Floquet Decomposition

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A method that performs eigenvalue decomposition on the monodromy matrix of a linear system with periodic coefficients. The eigenvalues are classified into unstable, neutral, and stable categories based on their magnitudes, corresponding to divergent, periodic (with linear growth), and quasi-periodic solutions, yielding the complete fundamental solution set of the linearized relative motion. For 2:1 DRO, the monodromy matrix contains two pairs of conjugate complex eigenvalues with unit modulus and one pair of real eigenvalues.

Application Value

This术语在地月空间任务的设计、分析和控制中具有important应用价值，为相关技术领域的研究和工程实践provides理论支撑。

Related Concepts

• 地心天体参考框架（Geocentric Celestial Reference Frame）
• 运行轨道库（Operational Orbit Library）
• 内部频率（Inner Frequencies）
• 准周期远距离逆行轨道（Quasi-Periodic Distant Retrograde Orbit, QPDRO）

References

• Yang et al. 2023
• Yang, Fu & Zhang 2023