Effects of Tow Parameters on Dynamic Behaviors of Beam-type Orbital Debris

The Earth orbit becomes more and more crowded with the space launch missions one after the other. Most of the spacecrafts launched will stay in the orbit when the mission completed and a large number of the orbital debris will be produced in the hypervelocity impact, the high-intensity explosion or the dysfunctional satellites. Nowadays, developing high-efficiency removal approaches is one of the most important missions. Taking the tethered tow method widely used for the removal of the beam-type orbital debris as an example, the effects of the tow parameters on the dynamic behaviors of the beam-type orbital debris are investigated by using the complex structure-preserving method in this paper. Considering the non-sphere perturbation as well as the nonlinear coupling effects between the plane motion and the transverse vibration, the dynamic model of the flexible damping beam-type orbital debris subjected to a tow force is deduced firstly. Then, for the equations controlling the plane motion of the beam, the second-level fourth-order symplectic Runge–Kutta scheme is constructed; and for the equation controlling the transverse vibration of the flexible damping beam, the generalized multi-symplectic Preissmann scheme is constructed. The iteration between these two schemes is performed to investigate the effects of the tow parameters on the orbital radius, the attitude angle as well as the transverse vibration of the spatial flexible damping beam and the associated numerical results are reported finally. From the numerical results, the suitable tow parameters, named as the tow parameter window are suggested to restrain the transverse vibration and the tumbling of the flexible beam-type orbital debris. In addition, we find that, to restrain the tumbling of the beam, the tow position should be designed near the end of the beam with the fixed tow angle, or the tow angle should be designed to be less than the half of the initial attitude angle with the fixed tow position. These conclusions can be used to guide the tow strategy design for the beam-type orbital debris.