Shane Ross
Control and Dynamical Systems 107-81
California Institute of Technology
Pasadena, CA 91125
http://www.cds.caltech.edu/~shane/
Abstract:
We find interesting solutions to the gravitational restricted
four-body problem by applying symbolic dynamics techniques
previously developed for the three-body problem. We approximate
the four-body system as two coupled three-body systems.
In each three-body system, we consider the unstable periodic
orbits about L1 and L2 and their stable and unstable invariant
manifolds, which are tubes in the energy surface. The tubes
contain orbits in transit to and from the vicinity of the smaller
of the two massive bodies. Computing the tubes and their
intersection on appropriate Poincare surfaces of section,
we find and classify phase space sets
which correspond to orbits of prescribed behavior for a nearly
massless spacecraft. Intersecting these sets,
we generate interesting four-body problem trajectories, such as a
space mission to the Jupiter moons Ganymede and Europa.