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Motion of Rolling Cylinder in Fixed Cylinder: Confusing Constraint Condition
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[QUOTE="Steve4Physics, post: 6527692, member: 681522"] Thought this might be worth adding as the animation below is fun to watch (well, it is for me). Starting with ##\theta = \phi = 0##, after some rolling we have ##(b-a)\theta = a\phi## (not ##b\theta = a\phi##). To see what is happening, suppose ##a = 1## and ##b = 4##. This give ##\phi = 3\theta## (not ##\phi = 4\theta##). For example when point G does one full ‘orbit’ (##\theta = 2\pi##) then the small cylinder performs 3 (not 4) full rotations (##\phi = 6\pi## not ##8\pi##). Watch it actually happen in the link below! Count the number of rotations of the small circle by noting the orientation of its radius. The small circle rotates only 3 times. (Warning: might make your eyes go funny!): [URL]https://en.wikipedia.org/wiki/File:Astroid2.gif[/URL] [/QUOTE]
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Motion of Rolling Cylinder in Fixed Cylinder: Confusing Constraint Condition
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