Richardson Third-Order Analytical Solution

Author: Tianjiang Shuo Website: https://cislunarspace.cn

Definition

A third-order approximate expansion of Halo orbits in the circular restricted three-body problem, derived by Richardson (1980) using the Lindstedt-Poincaré method. Expressed in terms of in-plane amplitude Ax, out-of-plane amplitude Az, and angular frequency ω, it successively corrects the linearized solution with nonlinear terms. Significantly more accurate than the first-order linear solution while avoiding the high computational cost of numerical integration, it serves as the foundational analytical tool for libration-point orbit analysis and formation design.

Application Value

This concept plays a key role in trajectory transfer design, helping evaluate transfer costs and flight time to provide quantitative basis for mission trade studies. Combined with global search algorithms, multiple solution families and Pareto frontiers can be identified to guide orbital design decisions.

References

  • Halo轨道的航天器编队构型设计
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Contributors: ouyangjiahong, Ou Yang Jiahong