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me5180_numerical/rotating_ball_bearing.ipynb

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"A ball bearing is rolling in a track without slipping as shown in Figure 1. The track\n",
"is spinning at a constant $\\Omega$. The ball\n",
"bearing weighs m=0.1 kg and has a radius of r=5 mm. The track has a radius of R=50 mm.\n"
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"function dy=myode(t,y,Omega,r,R)\n",
" g=9.81;\n",
" dy=zeros(size(y));\n",
" dy(1)=y(2);\n",
" dy(2)=5/7*Omega^2*sin(y(1)).*cos((y(1)))-g/(R-r)*sin(y(1));\n",
"end"
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"T =\n",
"\n",
" 0.42555 0.51899\n",
"\n"
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"wn=@(omega)sqrt(-(5/7*omega.^2-9.81/45e-3));\n",
"T=2*pi./wn([0,10])"
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"[t0,y0]=ode23(@(t,y) myode(t,y,0,5e-3,50e-3),[0,0.85],[pi/4,0]);\n",
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"source": [
"plot(t0,y0(:,1)*180/pi,t10,y10(:,1)*180/pi)\n",
"xlabel('time (s)')\n",
"ylabel('theta (deg)')\n",
"legend('w=0 rad/s','w=10 rad/s')"
]
},
{
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"text": "GNU Octave",
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{
"text": "Octave Kernel",
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