Homotopy Continuation
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A progressive root-finding algorithm that starts from a known solution of a simplified problem and gradually converges to the solution of a more complex problem by tracing an implicitly defined curve. The paper combines it with Theory of Functional Connections to perform trajectory continuation between simplified three-body models and high-fidelity four-body models.
Application Value
同伦延拓through 逐步changeproblemparameterwill已知解延拓到targetproblem, 沿零水平集路径追踪可捕捉同伦分支 of 转折点. is solve复杂boundary值problem of 有效method.
Related Concepts
- Libration Point Orbit
- Invariant Manifold
- Impulsive Maneuver
- Halo Orbit
References
- Zhang et al. - 2025 - Smoothing technique for indirect low-thrust trajectory optimization in cislunar space
- Caillau and Daoud 2012, SIAM J. Control Optim. 50(6)
- Campana 等 - 2024 - Low-energy earth–moon transfers via theory of functional connections and homotopy