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me5180_numerical/rotating_pendulum.ipynb

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{
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"%plot --format svg"
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"function dy=pend_rot(t,y,l,w,a)\n",
" dy=zeros(size(y));\n",
" dy(1)=y(2);\n",
" dy(2)=-9.81/l*sin(y(1))+w^2*sin(y(1))*cos(y(1))+a*w^2/l*cos(y(1));\n",
"end"
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"my_ode =\n",
"\n",
"@(t, y) pend_rot (t, y, l, w, a)\n",
"\n"
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"\n",
"l=0.3;\n",
"a=1;\n",
"w=1;\n",
"g=9.81; \n",
"\n",
"my_ode=@(t,y) pend_rot(t,y,l,w,a)\n",
"\n",
"[t,y]=ode23(my_ode,[0 4*pi/w],[pi/6,0]);\n",
"\n",
"plot(t,y(:,1),t,pi/6*cos(sqrt(g/l)*t),'--')\n",
"legend('w=1 rad/s','w=0 rad/s')\n",
"xlabel('time (s)')\n",
"ylabel('angle (rad)')\n"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
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"\t\t<text><tspan font-family=\"{}\">1.4</tspan></text>\n",
"\t</g>\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"\t<path d=\"M483.7,135.7 L496.2,135.7 \" stroke=\"black\"/></g>\n",
"\t<g id=\"gnuplot_plot_1a\"><title>gnuplot_plot_1a</title>\n",
"<g color=\"white\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
"\t<path d=\"M280.0,287.0 L280.0,172.4 L340.0,158.4 \" stroke=\"rgb( 0, 0, 255)\"/></g>\n",
"\t</g>\n",
"\t<g id=\"gnuplot_plot_2a\"><title>gnuplot_plot_2a</title>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
"\t<path d=\"M340.0,158.4 L346.8,188.6 \" stroke=\"rgb( 0, 0, 255)\"/>\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(340.0,158.4) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n",
"\t<use color=\"rgb( 0, 0, 255)\" transform=\"translate(346.8,188.6) scale(12.00)\" xlink:href=\"#gpPt5\"/>\n",
"</g>\n",
"\t</g>\n",
"<g color=\"white\" fill=\"none\" stroke=\"rgb( 0, 0, 255)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"</g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"\t<path d=\"M483.7,296.2 L253.2,356.6 \" stroke=\"black\"/></g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"\t<path d=\"M76.3,277.8 L253.2,356.6 \" stroke=\"black\"/></g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"\t<path d=\"M253.2,356.6 L253.2,184.7 \" stroke=\"black\"/></g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"\t<path d=\"M76.3,105.8 L253.2,184.7 \" stroke=\"black\"/></g>\n",
"<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
"\t<path d=\"M483.7,124.2 L253.2,184.7 \" stroke=\"black\"/></g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x1=cos(w*t).*(a+l*sin(y(:,1))); % x1-coordinate over time\n",
"y1=sin(w*t).*(a+l*sin(y(:,1))); % y1-coordinate over time\n",
"z1=a-l*cos(y(:,1)); % z1-coordinate over time\n",
"linkx=[zeros(length(t),1),zeros(length(t),1),a*cos(w*t)];\n",
"linky=[zeros(length(t),1),zeros(length(t),1),a*sin(w*t)];\n",
"linkz=[zeros(length(t),1),a*ones(length(t),1),a*ones(length(t),1)];\n",
"N=length(t);\n",
"nframes=100; \n",
"f=figure(1);\n",
"for i=1:floor(N/nframes):N\n",
" clf\n",
" plot3(linkx(i,:),linky(i,:),linkz(i,:))\n",
" hold on\n",
" plot3([linkx(i,3),x1(i)],[linky(i,3),y1(i)],[linkz(i,3),z1(i)],'-o')\n",
" frameid=sprintf('./figures/animation_rotating_pendulum/frame%2.3i.png',i);\n",
" axis([-2 2 -2 2 0 1.5])\n",
" saveas(f,frameid)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 4921 1\n",
"\n"
]
}
],
"source": [
"size(t)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"i = 780\r\n"
]
}
],
"source": [
"i"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1 3\n",
"\n"
]
}
],
"source": [
"size(linkx(3,:))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Octave",
"language": "octave",
"name": "octave"
},
"language_info": {
"file_extension": ".m",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "octave",
"version": "0.19.14"
}
},
"nbformat": 4,
"nbformat_minor": 2
}