Invariant Torus Manifold

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The stable or unstable manifold of an invariant torus in the bicircular four-body problem. On the Earth-Moon side, these manifolds resemble those of Lyapunov orbits in the CR3BP and can be determined directly from eigenvalues and eigenvectors of the state transition matrix over the invariant curve. This manifold provides the basis for continuing CR3BP manifold results to the four-body model.

Application Value

This term在cislunar space missions中has important application value. In orbit design, it can be used foroptimizing transfer trajectories, reducing mission fuel consumption. In attitude control and dynamics analysis, it helps understandthe motion characteristics of spacecraft in complex gravitational fields, providing theoretical support for mission planning. In navigation and orbit determination, methods based on this termcan improve orbit prediction accuracy, supporting the development of autonomous navigation algorithms.

  • Periodicity Conditions in Relative Orbital Motion
  • Helix Formation
  • Energy Dissipation Method
  • Unstable Manifold

References

  • Ren et al., Celest. Mech. Dyn. Astron. (2012)
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