Invariant Manifolds, the Spatial Three-Body Problem and Space
Shane D. Ross
Control and Dynamical Systems, California Institute of Technology
MC 107-81, Pasadena, CA 91125, USA. E-mail: email@example.com
The invariant manifold structures of the collinear libration points for
the spatial restricted three-body problem provide the framework for
understanding complex dynamical phenomena from a geometric point of view.
In particular, the stable and unstable invariant manifold "tubes"
associated to libration point orbits are the phase space structures that
provide a conduit for orbits between primary bodies for separate
three-body systems. These invariant manifold tubes can be used to
construct new spacecraft trajectories, such as a "Petit Grand Tour" of
the moons of Jupiter. Previous work focused on the planar circular restricted
three-body problem. The current work extends the results to the spatial