One invariant measure and different Poisson brackets for two nonholonomic systems

Details One invariant measure and different Poisson brackets for two nonholonomic systems One invariant measure and different Poisson brackets for two nonholonomic systems

2011-06-10

arxiv.org/abs/1106.1952v1

Rus. J. Nonlin. Dyn. , 2011, V.7, No.3, p. 577-599

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, LaTeX with AMSfonts

Scientific paper

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.

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