Impulsive Station-Keeping Strategy for Libration Point Orbits via Nondivergent Component Suppression

Center manifold theory describes the phase flow near collinear libration points as a combination of two harmonic oscillations and one hyperbolic motion, the latter driving exponential spacecraft divergence. The Floquet modes approach (FMA), based on Floquet theory, is widely studied but suffers from inefficiency due to its inability to suppress nondivergent components (NDCs) beyond the unstable motion. To overcome this limitation, we propose an improved FMA strategy that leverages the collateral effect of NDCs—a key factor in traditional FMA failures yet exploitable for enhanced control. First, a predictor–corrector algorithm computes a correction factor κ to refine unstable mode estimation, accounting for unmodeled nonlinearities. Next, the most critical NDC is identified and suppressed, the timing of the next maneuver is predicted, and a maneuver overshoot factor δ_v is introduced to regulate excessive NDCs. By strategically selecting maneuver types, our approach ensures effective suppression. Finally, three numerical simulations validate the method’s effectiveness, versatility, and robustness.