Cable towing of a space debris object with a cavity filled with liquid
Space debris active transportation employing a space tug with a tether link is one of the promising techniques of near-Earth space cleaning-up. When developing such transportation means, it is necessary to account for the specifics of space debris objects, particularly, the presence of elastic structure elements, and fuel remnants. There are two types of the space debris, namely, overaged spacecraft and orbital stages of rocket carriers. On one hand, orbital stages are simpler for transportation compared to spacecraft, since they do not contain large attached elastic elements, such as antennas or solar batteries. On the other hand, orbital stages might contain fuel remnants affecting the motion of space debris and the transportation system at large. The presented work is devoted to this phenomenon. The purpose of this work is development of a simple mathematical model of a transportation system with account for the fuel remnants onboard the space debris object of a space station type. The article studies the effect of fuel remnants on the safety of withdrawal the space debris with fuel remnants. The authors obtained equations of motion in central gravitational field of a mechanical system, consisting of a space tug, space debris object and a tether. The space debris object is considered as solid body, containing a moving mass of liquid. The liquid fluctuating in the tank is represented as an equivalent pendulum system. Stationary solutions of the equations of movement were found, and linearized equations in the neighborhood of stable stationary solutions were constructed. The results of numerical modeling, demonstrating the closeness of analytical solutions of the linearized equations and numerical solutions of the initial equations of motion are presented. The obtained linearized equations can be useful for determining transportation system parameters, ensuring safe withdrawal of the space debris.