Geometrisation of Chaplygin's reducing multiplier theorem
Dynamical Systems
2014-05-23 v1
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 -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.
Keywords
Cite
@article{arxiv.1405.5843,
title = {Geometrisation of Chaplygin's reducing multiplier theorem},
author = {Alexey V. Bolsinov and Alexey V. Borisov and Ivan S. Mamaev},
journal= {arXiv preprint arXiv:1405.5843},
year = {2014}
}