Transient chaotic oscillations of a tethered satellite system

For the simulation of large amplitude motions of thin, visco-elastic tethers connecting two satellites several numerical algorithms were developed recently. However, since we are dealing with highly nonlinear, nearly Hamiltonian multiple degree of freedom systems we typically will have to expect transient chaotic motions if the motion starts in the neighborhood of a saddle point. For tethered satellite systems we have two stable radial and two unstable tangent-to-orbit equilibria. By simulation with a specially adapted finite-element program we show that the asymptotic behaviour of the system strongly depends on the choice of the initial conditions. Thus, starting in the vicinity of an unstable equilibrium, we cannot predict in which of the attractors it settles down finally. A simple tether model by V. Beletsky and D. Pankova is used to demonstrate the fractal nature of the basin boundary of the two attractors.