Abstract
Quasi-periodic invariant tori are emerging as a powerful tool to populate the phase space and enable a better understanding of key astrodynamics problems. This chapter introduces modern numerical continuation techniques for generating two-dimensional invariant tori in the elliptical restricted three-body problem of the Earth–Moon system. As a test case and baseline trajectories for the upcoming Lunar Orbital Platform Gateway, the (2:9) and (1:4) synodic resonant near rectilinear halo orbits are hereby considered. Their dynamical substitutes are first calculated and later analyzed using two-dimensional torus maps that facilitate the creation of accurate initial guesses for real-ephemeris orbits. The transition process is demonstrated with a trajectory optimization procedure that successfully generates continuous ballistic arcs around the Moon for more than one year.