A nonlinear stability problem in the three dimensional restricted three body problem

The question of whether or not there is a transfer of energy between the in-plane motion and out-of-plane motion in the neighborhood ofL ₄ in the restricted problem of three bodies is investigated in this paper. The in-plane motion is assumed to be finite and the out-of-plane motion to be infinitesimal. The equation governing the out-of-plane motion becomes one with time varying coefficients. The stability of this equation is then investigated using Lie Series.Presented as a paper AAS No. 70-313, at the AAS/AIAA Astrodynamics Specialists Conference 1971 at Fort Lauderdale Fla., U.S.A.