Optimal control of deployment of a tethered subsatellite

One of the most important operations during a tethered satellite system mission is the deployment of a subsatellite from a space ship. We restrict to the simple but practically important case that the system is moving on a circular orbit around the Earth. The main problem during deployment due to gravity gradient is that the two satellites do not move along the straight radial relative equilibrium position which is stable for a tether of constant length. Instead, deployment leads to an unstable motion with respect to the radial relative equilibrium configuration. Therefore we introduce an optimal control strategy using the Maximum Principle to achieve a force controlled deployment of the tethered subsatellite from the radial relative equilibrium position close to the space ship to the radial relative equilibrium position far away from the space ship.