Abstract Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite relative motion solutions for linearization about a closed chief orbit. By identifying the analytic relationship between Lyapunov–Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration of the types of close-proximity natural relative motion available in various applications. The approach is demonstrated for the Keplerian relative motion problem with general eccentricities in multiple coordinate representations. The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.
Highlights The modal decomposition concept for spacecraft relative motion is introduced The concepts discussed can be extended to non-Keplerian orbits The effects of perturbations on the fundamental relative motion modes are derived Numerical examples demonstrate the modal decomposition of relative motion Some cases connect to prior analysis of the Tschauner–Hempel fundamental solutions
Geometric perspectives on fundamental solutions in the linearized satellite relative motion problem
Acta Astronautica ; 190 ; 48-61
2021-09-21
14 pages
Article (Journal)
Electronic Resource
English
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