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arXiv · 1405.5843

Geometrisation of Chaplygin's reducing multiplier theorem

Alexey V. Bolsinov·Alexey V. Borisov·Ivan S. Mamaev
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Abstract

We develop the reducing multiplier theory for a special class of nonholonomic dynamical systems and show that the non-linear Poisson brackets naturally obtained in the framework of this approach are all isomorphic to the Lie-Poisson $e(3)$-bracket. As two model examples, we consider the Chaplygin ball problem on the plane and the Veselova system. In particular, we obtain an integrable gyrostatic generalisation of the Veselova system.

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Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev. 2014-05-22. Geometrisation of Chaplygin's reducing multiplier theorem. https://arxiv.org/abs/1405.5843

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