Abstract:We consider the problem of finding paths of shortest transit time between two points (popularly known as Brachistochrone) for cylinders with off-centered center of mass, rolling down without slip, subject solely to the force of gravity. This problem is set up using principles of classical rigid body dynamics and the desired path function is solved for numerically using the method of discrete calculus of variations. We discover a distinct array of brachistochrone trajectories for off-centered cylinders, demons… Show more
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