An analytical method for instability analysis of electrodynamic tether systems

The Electro Dynamic Tether (EDT) system has been demonstrated to be inherently unstable due to a continuous energy input from Lorentz force. Previous studies have made some progress in understanding the instability of the EDT system, while the degree of instability remains insufficiently explored. It is known that strong instability degree means short time before the system turns unstable, which is detrimental to on-orbit mission. Therefore, it is of great significance to evaluate the instability degree of EDT system in depth. The novelty of this paper lies in obtaining the analytical solution of Instantaneous Equilibrium Points (IEPs) under given system parameters, analyzing the distribution characteristics of IEPs, as well as revealing the impact of IEPs on stability. Therefore, a rapid assessment method of the EDT system's instability degree is proposed. Compared with the numerical method, the obtained analytical solution of IEPs shows higher efficiency and accuracy. Additionally, two theorems are proven to preliminarily determine the existence of IEPs. According to the IEP distribution and dynamics simulation on typical initial parameters, it is found that the system exhibits lower instability degree within the IEP zones, and there exists a specific central IEP zone with the lowest instability degree near the origin of the parameter-state plane. Priority should be given to choose the initial parameters within this region to gain lower instability degree.