Gauss Equations for Local Action-Angle Orbital Elements in Cislunar Space

To track orbits in cislunar space, predict where they will naturally move over time, and identify where unbounded trajectories come from, one may consider local action-angle orbital elements—coordinates that relate a spacecraft state to specific trajectories and exist in approximately integrable regions of the Earth–moon circular restricted three-body problem (CR3BP). As local action-angle elements are a semi-analytical analog to two-body orbital elements, the theory is extended to allow for the study of arbitrary perturbations to the dynamics. Namely, we derive Gauss equations for an arbitrary perturbing acceleration—continuous or discrete—to the CR3BP. Examples for continuous thrust and impulsive ΔV are provided in cislunar space, i.e., around Earth–moon L1,2 in the CR3BP. Strategies for instantaneous maneuver design and transfers between quasi-periodic orbits and manifolds are developed.