论文信息 - Relative Motion between Elliptic Orbits: Generalized Boundedness Conditions and Optimal Formationkeeping

Relative Motion between Elliptic Orbits: Generalized Boundedness Conditions and Optimal Formationkeeping

Based on the concept of orbital commensurability, necessary and sufficient conditions are presented for bounded relative motion between any two spacecraft flying on elliptic Keplerian orbits. The proposed approach does not involve any simplifying assumptions regarding the relative dynamics but rather treats the general, nonlinear, eccentric relative motion problem. The methodology presented alleviates the difficulty in computing corrections to the linear equations of motion to account for nonlinearities and eccentricities. Instead of dealing with the local relative motion problem, the global relative motion problem is addressed by transforming the orbital resonance requirement into an energy-matching condition. The newly developed setup is then utilized to derive an optimal single-impulse formationkeeping maneuver based on relative state variables. The orbital elements interpretation of the optimal formationkeeping maneuver is also discussed.

P. Gurfil

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