Application of the Hamilton-Jacobi method to the study of rheo-linear oscillators

Abstract

In this paper we demonstrate that the well-known Hamilton-Jacobi method can be used in study of the rheo-linear (i.e. time dependent) harmonic oscillator with a single degree of freedom. It will be shown that the quadratic conservation laws (exact invariants) together with corresponding auxiliary equations follow immediately from the complete integral of Hamilton-Jacobi partial differential equation by application of the Jacobi theorem. Attention is also paid to the study of linear conservation laws and to the motion of rheo-linear dynamical systems. © 1992 Springer-Verlag.