On resonant periodic motions close to conical precession of a dynamically symmetric satellite in a weakly elliptic orbit

Abstract

The motion of a dynamically symmetric rigid body (satellite) about its centre of mass in an elliptical orbit is considered. It is assumed that the eccentricity of the orbit is small and an external resonance caused by gravitational torque takes place. Periodic motions emanating from conical precession of the satellite are studied. Such periodic motions can be constructed in a form of convergent series of fractional powers of the eccentricity. The first terms of these series expansion have been calculated in an explicit form. The bifurcation phenomenon of the above periodic motions is investigated.