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

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

Definition

This concept has important application value in cislunar space research and mission design.