Richardson三阶近似（An analytical approximation method for periodic orbits near libration points, developed by Richardson in 1980. It expands the equations of motion to third order about the libration point and uses the Lindstedt-Poincaré perturbation method to eliminate secular terms, yielding third-order analytical solutions for Halo orbits in both in-plane and out-of-plane components. This provides initial guesses for subsequent numerical differential correction and is the standard first step in Halo orbit computation.）

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定义

Richardson于1980年提出的平动点附近周期轨道解析近似方法。该方法将动力学方程在平动点处展开到三阶，利用Lindstedt-Poincaré摄动法消除长期项，得到Halo轨道在平面内和法向的三阶近似解析解。由此可为后续数值微分修正提供初始猜测值，是Halo轨道数值求解的标准第一步。

该概念在地月空间研究和任务设计中具有重要应用价值，涉及轨道设计、导航控制或任务规划等多个方面。