Unified Transition Scheme for Invariant Tori Across Various Models in the Cislunar Domain

Abstract

The invariant tori supply a fundamental basis for examining cislunar dynamics, offering options for long-term baseline solutions and a deeper understanding of the global phase space. While models of varying fidelity are leveraged to characterize these invariant tori within cislunar space, continued efforts are required to investigate the evolution of these structures from lower-fidelity models to their higher-fidelity counterparts. The current investigation focuses on periodic orbits within the Earth-Moon Circular Restricted Three-BodyProblem (CR3BP) and their analogs in Periodically Forced Models (PFMs) and the Higher-Fidelity Ephemeris Model (HFEM). In particular, this work leverages a unified numerical framework, termed the Unified Transition Scheme (UTS), to facilitate the numerical construction of the analogs across various models. Within the UTS, homotopy strategies with flexibilities in continuation directions are incorporated. This adaptability supplies reliable methods for characterizing invariant tori across models of evolving fidelity and addresses known challenges, e.g., broken bifurcations. Numerical examples, including the analysis of L2 halo orbits, illustrate the effectiveness of the proposed approach and highlight its potential to advance cislunar mission design and analysis.

Keywords: Invariant tori, Elliptical Restricted Three-Body Problem, Hill Restricted Four-Body Problem, Ephemeris Model