Homotopy Iteration Method

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A numerical method for solving nonlinear equations. By constructing a continuous deformation path (homotopy path) from a known solution to the target solution, it iteratively approaches the target. In the perturbational Lambert problem, since three-body perturbation prevents the two-body Lambert solution from reaching the target directly, the homotopy iteration method gradually 'pulls back' the target point from the Lambert solution position to the real target, adjusting the deviation proportionally at each iteration until convergence to an exact multi-body dynamics solution.

Application Value

This concept plays an important role in cislunar space mission design and orbital dynamics analysis.

References

  • Debris Cloud Evolution in Cislunar Space Using Eulerian Perspective Method
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Contributors: ouyangjiahong, Ou Yang Jiahong