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This paper explores expressing the relative state in the close-proximitysatellite relative motion problem in terms of fundamental solution constants.The nominal uncontrolled relative state can be expressed in terms of a weightedsum of fundamental and geometrically insightful motions. These fundamentalmotions are obtained using Lyapunov-Floquet theory. In the case that thedynamics are perturbed by the action of a controller or by unmodeled dynamics,the weights on each fundamental solution are allowed to vary as in avariation-of-parameters approach, and in this manner function as statevariables. This methodology reveals interesting insights about satelliterelative motion and also enables elegant control approaches. This approach canbe applied in any dynamical environment as long as the chief orbit is periodic,and this is demonstrated with results for relative motion analysis and controlin the eccentric Keplerian problem and in the circular restricted three-bodyproblem (CR3BP). Some commentary on extension of the methodology beyond theperiodic chief orbit case is also provided. This is a promising and widelyapplicable new approach to the close-proximity satellite relative motionproblem.

Spacecraft Relative Motion Dynamics and Control Using Fundamental Solution Constants