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<p>To be applicable for spaceflight, an analysis from the Circular Restricted Three-Body Problem (CR3BP) must be validated in the Higher-Fidelity Ephemeris Model (HFEM). While various numerical strategies exist, transition from the CR3BP to HFEM presents unique challenges in two key areas: (1) ensuring that numerical transitions faithfully preserve the characteristics of the lower-fidelity model and (2) understanding the complex behaviors that emerge in the higher-fidelity model. The challenges are compounded by the nuances associated with discrepancies in frames and independent variables across different dynamical models. The current investigation introduces a Unified Transition Scheme (UTS) to address these challenges by facilitating robust numerical transitions from the CR3BP to the HFEM and the systematic analysis of solution behaviors within the HFEM. The UTS is constructed within a common rotating frame, enabling the identification of key parameters that influence the transition process. Additionally, homotopy strategies within the UTS are developed, supplying a robust and smooth numerical transition process. Intermediate models, such as the Elliptic Restricted Three-Body Problem (ER3BP) and the Hill Restricted Four-Body Problem (HR4BP), are incorporated into the UTS, creating a comprehensive numerical transition framework between the CR3BP and the HFEM. The proposed UTS (1) not only ensures smooth and reliable transitions between models (2) but also enhances the systematic understanding of the transitioned solutions within the HFEM. Several numerical examples are presented to demonstrate the effectiveness of the proposed UTS approach.</p>

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Systematic Numerical Transitions of Cislunar Trajectories Across Dynamical Models

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Rohith Reddy Sanaga,
  • Beom Park,
  • Kathleen C. Howell

摘要

To be applicable for spaceflight, an analysis from the Circular Restricted Three-Body Problem (CR3BP) must be validated in the Higher-Fidelity Ephemeris Model (HFEM). While various numerical strategies exist, transition from the CR3BP to HFEM presents unique challenges in two key areas: (1) ensuring that numerical transitions faithfully preserve the characteristics of the lower-fidelity model and (2) understanding the complex behaviors that emerge in the higher-fidelity model. The challenges are compounded by the nuances associated with discrepancies in frames and independent variables across different dynamical models. The current investigation introduces a Unified Transition Scheme (UTS) to address these challenges by facilitating robust numerical transitions from the CR3BP to the HFEM and the systematic analysis of solution behaviors within the HFEM. The UTS is constructed within a common rotating frame, enabling the identification of key parameters that influence the transition process. Additionally, homotopy strategies within the UTS are developed, supplying a robust and smooth numerical transition process. Intermediate models, such as the Elliptic Restricted Three-Body Problem (ER3BP) and the Hill Restricted Four-Body Problem (HR4BP), are incorporated into the UTS, creating a comprehensive numerical transition framework between the CR3BP and the HFEM. The proposed UTS (1) not only ensures smooth and reliable transitions between models (2) but also enhances the systematic understanding of the transitioned solutions within the HFEM. Several numerical examples are presented to demonstrate the effectiveness of the proposed UTS approach.