Three-dimensional vibrations of Tethered Satellite System

An analytical model is presented to study the three-dimensional free vibrations of the Tethered Satellite System. In the model, the tether is considered as an elastic continuum with mass, while the Space Shuttle and the subsatellite are considered as two concentrated masses. Linearized equations of motion are given for out-of-plane and in-plane vibrations. Extended numerical analyses are performed for the geometrical and mechanical properties of the system. It is found that the two in-plane motion components are weakly coupled through the gyroscopic forces, with generally transversal or longitudinal type modes. The transversal modes are almost identical to the out-of-planes modes.