Mathematical model of a thread for space tether systems

Abstract

This article is devoted to the deployment and use of tether systems for solving emerging space tasks and promising projects. To ensure the safe use of tether systems, it is necessary to predict and model tether motion and to stabilize it when oscillations occur. For the deployment stage of a tether system, numerical modeling based on nonlinear partial differential equations describing the motion of an inextensible thread within the framework of solid mechanics is proposed. Confirmation by experiments conducted under constant gravity demonstrates the promise of this model for modeling space tether systems. During the deployment and operation of a tether system, wave processes may arise and lead to structural failure. To solve this problem, the possibility of stabilizing the tether system is considered. Possible tether stabilization mechanisms are obtained on the basis of the Lyapunov method. An experimental study conducted under constant gravity showed the effectiveness of the proposed stabilization mechanisms. The use of these mechanisms should be taken into account when developing mechanisms for tether systems to ensure safe operation.