Discrete Homotopy

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A homotopy path tracking method. Divides the homotopy parameter from initial to target value into discrete steps, solving each sub-problem sequentially and using the previous solution as the initial guess for the next. Simple and intuitive, but fails when the homotopy curve has turning points or when adjacent steps are too large.

Application Value

This concept is fundamental to cislunar orbital mechanics and mission analysis, providing essential theoretical support for trajectory design and operational planning.

  • Retrograde Motion
  • Absolute Phase Bias
  • Relative Attitude Quaternion
  • Radial-Tangential-Normal Coordinate System, RTN

References

  • Pan X. & Pan B. - 2019 - 基于同伦方法的地月系L2点小推力转移轨道优化
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Contributors: ouyangjiahong, Ou Yang Jiahong