Families of heteroclinic connections between quasi-periodic libration point trajectories

Abstract

Copyright © 2014 by the authors.Heteroclinic connections (HC) play a significant role in the design of complex libration point missions, since they provide natural channels connecting motions that are otherwise unrelated. The Genesis and ARTEMIS missions, for example, have used trajectories that followed closely HC between L<inf>1</inf> and L<inf>2</inf> Lissajous orbits of the Sun-Earth and Earth-Moon systems, respectively. HC are computed by intersecting the stable (unstable) manifold of the arrival orbit with the unstable (stable) manifold of the departure orbit, usually looking for intersections in a strategic hypersurface. When the endpoint trajectories are quasi-periodic and non-planar, continuation strategies are essential to deal with the challenges introduced by the dimensionality of the involved structures. In this paper we elaborate a continuation strategy to compute HC between quasi-periodic solutions in the spatial circular restricted three-body problem. In particular, we show examples of the continuation of HC detected between Lissajous orbits around the L<inf>1</inf> and L<inf>2</inf> libration points of the Earth-Moon system. These results indicate that this strategy can be extensively used as a tool for the elaboration of a map of connections between quasi-periodic trajectories around L<inf>1</inf> and L<inf>2</inf>.