  In recent years, stable and unstable manifolds of invariant objects (such as
libration points and periodic orbits) have been increasingly recognized as an
efficient tool for designing transfer trajectories in space missions. However,
most methods currently used in mission design rely on using eigenvectors of the
linearized dynamics as local approximations of the manifolds. Since such
approximations are not accurate except very close to the base invariant object,
this requires large amounts of numerical integration to globalize the manifolds
and locate intersections. In this paper, we study hyperbolic resonant periodic
orbits in the planar circular restricted 3-body problem, and transfer
trajectories between them, by: 1) determining where to search for resonant
periodic orbits; 2) developing and implementing a parameterization method for
accurate computation of their invariant manifolds as Taylor series; and 3)
developing a procedure to compute intersections of the computed stable and
unstable manifolds. We develop and implement algorithms that accomplish these
three goals, and demonstrate their application to the problem of transferring
between resonances in the Jupiter-Europa system.
