Invariants of Nearly Periodic Hamiltonian Systems. II

Abstract

In a previous paper the first few terms of the adiabatic invariant of a particular class of dynamical systems were found by solving Liouville's equation. The system considered was a periodic motion to which small perturbations were applied. The period of the unperturbed orbits was a constant and the perturbations were time‐independent. In this paper similar methods are used to find the invariant for the more general system, in which the period of the unperturbed orbits is a function of the coordinates and in which the perturbation varies slowly with time. The results are applied to a simple example, the Lorentz pendulum.