THE USE OP LIE SERIES GENERATING FUNCTIONS TO DERIVE ASYMPTOTIC SERIES EXPRESSIONS FOR ORBITAL PERTURBATIONS

摘要

This paper describes a new method, using Lie series transformations, for the development of asymptotic series expressions for the perturbations of the orbits in a planetary or satellite system. The aim is to overcome difficulties of slow convergence encountered in near-commensurability cases, in the use of traditional methods. The paper begins with a brief description of the Lie series type of transformation, then briefly describes the parameter sets used to describe the orbits in a planetary or satellite system, and how they may be put into a Hamiltonian formulation, then it addresses difficulties particular to cases of near small-integer commensurability of the orbital periods, with especial reference to the case of Saturn's satellite Hyperion, and ends with an indication of the current work on the use of the generating function for the Lie series transformation to derive expressions for the short-period perturbations.