The complete symmetry group of a forced harmonic oscillator

P. G. L. Leach
1980 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
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 M-dimensional systems is discussed.
doi:10.1017/s0334270000002502 fatcat:ivxeptohlnfvdhw73ujlcoh4mi