# Dynamic Behavior and Libration Control of an Electrodynamic Tether System for Space Debris Capture
## 1 Introduction
[PERSON] and [PERSON] [20] compared the behaviors in post-capture towing scenarios using the dumbbell model, the lumped-mass model, and the ANCF model. EDT systems generate Lorentz forces through the interaction of tether currents with Earth's magnetic field, enabling orbital control and debris removal. [PERSON] et al. [21] introduced an exposed tether system for efficient electron collection, applying the orbital motion limited (OML) theory. [PERSON] et al. [22] studied orbital departure strategies, while [PERSON] and [PERSON] [23] modeled orbital dynamics considering perturbations. [PERSON] et al. [24] proposed a current control method to stabilize EDT system vibrations. [PERSON] and [PERSON] [25] applied the finite element method to the OML theory for electron harvesting to establish discretized OML equations. [PERSON] and [PERSON] [26] demonstrated EDT system applications for microsatellites, achieving fuel-free orbit maintenance. [PERSON] et al. [27] investigated the electrical current control of a spinning bare electrodynamic tether system during its spin-up process. [PERSON] et al. [28] developed an advanced rigid-flexible coupling dynamic model for tethered satellite systems to improve space debris management. [PERSON] et al. [29] focused on designing collision-avoidance strategies for spinning electrodynamic tether systems utilizing electrodynamic forces. Our investigation reveals that few studies have thoroughly analyzed the dynamic behavior of flexible tethers in EDT systems following the capture of space debris usingelectrodynamic forces. The majority of existing research assumes a rigid tether in EDT systems, thereby neglecting the impact of tether deformations. Moreover, prior studies on EDT systems have predominantly focused on stabilizing tether dynamics during deployment and facilitating the deorbiting of space debris. Although the dynamic behavior induced by debris capture has been explored for flexible tether systems, the extension of this research to stabilization strategies utilizing electrodynamic forces remains limited. Effective control of the tumbling motions induced during debris capture is crucial for the reusability of tether systems in debris removal missions. Consequently, a comprehensive study of the dynamic behavior of EDT systems in debris capture scenarios necessitates modeling that accounts for both tether flexibility and the electrodynamic forces acting on the system. The innovative contributions of this study can be summarized as follows:  
* This study develops a three-dimensional dynamic model that accurately represents the behavior of an EDT system in space debris capture. The model incorporates tether flexibility, electrodynamic forces, and the effects of Earth's magnetic field, providing a more comprehensive and realistic analysis of EDT dynamics. * This research establishes the influence of tether length and diameter on current generation, Lorentz forces, and system dynamics. The findings offer essential design guidelines to optimize the efficiency and effectiveness of EDT systems for space debris removal. * The study demonstrates that applying Lorentz force control through an on-off switch mechanism can effectively suppress the libration angles induced during debris capture. This capability significantly enhances mission reliability and the reusability of EDT systems in active debris removal operations. * By analyzing the complex interactions between tether deformation, electrodynamic forces, and orbital mechanics, this research expands the theoretical framework for EDT-based space missions. The insights gained contribute to improving stabilization strategies and advancing sustainable space operations. The paper is organized as follows. Section 2 outlines the three-dimensional modeling of the EDT system. Section 3 describes the discretization using ANCF and the establishment of nonlinear motion equations using [PERSON]'s equation, with responses calculated using the fourth-order Runge-Kutta method.