Dynamic Model and Control of Mass-Distributed Tether Satellite System

A set of partial differential equations is developed to describe the mass-distributed and extensible tether satellite system. Supplemented with a range-rate control algorithm and proper boundary conditions, the system canbe studied either by the numerical integration of the equations or by considering the stationary motion (configuration) in the system. The former approach is not adequate because (if the integration is possible) it requires very high mathematical skill and huge amount of computations. On the contrary, the stationary configuration is easier to determine and provides more valuable information about the system as a whole. The stable stationary configuration is essentially all that is needed to carry out a tether mission in space. An iterative algorithm to compute the stationary configuration and a method of its stability analysis is proposed. Finally, a numerical simulation is given.