Hamiltonian Integrable Approximation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An approximation method that simplifies the non-integrable Hamiltonian of the circular restricted three-body problem into an integrable form through averaging and canonical transformation. The approximated Hamiltonian depends only on a few slow variables and admits analytical integrals, enabling computation of equilibrium points and initial guesses for periodic orbits in mean motion resonance. The key assumptions are small perturbation and planar motion, providing initial solutions for numerical continuation of resonant orbit families in the CRTBP.

Application Value

该轨道类型可作为地月空间运输网络的中转站或任务的目标轨道。该模型是分析地月空间动力学、设计低能量转移轨道的基础工具。通过平均化处理可简化长时间尺度的动力学分析。共振轨道可用于设计长期稳定的任务轨道，减少轨道维持代价。

References

  • Ding et al., 2025 — Cislunar Space Situational Awareness via Earth-Moon Resonant Orbits
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Contributors: ouyangjiahong, Ou Yang Jiahong