Invariant manifolds and orbit control in the solar sail three-body problem

In this paper, we consider issues regarding the control and orbit transfer of solar sails in the circular restricted Earth-sun system. Fixed points for solar sails in this system have the linear dynamic properties of saddles crossed with centers; thus, the fixed points are dynamically unstable and control is required. A natural mechanism of control presents itself: variations in the sail's orientation. We describe an optimal controller to control the sail onto fixed points and periodic orbits about fixed points. We find this controller to be very robust, and we define sets of initial data using spherical coordinates to get a sense of the domain of controllability; we also perform a series of tests for control onto periodic orbits. We then present some mission strategies involving transfers from the Earth to fixed points and onto periodic orbits and involving controlled heteroclinic transfers between fixed points on opposite sides of the Earth. Finally, we present some novel methods for finding periodic orbits in circumstances in which traditional methods break down, based on considerations of the center manifold theorem.