A tether tension control law for tethered subsatellites deployed along local vertical

A tethered subsatellite deployed along the local vertical is in stable equilibrium. This applies equally to subsatellites deployed in the direction towards the earth from the main spacecraft or away from the earth. Momentary perturbations from this stable equilibrium will result in a swinging motion, which decays very slowly if passive means are relied upon to provide damping. A control law is described which actively damps the swinging motion by employing a reel, or other mechanism, to apply appropriate tension as a function of tetherline length, rate of change of length, and desired length. The same control law is shown to be useful for deployment and retrieval of tethered subsatellites in addition to damping to steady state.