Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem
- 1 October 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 23 (2) , 173-186
- https://doi.org/10.1017/s0334270000000151
Abstract
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.Keywords
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