The equations of motion for two spherical dipoles moving freely in a plane are obtained. Special consideration is given to when the two spheres are in contact. Investigations of equilibria,… Click to show full abstract
The equations of motion for two spherical dipoles moving freely in a plane are obtained. Special consideration is given to when the two spheres are in contact. Investigations of equilibria, small-amplitude motion, and large-amplitude motion reveal that possible motions are exclusively quasi-periodic. Two distinct modes are identified, one of which is isomorphic with the simple pendulum, complete with a regime where it ceases to be periodic, and the angular displacement grows continuously at high energy.
               
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