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This question is too interesting to resist, so I'll talk about how to analyze the problem. Take a look at sketch above. It describes an arbitrary moment during the rolling. From the kinematics view, $P$ is the "instant center of rotation". From the energy view, the square's center of mass $O$ keeps its height, thus the potential of the square doesn't change,...


3

I'm trying to numerically solve a system of differential equations describing two pendula connected to each other by a spring, and then make an animation of their evolution in time Here is something to get you started. You can do all this in Mathematica directly by solving the equations of motion and then use NDSolve to solve them and then do the ...


3

Silvia already gave a pretty rigorous derivation (compare this with the treatment by Hall and Wagon), so let me show how to plot the desired trajectory of the rolling polygon's corner. One could certainly modify the code I gave here for this, but I will instead adapt this solution I previously wrote in OpenGL to Mathematica: With[{n = 4}, (* number of sides ...


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