Richardson Third-Order Expansion

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A third-order approximate analytical solution for Halo orbits near collinear libration points in the CR3BP, obtained using the Lindstedt-Poincaré perturbation method. It serves as the starting point for numerical Halo orbit computation: the Richardson expansion provides an analytical initial guess, which is then refined by Newton iteration differential correction. The expansion expresses Halo orbit states as functions of amplitude and phase, revealing the 1:1 resonance between in-plane and out-of-plane frequencies and the nonlinear frequency drift as amplitude increases.

Application Value

This term has significant application value in cislunar space missions。In the orbital design phase, engineers use relevant theories for trajectory optimization；In navigation and orbit determination, it is used to improve measurement accuracy；In attitude control and orbit maintenance tasks, it ensures stable spacecraft operation。In practical applications, parameter optimization and algorithm adaptation can be combined with mission requirements to improve mission success rate and resource utilization efficiency。

References

  • 徐明和徐世杰 - 2008 - Halo轨道维持的线性周期控制策略
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Contributors: ouyangjiahong, Ou Yang Jiahong