Exponentially Unstable
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
The instability property where state deviations grow exponentially when the equilibrium has eigenvalues with nonzero real parts. The linearized system at a collinear libration point has a real eigenvalue pair ±d₁, yielding an exponentially growing (unstable) and decaying (stable) direction. Any initial deviation along the unstable component grows as e^{d₁t}, making continuous orbit control mandatory for spacecraft operating near collinear libration points.
Related Concepts
References
- On the control problem of keeping a spacecraft near collinear libration points