Numerical determination of stability regions for orbital motion in uniformly rotating second degree and order gravity fields

The stability of orbital motion about a uniformly rotating arbitrary second degree and order gravity field is investigated. A normalized form of the equations of motion are derived and analyzed. A numerical stability criteria is proposed and used to evaluate the stability of initially near-circular orbits in the equatorial plane of the body. Regions of stable and unstable motion are clearly delineated, and are seen to be strongly related to resonances between the mean motion and the body rotation rate.