Hamiltonization and Integrability of the Chaplygin Sphere in R^n

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.

22 pages, Sections 1 and 5 are rewritten, to appear in Journal of Nonlinear Science

References in corpus (3)

• Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces
• Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics
• LR and L+R Systems

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• Hamiltonization of solids of revolution through reduction
• Rolling balls over spheres in R^n
• Gyroscopic Chaplygin systems and integrable magnetic flows on spheres
• Generalisation of Chaplygin's Reducing Multiplier Theorem with an application to multi-dimensional nonholonomic dynamics
• Integrability and dynamics of the n-dimensional symmetric Veselova top
• Demchenko's nonholonomic case of gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis
• Stochastic Chaplygin systems
• Integrability of the $n$-dimensional axially symmetric Chaplygin sphere