One invariant measure and different Poisson brackets for two nonholonomic systems

Abstract

We discuss the nonholonomic Chaplygin and the Borisov-Mamaev-Fedorov systems, for which symplectic forms are different deformations of the square root from the corresponding invariant volume form. In both cases second Poisson bivectors are determined by $L$-tensors with non-zero torsion on the configurational space, in contrast with the well known Eisenhart-Benenti and Turiel constructions.

18 pages, LaTeX with AMSfonts

References in corpus (4)

• Chaplygin ball over a fixed sphere: explicit integration
• Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
• On natural Poisson bivectors on the sphere
• On bi-integrable natural Hamiltonian systems on the Riemannian manifolds

Cited by in corpus (3)

• On the Routh sphere problem
• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?