Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Abstract

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 behaviour that can be resolved by incorporating the inertia of the hoop. A comprehensive analysis of this problem is presented in this paper. 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.