The motion of a system of two satellites connected by a flexible tether, the length of which can be controlled, is studied. The satellites are modelled as point masses and the tether is modelled as a massive continuous visco-elastic cable, allowing for three-dimensional displacements. Two different sets of equations of motion, one in a floating non-rotating frame (Lorentzian frame) and the other one in a floating rotating frame (shadow frame), are presented resulting in systems of coupled non-linear partial and ordinary differential equations. Large rotational motions of the whole system and large deformations of the tether are included in the formulation. External forces considered are gravitational attraction of a spherical Earth and atmospheric drag. Two different solution strategies, namely a Galerkin modal approach and a FE-discretization, are used to calculate large amplitude motions of the system.