Geometrization of the Chaplygin reducing-multiplier theorem

A. V. Bolsinov ; A. V. Borisov ; I. S. Mamaev

Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 627-640.

Résumé

This paper develops the theory of the reducing multiplier for a special class of nonholonomic dynamical systems, when the resulting nonlinear Poisson structure is reduced to the Lie–Poisson bracket of the algebra $e(3)$. As an illustration, the Chaplygin ball rolling problem and the Veselova system are considered. In addition, an integrable gyrostatic generalization of the Veselova system is obtained.

Détail

Keywords: nonholonomic dynamical system, reducing multiplier, Hamiltonization, conformally Hamiltonian system, Chaplygin ball.
Mots-clés : Poisson bracket, Poisson structure

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