Ill-Conditioned State Transition Matrix
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A phenomenon in solving the three-body Lambert problem where the state transition matrix inverse has an excessively large condition number, causing numerical iteration to diverge. When long-term integration or the reference trajectory approaches an unstable structure, matrix inversion amplifies errors and Newton-Raphson iteration diverges. The paper's improvement uses a genetic algorithm to pre-search for a reference trajectory closer to the target, then applies homotopy to bridge the gap smoothly.
Related Concepts
References
- Three-body Lambert algorithm for libration point rendezvous orbit design