Fundamental Solution Set

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A set of linearly independent solutions to a linearized equation with periodic coefficients, given by Floquet theory. For relative motion near a 2:1 DRO, the fundamental solution set consists of six solutions: two in-plane quasi-periodic, one periodic (corresponding to fore-aft formation), one divergent, and two out-of-plane quasi-periodic. Any relative motion state can be expressed as a linear combination of these fundamental solutions.

Application Value

This term has significant application value in cislunar space missions。In the orbital design phase, engineers use relevant theories for trajectory optimization；In navigation and orbit determination, it is used to improve measurement accuracy；In attitude control and orbit maintenance tasks, it ensures stable spacecraft operation。In practical applications, parameter optimization and algorithm adaptation can be combined with mission requirements to improve mission success rate and resource utilization efficiency。

  • Characteristic Exponents
  • Capture Docking Phase
  • Lunar Flyby Transfer

References

  • 航空学报, 2023, 44(5): 326563
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Contributors: ouyangjiahong, Ou Yang Jiahong