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A complete classification of dynamical symmetries in classical mechanics

Published online by Cambridge University Press:  17 April 2009

Geoff Prince
Geoff Prince
Affiliation:
Department of Mathematics, Royal Melbourne Institute of Technology, G.P.O. Box 2476V, Melbourne, Victoria 3001, Australia.
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Abstract

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This paper deals with the interaction between the invariance group of a second order differential equation and its variational formulation. In particular I construct equivalent Lagrangians from all such group actions, thereby successfully completing an earlier attempt of mine which dealt with some traditionally important classes of actions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 2 , October 1985 , pp. 299 - 308
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Crampin, M., “A note on non-Noether constants of motion”, Phys. Lett. 95A (1983), 209–212CrossRefGoogle Scholar
[2]Crampin, M., “Tangent bundle geometry for Lagrangian dynamics”, J. Phys. A: Math. Gen. 16 (1983), 3755–3772CrossRefGoogle Scholar
[3]Crampin, M. and Prince, G.E., “Equivalent Lagrangians and dynamical symmetries: some comments”, Phys. Lett. 108A (1985), 191–194.CrossRefGoogle Scholar
[4]Crampin, N., Prince, G.E. and Thompson, G., “A geometrical version of the Relmholtz conditions in time-dependent Lagrangian dynamics”, J. Phys. A: Math. Gen. 17 (1984), 1437–1447.CrossRefGoogle Scholar
[5]Prince, Geoff, “Toward a classification of dynamical symmetries in classical mechanics”, Bull. Austral. Math. Soc. 27 (1983), 53–71.CrossRefGoogle Scholar
[6]Prince, G.E. and Crampin, M., “Projective differential geometry and geodesic conservation laws in general relativity I: Projective actions”, Gen Rel. Grav. 16 (1984), 921–942.CrossRefGoogle Scholar
[7]Sarlet, Willy, “Note on equivalent Lagrangians and symmetries”, J. Phys. A: Math. Gen. 16 (1983), L229–L232.CrossRefGoogle Scholar