Application of dynamical systems theory to a very low energy transfer

We use lobe dynamics in the restricted three-body problem to design orbits with prescribed itineraries with respect to the resonance regions within a Hill's region. The application we envision is the design of a low energy trajectory to orbit three of Jupiter's moons using the patched three-body approximation (P3BA). We introduce the "switching region," the P3BA analogue to the "sphere of influence." Numerical results are given for the problem of finding the fastest trajectory from an initial region of phase space (escape orbits from moon A) to a target region (orbits captured by moon B) using small controls.