Toward a classification of dynamical symmetries in classical mechanics
- 1 February 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 27 (1) , 53-71
- https://doi.org/10.1017/s0004972700011485
Abstract
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.Keywords
This publication has 7 references indexed in Scilit:
- Lie symmetries of differential equations and dynamical systemsBulletin of the Australian Mathematical Society, 1982
- Generalizations of Noether’s Theorem in Classical MechanicsSIAM Review, 1981
- Higher-order Noether symmetries and constants of the motionJournal of Physics A: General Physics, 1981
- Differential geometry as a tool for applied mathematiciansPublished by Springer Nature ,1980
- Symmetry groups and conserved quantities for the harmonic oscillatorJournal of Physics A: General Physics, 1978
- Constants of the motion in lagrangian mechanicsInternational Journal of Theoretical Physics, 1977
- Ambiguities in the Lagrangian and Hamiltonian formalism: Transformation propertiesIl Nuovo Cimento B (1971-1996), 1977