Hamiltonization and Integrability of the Chaplygin Sphere in R^n

TL;DR

This paper generalizes the classical Chaplygin sphere problem to n dimensions, proving that under certain conditions, it becomes an integrable Hamiltonian system after a time change.

Contribution

It introduces an n-dimensional version of the Chaplygin sphere and demonstrates its integrability under specific inertia conditions and momentum constraints.

Findings

The generalized problem reduces to an integrable Hamiltonian system.

Time reparametrization is essential for integrability.

Specific inertia operator choice is crucial for the results.

Abstract

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.