Hamiltonization and integrability of the Chaplygin sphere in ℝn

Abstract

This paper studies a natural n-dimensional generalization of the classical nonholonomic Chaplygin sphere problem. We prove that for a specific choice of the inertia operator, the restriction of the generalized problem onto a zero value of the SO(n - 1)-momentum mapping becomes an integrable Hamiltonian system after an appropriate time reparametrization.