{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Polar and Cylindrical Frame of Reference\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Contents

\n", "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python setup" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import numpy as np\n", "import sympy as sym\n", "from sympy.plotting import plot_parametric,plot3d_parametric_line\n", "from sympy.vector import CoordSys3D\n", "import matplotlib.pyplot as plt\n", "# from matplotlib import rc\n", "# rc('text', usetex=True)\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Consider that we have the position vector $\\bf\\vec{r}$ of a particle, moving in a circular path indicated in the figure below by a dashed line. This vector $\\bf\\vec{r(t)}$ is described in a fixed reference frame as:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "{\\bf\\vec{r}}(t) = x(t){\\bf\\hat{i}} + y(t){\\bf\\hat{j}} + z(t){\\bf\\hat{k}}\n", "\\label{eq_1}\n", "\\end{equation}\n", "\n", "\n", "
Figure. Position vector of a moving particle moving in a circular path.
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Naturally, we could describe all the kinematic variables in the fixed reference frame. But in circular motions, is convenient to define a basis with a vector in the direction of the position vector $\\bf\\vec{r}$. So, the vector $\\bf\\hat{e_R}$ is defined as:\n", "\n", "\n", "\\begin{equation}\n", "{\\bf\\hat{e_R}} = \\frac{\\bf\\vec{r}}{\\Vert{\\bf\\vec{r} }\\Vert}\n", "\\label{eq_2}\n", "\\end{equation}\n", "\n", "\n", "The second vector of the basis can be obtained by the cross multiplication between $\\bf\\hat{k}$ and $\\bf\\hat{e_R}$:\n", "

\n", "\n", "\n", "\\begin{equation}\n", "{\\bf\\hat{e_\\theta}} = {\\bf\\hat{k}} \\times {\\bf\\hat{e_R}}\n", "\\label{eq_3}\n", "\\end{equation}\n", "\n", "\n", "\n", "The third vector of the basis is the conventional ${\\bf\\hat{k}}$ vector.\n", "\n", "
Figure. Position vector of a particle moving in a circular path and a time-varying basis>
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "This basis can be used also for non-circular movements. For a 3D movement, the versor ${\\bf\\hat{e_R}}$ is obtained by removing the projection of the vector ${\\bf\\vec{r}}$ onto the versor ${\\bf\\hat{k}}$:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "{\\bf\\hat{e_R}} = \\frac{\\bf\\vec{r} - ({\\bf\\vec{r}.{\\bf\\hat{k}}){\\bf\\hat{k}}}}{\\Vert\\bf\\vec{r} - ({\\bf\\vec{r}.{\\bf\\hat{k}}){\\bf\\hat{k}}\\Vert}}\n", "\\label{eq_4}\n", "\\end{equation}\n", "\n", "\n", "
Figure. Position vector of a moving particle and a time-varying basis>
\n", "\n", "Note that if the movement is on a plane, the expression above is equal to ${\\bf\\hat{e_R}} = \\frac{\\bf\\vec{r}}{\\Vert{\\bf\\vec{r} }\\Vert}$ since the projection of $\\bf\\vec{r}$ on the $\\bf\\hat{k}$ versor is zero." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Time-derivative of the versors ${\\bf\\hat{e_R}}$ and ${\\bf\\hat{e_\\theta}}$\n", "\n", "To obtain the expressions of the velocity and acceleration vectors, it is necessary to obtain the expressions of the time-derivative of the vectors ${\\bf\\hat{e_R}}$ and ${\\bf\\hat{e_\\theta}}$.\n", "\n", "This can be done by noting that:\n", "
\n", "
\n", "\n", "\\begin{align}\n", "{\\bf\\hat{e_R}} &= \\cos(\\theta){\\bf\\hat{i}} + \\sin(\\theta){\\bf\\hat{j}}\\\\\n", "{\\bf\\hat{e_\\theta}} &= -\\sin(\\theta){\\bf\\hat{i}} + \\cos(\\theta){\\bf\\hat{j}}\n", "\\label{eq_5}\n", "\\end{align}\n", "\n", "\n", "Deriving ${\\bf\\hat{e_R}}$ we obtain:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "\\frac{d{\\bf\\hat{e_R}}}{dt} = -\\sin(\\theta)\\dot\\theta{\\bf\\hat{i}} + \\cos(\\theta)\\dot\\theta{\\bf\\hat{j}} = \\dot{\\theta}{\\bf\\hat{e_\\theta}}\n", "\\label{eq_6}\n", "\\end{equation}\n", "\n", "\n", "Similarly, we obtain the time-derivative of ${\\bf\\hat{e_\\theta}}$:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", " \\frac{d{\\bf\\hat{e_\\theta}}}{dt} = -\\cos(\\theta)\\dot\\theta{\\bf\\hat{i}} - \\sin(\\theta)\\dot\\theta{\\bf\\hat{j}} = -\\dot{\\theta}{\\bf\\hat{e_R}}\n", "\\label{eq_7}\n", "\\end{equation}\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Position, velocity and acceleration" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Position\n", "\n", "The position vector $\\bf\\vec{r}$, from the definition of $\\bf\\hat{e_R}$, is:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "{\\bf\\vec{r}} = R{\\bf\\hat{e_R}} + z{\\bf\\hat{k}}\n", "\\label{eq_8}\n", "\\end{equation}\n", "\n", "\n", "where $R = \\Vert\\bf\\vec{r} - ({\\bf\\vec{r}.{\\bf\\hat{k}}){\\bf\\hat{k}}\\Vert}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Velocity\n", "\n", "The velocity vector $\\bf\\vec{v}$ is obtained by deriving the vector $\\bf\\vec{r}$:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "{\\bf\\vec{v}} = \\frac{d(R{\\bf\\hat{e_R}})}{dt} + \\dot{z}{\\bf\\hat{k}} = \\dot{R}{\\bf\\hat{e_R}}+R\\frac{d\\bf\\hat{e_R}}{dt}=\\dot{R}{\\bf\\hat{e_R}}+R\\dot{\\theta}{\\bf\\hat{e_\\theta}}+ \\dot{z}{\\bf\\hat{k}}\n", "\\label{eq_9}\n", "\\end{equation}\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Acceleration\n", "\n", "The acceleration vector $\\bf\\vec{a}$ is obtained by deriving the velocity vector:\n", "
\n", "
\n", "\n", "\\begin{align}\n", "{\\bf\\vec{a}} =& \\frac{d(\\dot{R}{\\bf\\hat{e_R}}+R\\dot{\\theta}{\\bf\\hat{e_\\theta}}+\\dot{z}{\\bf\\hat{k}})}{dt}=\\\\\\nonumber\n", " =&\\ddot{R}{\\bf\\hat{e_R}}+\\dot{R}\\frac{d\\bf\\hat{e_R}}{dt} + \\dot{R}\\dot{\\theta}{\\bf\\hat{e_\\theta}} + R\\ddot{\\theta}{\\bf\\hat{e_\\theta}} + R\\dot{\\theta}\\frac{d{\\bf\\hat{e_\\theta}}}{dt} + \\ddot{z}{\\bf\\hat{k}}=\\\\\\nonumber\n", " =&\\ddot{R}{\\bf\\hat{e_R}}+\\dot{R}\\dot{\\theta}{\\bf\\hat{e_\\theta}} + \\dot{R}\\dot{\\theta}{\\bf\\hat{e_\\theta}} + R\\ddot{\\theta}{\\bf\\hat{e_\\theta}} - R\\dot{\\theta}^2{\\bf\\hat{e_R}}+ \\ddot{z}{\\bf\\hat{k}} =\\\\\n", " =&\\ddot{R}{\\bf\\hat{e_R}}+2\\dot{R}\\dot{\\theta}{\\bf\\hat{e_\\theta}}+ R\\ddot{\\theta}{\\bf\\hat{e_\\theta}} - {R}\\dot{\\theta}^2{\\bf\\hat{e_R}}+ \\ddot{z}{\\bf\\hat{k}} =\\\\\\nonumber\n", " =&(\\ddot{R}-R\\dot{\\theta}^2){\\bf\\hat{e_R}}+(2\\dot{R}\\dot{\\theta} + R\\ddot{\\theta}){\\bf\\hat{e_\\theta}}+ \\ddot{z}{\\bf\\hat{k}}\\nonumber\n", "\\label{eq_10}\n", "\\end{align}\n", "\n", "\n", "+ The term $\\ddot{R}$ is an acceleration in the radial direction.\n", "\n", "+ The term $R\\ddot{\\theta}$ is an angular acceleration.\n", "\n", "+ The term $\\ddot{z}$ is an acceleration in the $\\bf\\hat{k}$ direction.\n", "\n", "+ The term $-R\\dot{\\theta}^2$ is the well known centripetal acceleration.\n", "\n", "+ The term $2\\dot{R}\\dot{\\theta}$ is known as Coriolis acceleration. This term may be difficult to understand intuitively. It appears when there is displacement in the radial and angular directions at the same time." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Important to note\n", "\n", "The reader must bear in mind that the use of a different basis to represent the position, velocity or acceleration vectors is only a different representation of the same vector. For example, for the acceleration vector:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "{\\bf\\vec{a}} = \\ddot{x}{\\bf\\hat{i}}+ \\ddot{y}{\\bf\\hat{j}} + \\ddot{z}{\\bf\\hat{k}}=(\\ddot{R}-R\\dot{\\theta}^2){\\bf\\hat{e_R}}+(2\\dot{R}\\dot{\\theta} + R\\ddot{\\theta}){\\bf\\hat{e_\\theta}} + \\ddot{z}{\\bf\\hat{k}}=\\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_11}\n", "\\end{equation}\n", "\n", "\n", "In which the last equality is the acceleration vector represented in the path-coordinate of the particle (see http://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/Time-varying%20frames.ipynb). " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "## Example\n", "\n", "Consider a particle following the spiral path described below:\n", "
\n", "
\n", "\n", "\\begin{equation}\n", "{\\bf\\vec{r}}(t) = (2\\sqrt{t}\\cos(t)){\\bf\\hat{i}}+ (2\\sqrt{t}\\sin(t)){\\bf\\hat{j}}\n", "\\label{eq_12}\n", "\\end{equation}\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Solving numerically " ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "t = np.linspace(0.01,10,30).reshape(-1,1) #create a time vector and reshapes it to a column vector\n", "R = 2*np.sqrt(t)\n", "theta = t\n", "rx = R*np.cos(t)\n", "ry = R*np.sin(t)\n", "r = np.hstack((rx, ry)) # creates the position vector by stacking rx and ry horizontally" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "e_r = r/np.linalg.norm(r, axis=1, keepdims=True) # defines e_r vector\n", "e_theta = np.cross([0,0,1],e_r)[:,0:-1] # defines e_theta vector\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "dt = t[1] #defines delta_t\n", "Rdot = np.diff(R, axis=0)/dt #find the R derivative\n", "thetaDot = np.diff(theta, axis=0)/dt #find the angle derivative\n", "v = Rdot*e_r[0:-1,:] +R[0:-1]*thetaDot*e_theta[0:-1,:] # find the linear velocity." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "Rddot = np.diff(Rdot, axis=0)/dt\n", "thetaddot = np.diff(thetaDot, axis=0)/dt" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "a = ((Rddot - R[1:-1]*thetaDot[0:-1]**2)*e_r[1:-1,:]\n", " + (2*Rdot[0:-1]*thetaDot[0:-1] + Rdot[0:-1]*thetaddot)*e_theta[1:-1,:])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The versors $\\bf\\hat{e_R}$, $\\bf\\hat{e_\\theta}$ are plotted below at some points of the path." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import FancyArrowPatch\n", "%matplotlib inline\n", "plt.rcParams['figure.figsize'] = (8,8)\n", "fig = plt.figure()\n", "\n", "ax = fig.add_axes([0,0,1,1])\n", "plt.plot(r[:,0],r[:,1],'.')\n", "for i in np.arange(len(t)-2):\n", " vec1 = FancyArrowPatch(r[i,:],r[i,:]+e_r[i,:],mutation_scale=30,color='r', label='e_r')\n", " vec2 = FancyArrowPatch(r[i,:],r[i,:]+e_theta[i,:],mutation_scale=30,color='g', label='e_theta')\n", " ax.add_artist(vec1)\n", " ax.add_artist(vec2)\n", "plt.xlim((-10,10))\n", "plt.ylim((-10,10))\n", "plt.grid()\n", "plt.legend([vec1, vec2],[r'$\\vec{e_r}$', r'$\\vec{e_{\\theta}}$'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The velocity and acceleleration of the particle are plotted below at some points of the path." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import FancyArrowPatch\n", "%matplotlib inline\n", "plt.rcParams['figure.figsize'] = (8,8)\n", "fig = plt.figure()\n", "plt.plot(r[:,0],r[:,1],'.')\n", "ax = fig.add_axes([0,0,1,1])\n", "for i in np.arange(len(t)-2):\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((-10,10))\n", "plt.ylim((-10,10))\n", "plt.grid()\n", "plt.legend([vec1, vec2],[r'$\\vec{v}$', r'$\\vec{a}$'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "### Solved symbolically" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "O = sym.vector.CoordSys3D(' ')\n", "t = sym.symbols('t')" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle (2 \\sqrt{t} \\cos{\\left(t \\right)})\\mathbf{\\hat{i}_{ }} + (2 \\sqrt{t} \\sin{\\left(t \\right)})\\mathbf{\\hat{j}_{ }}$" ], "text/plain": [ "(2*sqrt(t)*cos(t))* .i + (2*sqrt(t)*sin(t))* .j" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = 2*sym.sqrt(t)*sym.cos(t)*O.i+2*sym.sqrt(t)*sym.sin(t)*O.j\n", "r" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_parametric(r.dot(O.i),r.dot(O.j),(t,0,10))" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "e_r = r - r.dot(O.k)*O.k\n", "e_r = e_r/sym.sqrt(e_r.dot(O.i)**2+e_r.dot(O.j)**2+e_r.dot(O.k)**2)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle (\\frac{2 \\sqrt{t} \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{i}_{ }} + (\\frac{2 \\sqrt{t} \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{j}_{ }}$" ], "text/plain": [ "(2*sqrt(t)*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .i + (2*sqrt(t)*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .j" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e_r" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle (- \\frac{2 \\sqrt{t} \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{i}_{ }} + (\\frac{2 \\sqrt{t} \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{j}_{ }}$" ], "text/plain": [ "(-2*sqrt(t)*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .i + (2*sqrt(t)*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .j" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e_theta = O.k.cross(e_r)\n", "e_theta" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import FancyArrowPatch\n", "plt.rcParams['figure.figsize'] = (8,8)\n", "fig = plt.figure()\n", "ax = fig.add_axes([0, 0, 1, 1]) \n", "ax.axis(\"on\")\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))+float(e_r.dot(O.i).subs(t,instant)),\n", " float(r.dot(O.j).subs(t, instant))+float(e_r.dot(O.j).subs(t,instant))], \n", " mutation_scale=20,\n", " arrowstyle=\"->\",color=\"r\",label='${{e_r}}$')\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(e_theta.dot(O.i).subs(t, instant)),\n", " float(r.dot(O.j).subs(t, instant))+float(e_theta.dot(O.j).subs(t, instant))], \n", " mutation_scale=20,\n", " arrowstyle=\"->\",color=\"g\",label='${{e_{theta}}}$')\n", " ax.add_artist(vn)\n", " ax.add_artist(vt)\n", "plt.xlim((-10,10))\n", "plt.ylim((-10,10))\n", "plt.legend(handles=[vt,vn],fontsize=20)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "R = 2*sym.sqrt(t)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle - \\frac{1}{2 t^{\\frac{3}{2}}}$" ], "text/plain": [ " -1 \n", "──────\n", " 3/2\n", "2⋅t " ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Rdot = sym.diff(R,t)\n", "Rddot = sym.diff(Rdot,t)\n", "Rddot" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "v = Rdot*e_r + R*e_theta" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle (- \\frac{4 t \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}} + \\frac{2 \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{i}_{ }} + (\\frac{4 t \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}} + \\frac{2 \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{j}_{ }}$" ], "text/plain": [ "(-4*t*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2) + 2*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .i + (4*t*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2) + 2*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .j" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle (- \\frac{4 \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{i}_{ }} + (\\frac{4 \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{j}_{ }}$" ], "text/plain": [ "(-4*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .i + (4*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .j" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = (Rddot - R)*e_r + (2*Rdot*1+0)*e_theta\n", "aCor = 2*Rdot*1*e_theta\n", "aCor" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle (\\frac{2 \\sqrt{t} \\left(- 2 \\sqrt{t} - \\frac{1}{2 t^{\\frac{3}{2}}}\\right) \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}} - \\frac{4 \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{i}_{ }} + (\\frac{2 \\sqrt{t} \\left(- 2 \\sqrt{t} - \\frac{1}{2 t^{\\frac{3}{2}}}\\right) \\sin{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}} + \\frac{4 \\cos{\\left(t \\right)}}{\\sqrt{4 t \\sin^{2}{\\left(t \\right)} + 4 t \\cos^{2}{\\left(t \\right)}}})\\mathbf{\\hat{j}_{ }}$" ], "text/plain": [ "(2*sqrt(t)*(-2*sqrt(t) - 1/(2*t**(3/2)))*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2) - 4*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .i + (2*sqrt(t)*(-2*sqrt(t) - 1/(2*t**(3/2)))*sin(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2) + 4*cos(t)/sqrt(4*t*sin(t)**2 + 4*t*cos(t)**2))* .j" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "scrolled": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import FancyArrowPatch\n", "plt.rcParams['figure.figsize'] = (8,8)\n", "fig = plt.figure()\n", "ax = fig.add_axes([0, 0, 1, 1]) \n", "ax.axis(\"on\")\n", "time = np.linspace(0.1,10,30)\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))+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='${{v}}$')\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='${{a}}$')\n", " vc = 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(aCor.dot(O.i).subs(t, instant)),\n", " float(r.dot(O.j).subs(t, instant))+float(aCor.dot(O.j).subs(t, instant))], \n", " mutation_scale=20,\n", " arrowstyle=\"->\",color=\"b\",label='${{a_{Cor}}}$')\n", " ax.add_artist(vn)\n", " ax.add_artist(vt)\n", " ax.add_artist(vc)\n", "plt.xlim((-10,10))\n", "plt.ylim((-10,10))\n", "plt.legend(handles=[vt,vn,vc],fontsize=20)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further reading\n", "\n", "- Read pages 916-931 of the 18th chapter of the [Ruina and Rudra's book] (http://ruina.tam.cornell.edu/Book/index.html) about polar coordinates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Video lectures on the Internet\n", "\n", "- Khan Academy: \n", " - [Polar coordinates 1](https://www.youtube.com/watch?v=B5dOy4m6I1E)\n", " - [Polar coordinates 2](https://www.youtube.com/watch?v=1pQXJuWbz9w)\n", " - [Polar coordinates 3](https://www.youtube.com/watch?v=roSG9V3zApM) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Problems\n", "\n", "1. Find the polar basis (using the computer) for a projectile motion of a particle following the parametric equation below:\n", "\n", "\n", "\\begin{equation}\n", "\\vec{r}(t) = (10t-51){\\bf{\\hat{i}}} + \\left(-\\frac{9,81}{2}t^2+50t+100\\right){\\bf{\\hat{j}}}\n", "\\label{eq_13}\n", "\\end{equation}\n", "\n", "\n", "2. Problems from 15.1.1 to 15.1.14 from Ruina and Rudra's book,\n", "3. Problems from 18.1.1 to 18.1.8 and 18.1.10 from Ruina and Rudra's book." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "## Reference\n", "\n", "- Ruina A, Rudra P (2019) [Introduction to Statics and Dynamics](http://ruina.tam.cornell.edu/Book/index.html). Oxford University Press. " ] } ], "metadata": { "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": "3.7.3" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "nbTranslate": { "displayLangs": [ "*" ], "hotkey": "alt-t", "langInMainMenu": true, "sourceLang": "en", "targetLang": "pt", "useGoogleTranslate": true } }, "nbformat": 4, "nbformat_minor": 2 }