The purpose of the research was to build a mathematical model of an natural-artificial space tether system consisting of a space station and an asteroid, close in its dynamic characteristics to a dynamically symmetric solid body, connected by two tethers. The article describes some criteria of existence and stability for equilibrium configurations of the system deduced within the assumptions of the constructed model. Moreover, it classifies the types of the station motions near the asteroid surface, and gives the conditions ensuring the motions with taut tethers.
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