Reduction of invariant constrained systems using anholonomic frames

Mike Crampin; Tom Mestdag

doi:10.3934/jgm.2011.3.23

Article Contents

2011, Volume 3, Issue 1: 23-40. Doi: 10.3934/jgm.2011.3.23

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Reduction of invariant constrained systems using anholonomic frames

Mike Crampin^1, and
Tom Mestdag^1,

1.
Department of Mathematics, Ghent University, Krijgslaan 281, S9, B-9000 Gent

Received: September 30, 2010

Revised: March 31, 2011

Published: February 2011

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Abstract

We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics can be represented by a second-order differential equations vector field and that in both cases the reduced dynamics can be described by expressing that vector field in terms of an appropriately chosen anholonomic frame.

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Mathematics Subject Classification: 34A26, 37J60, 70G45, 70H03.

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