The complete symmetry group of a forced harmonic oscillator
- 1 July 1980
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 22 (1) , 12-21
- https://doi.org/10.1017/s0334270000002502
Abstract
The complete symmetry group of a forced harmonic oscillator is shown to be Sl(3, R) in the one-dimensional case. Approaching the problem through the Hamiltonian invariants and the method of extended Lie groups, the method used is that of time-dependent point transformations. The result applies equally well to the forced repulsive oscillator and a particle moving under the influence of a coordinate-free force. The generalization to na-dimensional systems is discussed.Keywords
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