Analytical Modeling of the Dynamics of an Unrolling Space Tether Deployer

The study presented in this paper deals with the modeling of the attitude motion of an unrolling reel after deployment from a carrier spacecraft. Among the different dynamical loads, the friction forces - due to the sliding wire - acting on the reel are particularly hard to model due to the very uncertain path of the unwinding wire on the deployer. This is why, in the approach presented herein, the whole wire is split in an unperturbed part, a sliding part and a straight part, still connected to the carrier spacecraft. A set of dynamic equations is written for the sliding part, and solved analytically in order to extract a closed-form solution for the applied loads. These equations are then implemented in a software code where the attitude and the motion of the center of mass of the reel are numerically integrated, given a set of initial conditions. Numerical results fully validate the newly developed analytical model and show that, as expected, the wire friction and the deployer’s attitude motion are mutually dependent.