Simulation of the motions of a tethered satellite system by means of three different numerical methods

We study the dynamics of a system of two satellites connected by a long massive cable by means of computer-simulations. The length of the cable may be variable. The cable can be extensible following a visco-elastic constitutive law or inextensible and may perform three-dimensional motions without any restrictions concerning the amplitude. Bending and torsional stiffnesses are neglected. Three numerical solution strategies are presented, each of them starting from different formulations of the equations of motion and using various discretization techniques, namely the Finite Element Method, a Galerkin Modal Approach and a Finite Difference Scheme. It is shown that these solution strategies yield nearly equal results. Furthermore, the advantages and disadvantages of each method are discussed.