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.
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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