Center Manifold

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A local invariant manifold near a saddle-type equilibrium, spanned by eigendirections corresponding to purely imaginary eigenvalues. The linearization at a collinear libration point has one real eigenvalue pair (±d₁, unstable) and two purely imaginary pairs (±id₂, ±id₃, oscillatory). The center manifold, spanned by the two oscillatory eigenspaces, is the phase-space structure on which Lissajous and Halo orbits exist.

Application Value

The Center Manifold 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

  • 关于探测器定点在共线平动点附近的控制问题
  • Colagrossi 等 - 2021
  • Gómez 等 - 2001
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Contributors: ouyangjiahong, Ou Yang Jiahong