Application of Hamilton's law of varying action to the restricted three-body problem

Abstract

The ‘Law of Varying Action’, originally published by Hamilton in 1834, was recently employed by Bailey in devising a technique for generating power series characterizing the motions of dynamical systems. Furthermore, Bailey's method permits one to construct these series in a simple and direct way, without using the associated differential equations of motion. In the present paper, Hamilton's law is developed in its most general form and is used to produce series solutions of the restricted three-body problem. Finally, for illustrative purposes, numerical results are presented for several symmetric periodic orbits.