Calculation of libration point orbits in the circular restricted three-body problem

Abstract

This study investigates possibilities for extension and improvement of algorithms for generation of libration point orbits in the framework of the circular restricted three body problem. Two algorithms for orbit generation based on bisection approach using different ways for evaluation of unstable component of motion are considered. The spacecraft’s state vector is periodically adjusted in such a way that unstable component of motion is neutralized and the trajectory corresponding to the corrected state vector belongs to the central manifold associated with libration point. The first algorithm uses expression for unstable component derived from linearized equations of motion. The second one is based on the procedure of reduction to central manifold, utilizing canonical coordinate transformations to nullify high order monomials in the expansion of Hamiltonian of the system in terms of Legendre polynomials. This allows expressing unstable component as one of generalized coordinates of Hamiltonian system obtained as the result of aforementioned transformation. Evaluation of these techniques proved their applicability for orbit generation. However, the second approach allows generating orbits in greater vicinity of libration point.