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Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem

Published online by Cambridge University Press:  17 February 2009

P. G. L. Leach
P. G. L. Leach
Affiliation:
Department of Applied Mathematics, La Trobe University, Bundoora, Victoria 3083
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Abstract

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The method of the Lie theory of extended groups has recently been formulated for Hamiltonian mechanics in a manner which is consistent with the results obtained using the Newtonian equation of motion. Here the method is applied to the three-dimensional time-independent harmonic oscillator and to the classical Kepler problem. The expected constants of motion are obtained. Previously unobserved relations between generators and invariants are also noticed.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 2 , October 1981 , pp. 173 - 186
Copyright
Copyright © Australian Mathematical Society 1981

References

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