Symmetry groups and conserved quantities for the harmonic oscillator

Lutzky, M.

doi:10.1088/0305-4470/11/2/005

Cited by 118 publications

(79 citation statements)

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“…The corresponding result for Lie symmetries is given in the following theorem (see Prince [5] and also Lutzky [3] and Marmo and Saletan [4]). Moreover,…”

Section: Invariance Groups -Towards a Classificationmentioning

confidence: 94%

Toward a classification of dynamical symmetries in classical mechanics

Prince

1983

Bull. Austral. Math. Soc.

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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.

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“…The corresponding result for Lie symmetries is given in the following theorem (see Prince [5] and also Lutzky [3] and Marmo and Saletan [4]). Moreover,…”

Section: Invariance Groups -Towards a Classificationmentioning

confidence: 94%

Toward a classification of dynamical symmetries in classical mechanics

Prince

1983

Bull. Austral. Math. Soc.

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“…In this appendix we prove that (34) is a special case of the Euler-like functionals (42). Let us first show that (34) can be replaced by an action of the form (42).…”

Section: Biimentioning

confidence: 96%

“…Let us first show that (34) can be replaced by an action of the form (42). Indeed, because of the homogeneity of (34) …”

Section: Biimentioning

confidence: 99%