Development and verification of a flexible tethered satellite system model considering the fuel slosh

Removing space debris of various sizes, configurations, and properties from Earth's orbits is one of the main missions of world space agencies. The existence of deactivated bodies within the path of other spacecraft increases the risk of collision. Althgough towing a satellite through a tether and taking it out of orbit may be a definite solution for space debris removal, most deactivated satellites have some fuel remaining in their fuel tank. This remaining liquid slosh within the tank directly affects satellite motion. To improve the mathematical modeling, the existence of unburned fuel is considered. More specifically, this research focuses on dynamic modeling and control of a selected type of satellite by taking into account the sloshing effect of debris captured using a tug and a tether. In this work, we consider the postcapture phase and consider the combined set of debris as a tethered satellite system (TSS). In this regard, we use both the classic and modified forms of the Lagrange method to derive the governing equation, which entails the calculation of the total kinetic and potential energies of the system. This system is modeled using two completely different simulation methods to create confidence and ensure the performance of our modeling: the MATLAB simulator and NX Siemens software, which is a type of CAD software. The final results of these two programs show an acceptable correlation. Finally, to reveal the effects of different parameters on the system variables, we perform a parametric study.