Hyperbolic Character of Collinear Points

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The instability property of the linearized dynamics at collinear libration points (L₁, L₂, L₃). The linear behaviour is of centre-centre-saddle type: the saddle component produces exponentially diverging hyperbolic directions, rendering the equilibrium unstable and giving rise to stable and unstable invariant manifolds for each periodic/quasi-periodic orbit.

Application Value

This concept provides fundamental support in cislunar space research and mission design. In practical applications, the appropriate analysis method should be selected based on specific mission scenarios and constraints.

References

  • Low-Energy Transfers in the Earth–Moon System (Alessi et al., 2011)
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Contributors: ouyangjiahong, Ou Yang Jiahong