Equilibrium analysis of the tethered tug debris system with fuel residuals

The problem of tethered transportation of space debris is considered. The system consists of orbit tug, tether, and passive spacecraft with fuel residuals. The planar motion on circular orbit is studied in the orbital frame. Nonlinear motion equations are obtained by Lagrangian formalism. They consider action of the space tug-thrust and gravitational moments. Two variants of stable positions of relative equilibrium are defined. They depend on main parameters of the tethered system: aspect ratio and mass ratio. The equations of the first approximation for the each of the stable position variants are obtained. Their coefficients analysis give evidence of approachment all of the natural frequency of the system and permit to find corresponding conditions. The results of numerical simulation of the motion of the tethered system and their comparison with small oscillations determined by are presented. Proposed equations can be used to analyze the attitude motion of the tug–debris system and to determine the conventional parameters for safe tethered transportation of space debris.