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Littlewood's Curious Hoop: Sliding, Gliding, Jumping, and Rolling Motions

oliver oreilly's picture

In "Littlewood's Miscelleny" the celebrated mathematician John E. Littlewood noted that a hoop with an attached mass rolling on a ground plane may exhibit self-induced jumping. Subsequent works showed that his analysis was flawed and revealed paradoxical behavior that can be resolved by incorporating the inertia of the hoop. In our newly published paper in the Transactions A of the Royal Society  a comprehensive analysis of the dynamics of the hoop is presented. The analysis illuminates the regularity induced in the model of the hoop when its mass moment of inertia is incorporated, shows that the paradoxical motions of the hoop are consistent with the principles of mechanics, and demonstrates the simplest example in the dynamics of rigid bodies that exhibits self-induced jumping.  


Rolling, Sliding, and Self-Induced Jumping

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