Modal Control of a Satellite in an Unstable Periodic Orbit About the Earth-Sun Interior Lagrange Point

A periodic halo orbit which exists about the interior Lagrange point for the Earth-sun system was decomposed using Floquet theory into modal variables, which are dynamically decoupled subspaces for the six degree of freedom system. Modal control consisted of evaluating the diverging mode and maneuvering to counteract its divergence. In the unperturbed system, this was successful. Control costs were low, and the significance is that the controller did nothing to suppress modes that were oscillatory or converging. The effect of the moons motion allowed the scheme to operate with reasonable control costs, but the effect of eccentricity caused divergence in spite of the controller