Hyperbolic Manifold

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The collection of stable and unstable invariant manifolds associated with the central manifold of a collinear libration point. Trajectories on the stable manifold approach the reference orbit exponentially forward in time; those on the unstable manifold depart exponentially. These tube-shaped structures serve as dynamical conduits near libration points and form the basis for manifold-based transfer orbit design.

Application Value

Hyperbolic manifolds have tube-shaped structures serving as dynamical conduits near libration points. Using unstable manifolds to design departure orbits and stable manifolds to design arrival orbits is a fundamental method for low-energy transfer trajectory design.

  • Orbital State Vector
  • Coordinate Time
  • Hill Frame
  • Kepler's Laws

References

  • Alessi 等 - 2009 - Leaving the moon by means of invariant manifolds of libration point orbits
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Contributors: ouyangjiahong, Ou Yang Jiahong