Newton Homotopy

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A homotopy function construction method. Sets the initial homotopy problem as G(y) = F(y) - F(y₀), where y₀ is a known initial guess. As the homotopy parameter varies from 0 to 1, the problem transitions from near the initial guess to the original problem. Simple to construct, but requires a reasonable initial guess.

Application Value

The Newton Homotopy plays a significant role in cislunar space mission design, analysis, and control. In orbital design, it can be leveraged for transfer trajectory optimization; in navigation and control, it improves mission execution precision and reliability; in system analysis, it facilitates deeper understanding of complex multi-body dynamical behavior, guiding mission planning and risk assessment.

  • J2-Invariant Orbit
  • Interior Point Optimization
  • N-Body Dynamics
  • Start-End State Constraint

References

  • 潘迅和泮斌峰 - 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