Hamiltonization and Integrability of the Chaplygin Sphere in Rⁿ

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The 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 zero value of the SO(n-1)-momentum mapping becomes an integrable Hamiltonian system after an appropriate time reparametrization.