This article is cited in 26 papers

A generalization of Chaplygin’s Reducibility Theorem

O. E. Fernandez^a, T. Mestdag^b, A. M. Bloch<sup>a

a</sup> Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI-48109, USA
^b Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium

Abstract: In this paper we study Chaplygin’s Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton–Poincaré–d’Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler–Poincaré–Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.

Keywords: Hamiltonization, nonholonomic systems, reducing multiplier.

MSC: 70F25, 70H05, 53D17, 70H33

Received: 02.06.2009
Accepted: 10.10.2009

Language: English

DOI: 10.1134/S1560354709060033

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