Regular and Chaotic Dynamics

, 14:635 | Cite as

A generalization of Chaplygin’s Reducibility Theorem

Research Articles

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.

Key words

Hamiltonization nonholonomic systems reducing multiplier 

MSC2000 numbers

70F25 70H05 53D17 70H33 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of Mathematical Physics and AstronomyGhent UniversityGentBelgium

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