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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2020
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