N-PARAMETRIC CANONICAL PERTURBATION METHOD BASED ON LIE TRANSFORMS

Abstract

ABSTRACT In the dynamical analysis of multiple stellar systems, one usually has to deal with problems involving several perturbations: more than two bodies, mass loss, nonspherical shape, rotation, and such. In order to take into account all of them, we have derived a multiparametric theory based on Lie transforms. It allows us to solve perturbation problems involving an arbitrary number of small parameters in the Hamiltonian formulation. Based on the Lie transforms theory, a complete generalization of the Hori–Deprit method is obtained for N parameters—with N arbitrary—and general expressions are explicitly provided. This method is used to solve the classical Gyldén–Meščerskij problem—the relative motion of a binary system the components of which are losing mass over time—when the primary's oblateness, as well as relativistic effects, is taken into account. Besides this, speed and accuracy comparisons between this analytical method and a numerical one are accomplished.