Symplectic analysis on dynamic behaviors of tethered tug–debris system

As one of the potential active debris removal approaches, removal of space debris by a tether tow may be applied to perform the large space debris removal mission. To remedy the omissions of the current references, including effects of the initial state and the considerable elongation of the tether on the evolution of the tumbling angle of the target debris, the dynamic behaviors of the tethered tug–debris system are investigated by using the symplectic Runge-Kutta method in this paper. Introducing the generalized momentum vector for the generalized coordinate vector, the finite-dimensional generalized Hamiltonian function is yielded and the generalized Hamiltonian dual equation describing the coupling dynamic behaviors of the tethered tug–debris system is deduced. To investigate the coupling dynamic behaviors of the tethered tug–debris system, the second-level fourth-order symplectic Runge-Kutta scheme is constructed and the perfect structure-preserving properties of it is verified. The effects of the elastic constant of the tether and the initial Euler angular velocity on the evolution of the tumbling angle are investigated in the numerical experiments in detail. The beat characteristic and the “window” characteristic in the evolution of the tumbling angle with small elastic constants of the tether are reproduced. In addition, the sharp change phenomenon in the evolution of the tumbling angle is found when the elastic constant of the tether is extremely small. The above findings can be used to guide the strategy design of the removal of space debris by a tether tow.