Uniform rotations of tethered system connected to a moon surface

• We consider control of orientation for a tether anchored to the surface of one of two primaries which move in elliptic orbits.
• We study possibilities to cause uniform rotations of the tether via control of the tether length.
• Rotations with some angular velocities and initial conditions are caused by 2p- periodic control.
• Some uniform rotations are proved to be stable.
• The developed approach can be applied to tether systems for asteroids׳ and moon׳s exploration.

We consider the problem of in-plane rotations of a space elevator with variable tether length attached to a surface of one of the primaries in a double system. The planet and its moon (or two asteroids) move about their center of mass in unperturbed elliptic Keplerian orbits. We discuss the possibilities to cause a prescribed motion of the system by changing the tether׳s length. Periodic solutions of the equation for the tether length control are studied using the method of small parameter. The stability of these solutions is studied numerically. The analysis shows that there exists a control law that implements tether rotations which are uniform with respect to true anomaly; one can indicate conditions when the above rotations are stable in the first approximation. These results can be used for the development of a planet elevator or a system for payload transportation to and from asteroid surface.