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Adjoint symmetries and the generation of first integrals in non-holonomic mechanics

Sarlet, W.; Saunders, D. J. and Cantrijn, F. (2005). Adjoint symmetries and the generation of first integrals in non-holonomic mechanics. Journal of Geometry and Physics, 55(2) pp. 207–225.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.geomphys.2004.12.006
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Abstract

We discuss a general mechanism by which first integrals of mechanical systems, in particular systems that satisfy non-holonomic constraints, can be obtained from a systematic search for adjoint symmetries. Such an approach has already been used in our earlier work and is re-advocated here in the context of a recent analysis by Giachetta, in which first integrals are generated by vector fields which are not symmetries. Further advantages of our approach are: the fact that an essential projection operator associated to the constraints need not be related to some given fibre metric on the full evolution space, and the specific selection of a connection, which is naturally associated to this projection and the second-order dynamics on the constraint submanifold. The computational aspects of the method are illustrated by some simple examples.

Item Type: Journal Article
Copyright Holders: 2004 Elsevier B.V.
ISSN: 0393-0440
Keywords: non-holonomic systems; first integrals; adjoint symmetries
Academic Unit/Department: Social Sciences > Sociology
Item ID: 18205
Depositing User: Colin Smith
Date Deposited: 07 Sep 2009 13:54
Last Modified: 02 Dec 2010 20:37
URI: http://oro.open.ac.uk/id/eprint/18205
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