Unstable Manifold

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The set of trajectories that asymptotically depart from an unstable periodic orbit at an exponential rate. In Hamiltonian systems, the unstable manifold forms a tube-like structure of escaping trajectories. Contrasted with the stable manifold (trajectories approaching the orbit), the unstable manifold enables escape or return transfers. In the three-impulse Halo transfer, the return design uses the unstable manifold with forward time integration instead of the stable manifold with backward integration.

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
• Li Mingtao, Zheng Jianhua. Impulsive lunar Halo transfers using the stable manifolds and lunar flybys. Acta Astronautica, 2010, 66(1-2): 169-177
• Transfer to Distant Retrograde Orbits Using Manifold Theory
• Colagrossi 等 - 2021
• 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