Richardson Third-Order Analytical Solution
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
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-Poincare perturbation method to eliminate secular terms, yielding third-order analytical solutions for Halo orbit in-plane and out-of-plane components. This provides initial guesses for subsequent numerical differential correction.
Application Value
This concept is applicable in cislunar space mission design, orbit optimization, and trajectory planning for spacecraft transfers and maneuver strategies.
Related Concepts
References
- 测绘学报, 2013, 42(2): 184-190