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me5180_numerical/double_pendulum.ipynb

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"![double pendulum](./figures/p1-10_double_pendulum.png)"
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"clear all; close all\n",
"t=linspace(0,2*pi/50,100); % create time varying from 0-0.126 s (or one period)\n",
"x=20*sin(50*t);dx=20*50*cos(50*t); % define x and dx/dt in terms of time (note dx=dx/dt)\n",
"t1=0.2*pi*cos(50*t); dt1=-10*pi*sin(50*t); % define theta1 (t1) and dtheta1/dt\n",
"t2=0.2*pi*sin(50*t-pi/3); dt2=10*pi*sin(50*t-pi/3); % define theta2 (t2) and dtheta2/dt;\n",
"L1=1;L2=1.5; % set lengths for L1 and L2 (none were given in problem so 1 and 1.5 mm were\n",
" % chosen arbitrarily\n",
"rcc=[x+L1*sin(t1);-L1*cos(t1)]; % position of connection between links\n",
"rco=[x+L1*sin(t1)+L2*sin(t2);-(L1*cos(t1)+L2*cos(t2))]; % create a row vectors of\n",
" % x-component and y-component of\n",
" % pendulum position C (r_C/O) \n",
"vco=[dx+L1*cos(t1).*dt1+L2*cos(t2).*dt2;(L1*sin(t1).*dt1+L2*sin(t2).*dt2)]; % create row\n",
" % vectors of\n",
" % the x- and\n",
" % y-component\n",
" % velocity of\n",
" % point C\n",
"\n",
"\n",
"figure(1)\n",
"plot(t,vco(1,:),t,vco(2,:))\n",
"xlabel('time (s)')\n",
"ylabel('velocity (mm/s)')\n",
"legend('x-component','y-component')\n",
"title('Velocity of end point')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Link positions over time (animation)\n",
"\n",
"![links](./pendulum.gif)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Octave",
"language": "octave",
"name": "octave"
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"language_info": {
"file_extension": ".m",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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