Orbital-attitude coupling effects on the motion of a dumbbell space tether

The effects of the divergence between the centre of mass and centre of gravity on the orbital motion of a dumbbell space tether, treated as a satellite of finite size, are investigated. For a radially aligned dumbbell tether with the angular speed required for a circular orbit of its centre of mass; the centre of mass of the system will traverse a trajectory from orbital apogee to perigee. This is found to be a direct result of this mass and gravity centre divergence and the system only undertakes a circular orbit when it has the angular speed required for a circular orbit of a particle at its centre of orbit. The coupling between the orbital and attitude motion for a radially aligned dumbbell tether is investigated and it is shown that for small deviations from the angular speed required for a circular orbit a libration of the tether spans is generated. This can progress to spin if the angular speed is increased further. Furthermore, it is shown that tether spans with a small initial speed relative to the centre of mass result in significant variations in orbital motion of the system. Finally, the exchange of energy between the orbital and attitude motion is investigated.