A Frequency-Based Model Hierarchy within Cislunar Space

Understanding the applicability and limitations of different dynamical models within the cislunar domain remains a fundamental challenge in astrodynamics. The current investigation presents a unified, frequency-based framework for organizing and interpreting spacecraft dynamics by constructing a hierarchy of dynamical models within a common rotating reference frame. Within this formulation, the Higher-Fidelity Ephemeris Model (HFEM) is expressed as a quasi-periodically perturbed system, extending the baseline Circular Restricted Three-Body Problem (CR3BP) through the inclusion of multiple time-dependent frequencies: most notably, the anomalistic, synodic, and draconic frequencies. To support model selection and interpretation, a set of intermediate models is evaluated based on the types and number of frequencies they incorporate. Analytical tools are developed to identify dominant perturbations and to characterize the resulting behaviors within the hierarchy. These findings are validated through numerical investigations that track the evolution of CR3BP structures across different models. The geometric and spectral characteristics of Lagrange points and periodic orbits are examined across the hierarchy and into the HFEM. As a focused application, the Earth-Moon L₂ halo region is investigated in detail, with particular attention to transition-challenging behaviors that arise when moving directly from CR3BP to the HFEM. Within this region, the Elliptic Restricted Three-Body Problem (ER3BP) is demonstrated to effectively capture dominant perturbations and provide insight into bifurcation behavior and quasi-periodic motion. Collectively, the results provide a structured approach for selecting and leveraging dynamical models of varying fidelity and for improving the interpretability and robustness of cislunar trajectory design.