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Quasivelocities and symmetries in non-holonomic systems

Bloch, Anthony M. and Marsden, Jerrold E. and Zenkov, Dmitry V. (2009) Quasivelocities and symmetries in non-holonomic systems. Dynamical Systems, 24 (2). pp. 187-222. ISSN 1468-9367.

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This article is concerned with the theory of quasivelocities for non-holonomic systems. The equations of non-holonomic mechanics are derived using the Lagrange-d'Alembert principle written in an arbitrary configuration-dependent frame. The article also shows how quasivelocities may be used in the formulation of non-holonomic systems with symmetry. In particular, the use of quasivelocities in the analysis of symmetry that leads to unusual momentum conservation laws is investigated, as is the applications of these conservation laws and discrete symmetries to the qualitative analysis of non-holonomic dynamics. The relationship between asymptotic dynamics and discrete symmetries of the system is also elucidated.

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Additional Information:© 2009 Taylor & Francis. (Received 11 April 2008; final version received 7 November 2008) We thank Yakov Berchenko-Kogan, Hernán Cendra, Michael Coleman, Brent Gillespie, P.S. Krishnaprasad, Jared Maruskin, Richard Murray, Tudor Ratiu, and Andy Ruina for numerous discussions, and the referees for helpful suggestions. The research of AMB was supported by NSF grants DMS-0604307 and CMS-0408542. The research of JEM was partially supported by AFOSR Contract FA9550-08-1-0173. The research of DVZ was partially supported by NSF grants DMS-0306017 and DMS-0604108. AMS Subject Classifications: 70F25; 37J60; 70H33
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Air Force Office of Scientific ResearchFA9550-08-1-0173
Subject Keywords:Hamel equations; momentum; symmetry
Issue or Number:2
Record Number:CaltechAUTHORS:20090908-083705980
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15657
Deposited By: George Porter
Deposited On:07 Oct 2009 18:13
Last Modified:03 Oct 2019 01:00

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