Computation of Invariant Tori in the Hill Restricted Four-Body Problem via Collocation

The Hill Restricted Four-Body Problem offers a promising framework for analyzing spacecraft dynamics in the Sun–Earth–Moon system. This study explores the computation of families of quasi-periodic orbits, or 2-dimensional invariant tori, that emerge from isolated periodic orbits, opening up new possibilities for advanced trajectory design. The outlined method combines the Fourier discretization of an invariant curve of a stroboscopic map with a Gauss–Legendre collocation scheme. Stability analysis is performed as a by-product of the implementation. Compared to the shooting-based variants of the algorithm, the collocation approach demonstrated superior efficiency while providing a continuous representation of the tori.