Floquet Mode Method
Author: Tianjiang Says
Website: https://cislunarspace.cn
Definition
The Floquet mode method is an orbit keeping strategy based on the special dynamic characteristics near libration points, proposed by Gomez et al. This method achieves orbit keeping by eliminating the unstable Floquet modes associated with the reference orbit.
Basic Principle
For a linear periodic system, Floquet theory decomposes the state transition matrix as:
where is a constant matrix whose eigenvalues (Floquet multipliers) determine orbital stability. Unstable Floquet modes correspond to eigenvalues with magnitude greater than 1, causing orbit deviations to grow exponentially.
The core idea of the Floquet mode method is: by applying control maneuvers, eliminate the unstable components of orbit deviations, thereby preventing orbit divergence.
Comparison with Other Methods
| Method | Design Approach | Characteristics |
|---|---|---|
| Floquet mode method | Eliminate unstable components | Leverages dynamics, computationally efficient |
| Targeting method | Minimize deviation-control weighted sum | General-purpose, controllable fuel consumption |
| LQR | Optimal control theory | Requires precise model |
Related Concepts
References
- Gomez G, et al. Dynamics and mission design near libration point orbits[M]. World Scientific, 2001.