Mathematical modeling of a space tether considering the transition from the slack cable configuration to the tensioned cable configuration

Resumo

This paper proposes a mathematical model for the dynamics of a space tether in the unstretched configuration (cable deformed but not tensioned; also named slack cable configuration), in the stretched configuration (cable deformed and tensioned) and considers the transition from one configuration to the other. Hamilton's principle is applied to obtain the governing equations of motion and boundary conditions for both configurations. Constraint equations are presented that determines the transition from the untensioned configuration to the tensioned configuration and vice-versa. External forces applied to the masses (satellites) at the ends of the space tether are responsible for the stretching of the cable, which is the desired configuration. The ultimate goal of this research is that in the stretched configuration, a desired value for the tension developed in the cable must be achieved and maintained so that the space-tether operation is satisfactory.