A Third-Order Analytical Solution for Relative Motion with a Circular Reference Orbit

Abstract

Abstract : From a Lagrangian approach for the development of the relative motion equations for a nonlinear Hill's problem, it is shown that the influence of a spherical primary mass takes the form of a third-body-like disturbing function expressed relative to the origin of Hill's rotating frame. The resulting Lagrangian and corresponding equations of motion are compact and can provide an easily obtainable representation of the nonlinear contributions to the motion to an arbitrary order using recursion relations. The relative equations are expanded through third-order in the local Hill's coordinates and a correspondingly accurate successive approximations solution is developed to describe nonlinear periodic motions in the Hill's frame.