Homotopy Method

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A numerical continuation technique that gradually deforms an easily solvable problem into the target problem by introducing a continuously varying parameter, tracking along the solution curve to obtain the target solution. In trajectory design, homotopy starts from an easily obtained initial solution and gradually approaches the target transfer trajectory, overcoming Newton-Raphson's sensitivity to initial guesses. This paper uses the genetic-algorithm-derived reference trajectory as the homotopy starting point for solving long-time rendezvous trajectories.

Application Value

This concept is essential for understanding motion characteristics in spacecraft dynamics analysis and design, and plays a vital role in mission success.

References

  • 基于三体Lambert算法的平动点交会轨道设计
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Contributors: ouyangjiahong, Ou Yang Jiahong