On the Lie integrability theorem for the Chaplygin ball

Abstract

The necessary number of commuting vector fields for the Chaplygin ball in the absolute space is constructed. We propose to get these vector fields in framework of the Poisson geometry similar to the Hamiltonian mechanics.

12 pages, LaTeX with AMS fonts, in the second version we added discussion of the compatible rank-two Poisson structures

References in corpus (5)

• On the Integration Theory of Equations of Nonholonomic Mechanics
• Routh's procedure for non-Abelian symmetry groups
• On the Routh sphere problem
• On generalized nonholonomic Chaplygin sphere problem
• On the nonholonomic Stubler model

Cited by in corpus (3)

• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Hamiltonization of Elementary Nonholonomic Systems
• On Integrable Perturbations of Some Nonholonomic Systems