Dynamics, analytical solutions and choice of parameters for towed space debris with flexible appendages

•The active debris removal system using tethered tug is studied.•The space debris is considered as a large spacecraft with flexible appendages.•We examine the influence of flexible appendages to the active debris removal.•Parameters of the system are determined to avoid high amplitude vibrations.

Active debris removal is one of the promising techniques that will decrease the population of large, non-functional spacecraft (space debris) on orbit. Properties of space debris should be taken into account during planning an active debris removal mission. In this paper the thrusting phase of tethered deorbit of large space debris with flexible appendages is considered. The goal of the work is to investigate the mutual influence of the tether vibrations and the vibrations of flexible appendages during thrusting phase. A mathematical model of the space tug and the towed space debris with flexible appendages is developed. Parameters of the system are determined with assumptions that the system is moving in straight line, avoiding high amplitude vibrations of flexible appendages. The expression of the discriminant indicates that the vibrations of the tether and flexible appendages influence each other. A critical tether stiffness exists for the given space tug mass that should be avoided.