Orbital oscillations of an elastic vertically-tethered satellite

The motion of a satellite in a circular orbit with respect to its center of mass is considered. The satellite bears an elastic tether system unrolled along the local vertical. The load at the end of the tether oscillates harmonically. The satellite motion under the action of the gravitational moment and the moment due to the tether tension force is studied. The bifurcation diagram is constructed and the hetero- and homoclinic separatrix trajectories are determined. Mel'nikov's method is used to study the satellite chaotic behavior near separatrices under the action of the periodic tether tension force. The results of the present paper can be used to analyze tether systems of gravitational stabilization and to study the orbital behavior of a satellite with an unrolled tether system with respect to the satellite center of mass.