Exponential Instability

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A dynamical property of periodic orbits near collinear libration points. Characterized by the Floquet multiplier lambda_5 > 1: the orbit diverges at an exponential rate of lambda_5 - 1 under perturbation. This is dictated by the saddle-point nature of collinear libration points, meaning the spacecraft will exponentially depart the Halo orbit along the unstable manifold without control. The paper notes that from a stability perspective, amplitudes with Floquet multipliers closer to 1 are preferred, but large-amplitude orbits have larger multipliers and higher maintenance costs; small-amplitude orbits with worse stability may be chosen for mission requirements (e.g., Genesis mission amplitude of 260,000 km).

Application Value

This concept is applicable in cislunar space mission design, orbit optimization, and trajectory planning for spacecraft transfers and maneuver strategies.

References

  • 徐明和徐世杰 - 2008 - Halo轨道维持的线性周期控制策略
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Contributors: ouyangjiahong, Ou Yang Jiahong