Mathematical modeling of the deployment of the orbital tether system

The well-known mathematical model of an orbital tether system treats the tether as a set of mass points that are connected in series by weightless non-stretched threads. This model is described by ordinary differential equations and allows to take into account the tether mass and action of external forces upon the tether. The forces are considered to be applied to those mass points and depend on their physical characteristics. Such models allow to study motions of a deployed tether system. The given preprint demonstrates the use of such models for analysis of the deployment processes. The demonstration is given by the example in which the tether of 31 km is winded off the satellite with the mass of 6.3 t. The spherical capsule at the tether end has the diameter of 2.5 m and the mass of 17 kg. The special emphasis is placed to evaluation of the aerodynamic drag upon this system.