Stable Manifold

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

In manifold theory, the stable manifold of a periodic orbit consists of all phase trajectories that asymptotically approach it. A spacecraft on the stable manifold naturally approaches the target orbit without external energy input, making it a core tool for low-energy transfer trajectory design. The paper exploits the property that stable manifolds of L1-centered HLOs approach Earth closely, using them as initial estimates for LEO departure transfer trajectories.

Application Value

This concept has important application value in cislunar space research and mission design.

Related Concepts

• Nonlinear Programming
• Zero-Velocity Curve
• Shape-Based Method

References

• DOI:10.16804/j.cnki.issn1006-3242.2023.05.009
• Transfer to Distant Retrograde Orbits Using Manifold Theory
• Belbruno 等 - 2010 - Weak stability boundary and invariant manifolds
• Gómez et al. 2001, Ch.1,4
• /home/ouyangjiahong/Downloads/地月空间相关/output/Gordon - 2008 - Transfers to Earth-moon L2 halo orbits using lunar proximity and invariant manifolds/hybrid_auto/Gordon - 2008 - Transfers to Earth-moon L2 halo orbits using lunar proximity and invariant manifolds.md
• Perozzi和Ferraz-Mello - 2010 - Space manifold dynamics