Vertical instability of the planar resonant orbits and the application in transfer design to three-dimensional periodic orbits

This work aims to investigate the vertical instability of planar resonant orbits in the circular restricted three-body problem as well as to present a novel methodology to design transfers to three-dimensional periodic orbits by leveraging this dynamical mechanism. With the Jupiter-Europa system as an example, the vertical stability index for typical resonant orbit families is calculated. Both the vertically stable and unstable resonant orbits are found to exist. The vertical invariant manifolds associated with the unstable resonant orbits are computed and examined through a Poincaré section. The vertical instability is found to be more significant for resonant orbits with smaller periapsis altitudes relative to the smaller primary. By taking advantage of the vertical instability, a three-step methodology is then developed to design transfers from the planar resonant orbits to three-dimensional periodic orbits. The methodology includes the construction of the dataset, matching and selection, and optimization. Numerical experiments are carried out to demonstrate the effectiveness of the methodology. Results indicate that the inclusion of the vertical instability can effectively reduce the transfer ΔV cost.