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Published June 2009 | public
Journal Article

Quasivelocities and symmetries in non-holonomic systems

Abstract

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.

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

Additional details

Created:
August 21, 2023
Modified:
October 19, 2023