Numerically efficient formulation of the equations of motion of tethered satellite systems

Simulation of tethered satellite systems requires the numerical solution of a coupled system of nonlinear partial and ordinary differential equations. Due to the technical design of such systems the set of governing equations of motion results in a stiff system of differential equations. In order to avoid long integration times, contrary to the formulation usually used in the literature, an alternative description of the deformation of the tether is given. In the new variables after discretization of the continuous tether in space (for example by Finite Elements or Finite Differences) a system of ordinary differential equations is obtained in which the fast motion is separated from the slow motion. For the integration of such systems specialized software is available reducing integration time considerably.