  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.
