Poincaré-Lindstedt Method
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
An analytical method for finding periodic solutions of conservative nonlinear systems by eliminating secular terms through coordinate and timescale transformations, commonly used to derive approximate analytical solutions for orbits near libration points.
Application Value
The Poincaré-Lindstedt method extends linear eigenvalue analysis to nonlinear conservative systems by introducing a scaled time variable (the Lindstedt transformation) that absorbs secular terms arising from perturbation expansions. This yields uniformly valid approximate solutions for periodic orbits without divergent terms. In cislunar dynamics, it is the foundational technique behind the Richardson third-order approximations for Halo and Lyapunov orbits, providing rapid analytical initial guesses that would otherwise require expensive numerical search or continuation methods.
Related Concepts
References
- Marchal - 1990 - The three-body problem