Hamiltonization and Integrability of the Chaplygin Sphere in ℝn

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.