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arXiv · 1106.1952

One invariant measure and different Poisson brackets for two nonholonomic systems

A. V. Tsiganov
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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.

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A. V. Tsiganov. 2011-06-10. One invariant measure and different Poisson brackets for two nonholonomic systems. https://doi.org/10.1134/s1560354712010078

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