Fundamental frequencies of satellite relative motion and control of formations

Expressions for the fundamental natural frequencies associated with J 2-perturbed relative motion of satellites in near-circular orbits are derived. Special values of the orbit inclination, dependent on initial conditions, are obtained, for which the in-plane and out-of-plane fundamental frequencies remain equal to each other over an extended period of time, resulting in nonprecessing relative orbits. This result validates and generalizes a similar finding, based on numerical investigations by other researchers. The analysis is extended to the developments of accurate prediction and control models for fuel-optimal formation maintenance and intersatellite fuel balancing. Numerical simulation results are presented to demonstrate the accuracy of the developed models and the effects of frequency matching on control requirements.

Fundamental frequencies of satellite relative motion and control of formations Academic Article