Geometric Perspectives on Fundamental Solutions in the Linearized Satellite Relative Motion Problem
This work addresses fuel-efficient multi-satellite mission planning by offering improved methods for analyzing relative motion, though it is incremental as it builds on prior linearized solutions.
The paper tackled the problem of computing and parameterizing satellite relative motion solutions for linearized dynamics around a closed orbit, providing new geometric insights and enabling rapid exploration of natural relative motion types, demonstrated analytically for Keplerian cases with general eccentricities.
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.