\n",
    "First, data will be obtained from the expression of $r(t)$. This is done to replicate the example above. You could use data collected experimentally, for example."
   ]
  },
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   "source": [
    "t = np.linspace(0, 10, 1000).reshape(-1,1)\n",
    "r = np.hstack((10*t + 100, -9.81/2*t**2 + 50*t + 100))"
   ]
  },
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   },
   "source": [
    "Now, to obtain the <span class=\"notranslate\"> $\\bf{\\hat{e_t}}$ </span> versor, we can use Equation (4)."
   ]
  },
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   "execution_count": 3,
   "metadata": {
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     "end_time": "2020-10-11T03:44:08.299722Z",
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   "source": [
    "dt = t[1]\n",
    "v = np.diff(r,axis=0)/dt\n",
    "vNorm  = np.linalg.norm(v, axis=1, keepdims=True)\n",
    "\n",
    "et = v/vNorm"
   ]
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   "source": [
    "And to obtain the versor <span class=\"notranslate\">$\\bf{\\hat{e_n}}$</span>, we can use Equation (8)."
   ]
  },
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   "source": [
    "C = np.diff(et,axis=0)/dt\n",
    "C = C/vNorm[1:]\n",
    "\n",
    "CNorm = np.linalg.norm(C, axis=1, keepdims=True)\n",
    "en = C/CNorm"
   ]
  },
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   "execution_count": 5,
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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(r[:, 0], r[:, 1], '.')\n",
    "ax = fig.add_axes([0, 0, 1, 1])\n",
    "time = np.linspace(0, 10, 10)\n",
    "for i in np.arange(0, len(t)-2, 50):\n",
    "    vec1 = FancyArrowPatch(r[i, :], r[i, :]+10*et[i, :], mutation_scale=20, color='r')\n",
    "    vec2 = FancyArrowPatch(r[i, :], r[i, :]+10*en[i, :], mutation_scale=20, color='g')\n",
    "    ax.add_artist(vec1)\n",
    "    ax.add_artist(vec2)\n",
    "plt.xlim((80, 250))\n",
    "plt.ylim((80, 250))\n",
    "plt.legend([vec1, vec2], [r'$\\vec{e_t}$', r'$\\vec{e_{n}}$'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:08.782372Z",
     "start_time": "2020-10-11T03:44:08.780178Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "v  = vNorm*et\n",
    "vNormDot  = np.diff(vNorm, axis=0)/dt\n",
    "\n",
    "a = vNormDot*et[1:,:] + CNorm*en*vNorm[1:]**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.150683Z",
     "start_time": "2020-10-11T03:44:08.783198Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(r[:, 0], r[:, 1], '.')\n",
    "ax = fig.add_axes([0, 0, 1, 1])\n",
    "for i in range(0, len(t)-2, 50):\n",
    "    vec1 = FancyArrowPatch(r[i, :], r[i, :]+v[i, :], mutation_scale=10, color='r')\n",
    "    vec2 = FancyArrowPatch(r[i, :], r[i, :]+a[i, :], mutation_scale=10, color='g')\n",
    "    ax.add_artist(vec1)\n",
    "    ax.add_artist(vec2)\n",
    "plt.xlim((80, 250))\n",
    "plt.ylim((80, 250))\n",
    "plt.legend([vec1, vec2], [r'$\\vec{v}$', r'$\\vec{a}$'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Symbolic solution (extra reading)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The computation here will be performed symbolically, with the symbolic math package of Python, Sympy. Below,a reference frame, called O,  and a varible for time (t) are defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.154388Z",
     "start_time": "2020-10-11T03:44:09.152278Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "O = sym.vector.CoordSys3D(' ')\n",
    "t = sym.symbols('t')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Below the vector $r(t)$ is defined symbolically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.276352Z",
     "start_time": "2020-10-11T03:44:09.155751Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle (10 t + 100)\\mathbf{\\hat{i}_{ }} + (- 4.905 t^{2} + 50 t + 100)\\mathbf{\\hat{j}_{ }}$"
      ],
      "text/plain": [
       "(10*t + 100)* .i + (-4.905*t**2 + 50*t + 100)* .j"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = (10*t+100)*O.i + (-9.81/2*t**2+50*t+100)*O.j+0*O.k\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.425806Z",
     "start_time": "2020-10-11T03:44:09.277382Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot_parametric(r.dot(O.i), r.dot(O.j), (t, 0, 10), line_width=4, aspect_ratio=(2, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.547462Z",
     "start_time": "2020-10-11T03:44:09.426760Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle (10)\\mathbf{\\hat{i}_{ }} + (50 - 9.81 t)\\mathbf{\\hat{j}_{ }}$"
      ],
      "text/plain": [
       "10* .i + (50 - 9.81*t)* .j"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = sym.diff(r)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.672532Z",
     "start_time": "2020-10-11T03:44:09.548563Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle (\\frac{10}{\\sqrt{2500 \\left(1 - 0.1962 t\\right)^{2} + 100}})\\mathbf{\\hat{i}_{ }} + (\\frac{50 - 9.81 t}{\\sqrt{2500 \\left(1 - 0.1962 t\\right)^{2} + 100}})\\mathbf{\\hat{j}_{ }}$"
      ],
      "text/plain": [
       "(10/sqrt(2500*(1 - 0.1962*t)**2 + 100))* .i + ((50 - 9.81*t)/sqrt(2500*(1 - 0.1962*t)**2 + 100))* .j"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "et = v/sym.sqrt(v.dot(v))\n",
    "et"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:09.812340Z",
     "start_time": "2020-10-11T03:44:09.673587Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle (\\frac{10 \\left(490.5 - 96.2361 t\\right)}{\\left(2500 \\left(1 - 0.1962 t\\right)^{2} + 100\\right)^{2}})\\mathbf{\\hat{i}_{ }} + (\\frac{\\frac{\\left(50 - 9.81 t\\right) \\left(490.5 - 96.2361 t\\right)}{\\left(2500 \\left(1 - 0.1962 t\\right)^{2} + 100\\right)^{\\frac{3}{2}}} - \\frac{9.81}{\\sqrt{2500 \\left(1 - 0.1962 t\\right)^{2} + 100}}}{\\sqrt{2500 \\left(1 - 0.1962 t\\right)^{2} + 100}})\\mathbf{\\hat{j}_{ }}$"
      ],
      "text/plain": [
       "(10*(490.5 - 96.2361*t)/(2500*(1 - 0.1962*t)**2 + 100)**2)* .i + (((50 - 9.81*t)*(490.5 - 96.2361*t)/(2500*(1 - 0.1962*t)**2 + 100)**(3/2) - 9.81/sqrt(2500*(1 - 0.1962*t)**2 + 100))/sqrt(2500*(1 - 0.1962*t)**2 + 100))* .j"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = sym.diff(et)/sym.sqrt(v.dot(v))\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:10.627457Z",
     "start_time": "2020-10-11T03:44:09.813393Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle (\\frac{2500000 \\left(1.0 - 0.1962 t\\right)}{\\sqrt{\\frac{6250000000000 \\left(0.1962 t - 1\\right)^{2} + 156250000000000.0 \\left(- \\left(0.1962 t - 1\\right)^{2} + 4.07747196738022 \\cdot 10^{-5} \\left(9.81 t - 50\\right) \\left(96.2361 t - 490.5\\right) - \\frac{1}{25}\\right)^{2}}{\\left(25 \\left(0.1962 t - 1\\right)^{2} + 1\\right)^{4}}} \\left(25 \\left(0.1962 t - 1\\right)^{2} + 1\\right)^{2}})\\mathbf{\\hat{i}_{ }} + (\\frac{250000 \\left(- 50.0 \\left(0.1962 t - 1\\right)^{2} + 0.00203873598369011 \\left(9.81 t - 50\\right) \\left(96.2361 t - 490.5\\right) - 2.0\\right)}{\\sqrt{\\frac{6250000000000 \\left(0.1962 t - 1\\right)^{2} + 156250000000000.0 \\left(- \\left(0.1962 t - 1\\right)^{2} + 4.07747196738022 \\cdot 10^{-5} \\left(9.81 t - 50\\right) \\left(96.2361 t - 490.5\\right) - \\frac{1}{25}\\right)^{2}}{\\left(25 \\left(0.1962 t - 1\\right)^{2} + 1\\right)^{4}}} \\left(25 \\left(0.1962 t - 1\\right)^{2} + 1\\right)^{2}})\\mathbf{\\hat{j}_{ }}$"
      ],
      "text/plain": [
       "(2500000*(1.0 - 0.1962*t)/(sqrt((6250000000000*(0.1962*t - 1)**2 + 156250000000000.0*(-(0.1962*t - 1)**2 + 4.07747196738022e-5*(9.81*t - 50)*(96.2361*t - 490.5) - 1/25)**2)/(25*(0.1962*t - 1)**2 + 1)**4)*(25*(0.1962*t - 1)**2 + 1)**2))* .i + (250000*(-50.0*(0.1962*t - 1)**2 + 0.00203873598369011*(9.81*t - 50)*(96.2361*t - 490.5) - 2.0)/(sqrt((6250000000000*(0.1962*t - 1)**2 + 156250000000000.0*(-(0.1962*t - 1)**2 + 4.07747196738022e-5*(9.81*t - 50)*(96.2361*t - 490.5) - 1/25)**2)/(25*(0.1962*t - 1)**2 + 1)**4)*(25*(0.1962*t - 1)**2 + 1)**2))* .j"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "en = C/(sym.sqrt(C.dot(C)))\n",
    "sym.simplify(en)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:11.193210Z",
     "start_time": "2020-10-11T03:44:10.628587Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes([0, 0, 1, 1])    \n",
    "time = np.linspace(0, 10, 30)\n",
    "for instant in time:\n",
    "    vt = FancyArrowPatch([float(r.dot(O.i).subs(t,instant)),float(r.dot(O.j).subs(t,instant))], \n",
    "                         [float(r.dot(O.i).subs(t,instant))+10*float(et.dot(O.i).subs(t,instant)),\n",
    "                          float(r.dot(O.j).subs(t, instant))+10*float(et.dot(O.j).subs(t,instant))], \n",
    "                         mutation_scale=20,\n",
    "                         arrowstyle=\"->\",color=\"r\",label='${\\hat{e_t}}$', lw=2)\n",
    "    vn = FancyArrowPatch([float(r.dot(O.i).subs(t, instant)),float(r.dot(O.j).subs(t,instant))], \n",
    "                         [float(r.dot(O.i).subs(t, instant))+10*float(en.dot(O.i).subs(t, instant)),\n",
    "                          float(r.dot(O.j).subs(t, instant))+10*float(en.dot(O.j).subs(t, instant))], \n",
    "                         mutation_scale=20,\n",
    "                         arrowstyle=\"->\",color=\"g\",label='${\\hat{e_n}}$', lw=2)\n",
    "    ax.add_artist(vn)\n",
    "    ax.add_artist(vt)\n",
    "plt.xlim((90, 250))\n",
    "plt.ylim((90, 250))\n",
    "plt.xlabel('x')\n",
    "plt.legend(handles=[vt, vn], fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Now we can find the vectors ${\\bf\\vec{v}}$ and ${\\bf\\vec{a}}$ described in the time varying frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:11.197721Z",
     "start_time": "2020-10-11T03:44:11.194309Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "v = sym.sqrt(v.dot(v))*et"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:11.440643Z",
     "start_time": "2020-10-11T03:44:11.198650Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle (- \\frac{245250.0 \\left(0.1962 t - 1\\right)^{2} + 9810.0}{25000 \\left(0.1962 t - 1\\right)^{2} + 1000})\\mathbf{\\hat{j}_{ }}$"
      ],
      "text/plain": [
       "(-(245250.0*(0.1962*t - 1)**2 + 9810.0)/(25000*(0.1962*t - 1)**2 + 1000))* .j"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = sym.diff(sym.sqrt(v.dot(v)))*et+v.dot(v)*sym.sqrt(C.dot(C))*en\n",
    "sym.simplify(sym.simplify(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-11T03:44:11.708072Z",
     "start_time": "2020-10-11T03:44:11.441849Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes([0, 0, 1, 1])    \n",
    "time = np.linspace(0, 10, 10)\n",
    "for instant in time:\n",
    "    vt = FancyArrowPatch([float(r.dot(O.i).subs(t,instant)),float(r.dot(O.j).subs(t,instant))], \n",
    "                         [float(r.dot(O.i).subs(t,instant))+float(v.dot(O.i).subs(t,instant)),\n",
    "                          float(r.dot(O.j).subs(t, instant))+float(v.dot(O.j).subs(t,instant))], \n",
    "                         mutation_scale=20,\n",
    "                         arrowstyle=\"->\",color=\"r\",label='${{v}}$', lw=2)\n",
    "    vn = FancyArrowPatch([float(r.dot(O.i).subs(t, instant)),float(r.dot(O.j).subs(t,instant))], \n",
    "                         [float(r.dot(O.i).subs(t, instant))+float(a.dot(O.i).subs(t, instant)),\n",
    "                          float(r.dot(O.j).subs(t, instant))+float(a.dot(O.j).subs(t, instant))], \n",
    "                         mutation_scale=20,\n",
    "                         arrowstyle=\"->\",color=\"g\",label='${{a}}$', lw=2)\n",
    "    ax.add_artist(vn)\n",
    "    ax.add_artist(vt)\n",
    "plt.xlim((60, 250))\n",
    "plt.ylim((60, 250))\n",
    "plt.legend(handles=[vt, vn], fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading\n",
    "\n",
    " - Read pages 932-971 of the 18th chapter of the [Ruina and Rudra's book](http://ruina.tam.cornell.edu/Book/index.html) about time-varying basis vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Video lectures on the Internet\n",
    "\n",
    " - [Time Varying Vectors](https://youtu.be/Xbl7U9HvP9A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problems\n",
    "\n",
    "1. Obtain the vectors <span class=\"notranslate\"> $\\hat{e_n}$ </span> and <span class=\"notranslate\"> $\\hat{e_t}$ </span> for the problem 17.1.1 from Ruina and Rudra's book.\n",
    "2. Solve the problem 17.1.9 from Ruina and Rudra's book.\n",
    "3. Write a Python program to solve the problem 17.1.10 (only the part of <span class=\"notranslate\"> $\\hat{e_n}$ </span> and <span class=\"notranslate\"> $\\hat{e_t}$</span>)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## References\n",
    "\n",
    "+ Ruina A, Rudra P (2019) [Introduction to Statics and Dynamics](http://ruina.tam.cornell.edu/Book/index.html). Oxford University Press. "
   ]
  }
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