Manifold Overlap

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The phenomenon where the position projections of stable and unstable manifolds from different restricted three-body problems intersect on a Poincaré section. The overlapping region in yz-coordinates is the geometric prerequisite for constructing cross-system connecting trajectories: each point in the overlap corresponds to a pair of initial phases in the two RTBPs, which when joined yield a position-continuous transfer.

Application Value

The Manifold Overlap 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

  • Canalias and Masdemont, Acta Astronautica, 2008
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Contributors: ouyangjiahong, Ou Yang Jiahong