Homoclinic Connection

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An orbit in phase space that belongs to both the stable and unstable invariant manifolds of the same periodic orbit, asymptotically approaching it in both forward and backward time. In the cylindrical isomorphic mapping, homoclinic connections appear as intersection points of the stable and unstable manifold tube cross-sections and serve as separatrices that divide transit orbits from capture orbits.

Application Value

This concept is fundamental to cislunar orbital mechanics and mission analysis, providing essential theoretical support for trajectory design and operational planning.

  • Retrograde Motion
  • Absolute Phase Bias
  • Relative Attitude Quaternion
  • Radial-Tangential-Normal Coordinate System, RTN

References

  • Lunar capture trajectories and homoclinic connections through isomorphic mapping (Giancotti et al., 2012)
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Contributors: ouyangjiahong, Ou Yang Jiahong