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Toward a classification of dynamical symmetries in classical mechanics

Published online by Cambridge University Press:  17 April 2009

Geoff Prince
Geoff Prince
Affiliation:
Department of Applied Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
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Abstract

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A one-parameter group on evolution space which permutes the classical trajectories of a Lagrangian system is called a dynamical symmetry. Following a review of the modern approach to the “symmetry-conservation law” duality an attempt is made to classify such invariance groups according to the induced transformation of the Cartan form. This attempt is fairly successful inasmuch as the important cases of Lie, Noether and Cartan symmetries can be distinguished. The theory is illustrated with a presentation of results for the classical Kepler problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1983 , pp. 53 - 71
Copyright
Copyright © Australian Mathematical Society 1983

References

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