Summary
Missions aiming for periodic orbits around the Moon are becoming increasingly attractive, largely due to the influence of NASA's Artemis program. However, chaotic dynamics around these orbits still represents a hindrance to optimal design of such space missions. Therefore, informed mission design needs a deeper understanding of cislunar dynamics. To this end, we propose high-order techniques that make use of differential algebra (DA), which we apply to both well-known and novel problems in astrodynamics. In particular, we compute periodic orbits (POs) families of the circular restricted three-body problem with pseudo-arclength continuation and numerically construct transfer maps from a Poincaré section back to itself. The latter can be used for the analysis of the cislunar chaotic dynamics, because they help explain the behavior of ballistic capture trajectories and their connection with POs.
