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A spatial motion of a large passive satellite (space debris) and a space tug connected by an elastic tether is considered. The motion of the system is excited by a thrust force acting on the space tug. Major attention is given to a derivation of the equations of the motion based on the Lagrange formalism. Correctness of the mathematical model is proved by the theorem on variation of angular momentum and by the numerical simulations. The influence of the initial conditions and the system parameters on the behavior of the passive satellite is studied. The possibility of critical modes of the system motion leading to entanglement of the tether is shown by means of the numerical simulations.Nomenclature A, B, C = moments of inertia of the passive satellite, kg · m 2 a, b, c = coordinates of the tether-attachment point in the coordinate frame Sxyz, m c t = tether stiffness, N∕m K H = angular-momentum vector of the system relative to the point T, kg · m 2 ∕s K S = angular-momentum vector of the passive satellite relative to the point S, kg · m 2 ∕s k t = tether-damping coefficient, N · s∕m l = length of the tether, m m H = mass of the space tug, kg m S = mass of the passive satellite (space debris), kg p ψ , p φ = generalized impulses, kg · m 2 ∕s s = distance between centers of mass of the space tug and the passive satellite, m Sxyz = principal coordinate frame of the passive satellite Sx c y c z c = coordinate frame aligned to the line between the center mass of the passive satellite and the center mass of the space tug T = kinetic energy of the system, J ψ, θ, φ = Euler angles that describe attitude motion of the passive satellite relative to the frame Sx c y c z c , rad

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