Theorem of Image Trajectories

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

If a trajectory is feasible in the CR3BP, then three trajectories generated via time reflection and sign changes (image trajectories) are also feasible. This theorem enables rapid construction of other periodic orbits from a known one, and derivation of stable manifolds from unstable manifolds. Corollary: if a trajectory has two orthogonal crossings on the x-z plane (y=0 and vx=0), it is symmetric about the x-z plane and periodic.

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。利用流形结构可设计低能量转移轨道，减少对推进剂的依赖。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。

References

  • Pontani和Teofilatto - 2016 - Polyhedral representation of invariant manifolds applied to orbit transfers in the Earth–moon system
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Contributors: ouyangjiahong, Ou Yang Jiahong