Modeling the spatial motion of a space tether system with an inflatable balloon for raising payload orbit

The use of an auxiliary space tether system for putting payload into orbit is considered. It is assumed that initially the space tether system moves in circular orbit in a stable radial position. The payload is launched into a low orbit by a light rocket, where it is docked to a module at the lower tether end. After docking, a balloon is inflated by the module, and the tether system is transferred into rotation mode by the aerodynamic drag force. The aim of the work is to develop a mathematical model of the space tether system 3D motion and to analyse the influence of the balloon's center of mass position on the oscillations of the tether. Lagrange equations of second kind were used to obtain equations of motion. The results of numerical simulation of the system 3D motion with a spherical balloon showed that the considered payload lifting scheme can be implemented. It was shown that the spatial oscillations of the balloon have a weak effect on the tether oscillations. The position of the balloon center of mass significantly affects its oscillations. The most preferred situation is when the center of mass is below the geometric center of the balloon.