Aas 12-189 Canonical Perturbation Theory for the Elliptic Restricted-three-body Problem

The distinguishing characteristic of the elliptic restricted three-body problem is a time-varying potential field resulting in non-autonomous and non-integrable dynamics. The purpose of this study is to normalize the system dynamics about the circular case and about one of the triangular Lagrange points by applying a method of canonical perturbation theory introduced by Hori and Deprit in the 1960s. The classic method derives a near-identity transformation for a Hamiltonian function expanded about a single parameter such that the transformed form possesses ideal properties of integrability. In this study, the method is extended to two-parameter expansions and applied to motion about the triangular elliptic Lagrange points. The transformed system is expressed in Birkhoff normal form for which the stability properties may be analyzed using KAM theory and the motion by local integrals and level sets.