Designing Ballistic Connections between Cislunar Orbits Leveraging Hamiltonian Normal Forms

In this paper, the Birkhoff and resonant Hamiltonian normal forms are leveraged to find homoclinic and heteroclinic connections between center manifold trajectories near the libration points of the Earth-Moon system. These connections are interesting dynamical structures that can be viewed as completely ballistic transfers between periodic or quasiperiodic trajectories, potentially allowing a satellite to traverse multiple trajectory families with near-zero fuel consumption. This work builds upon the existing literature by utilizing the simplistic parameterization capabilities of the two normal forms, in addition to extending analysis from the circular restricted three-body problem to the more sensitive elliptic case. Somewhat unintuitively, it is found that the normal forms allow one to obtain heteroclinic connections within the elliptic problem, despite the lack of a Jacobi energy equivalent.