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The escalating threat posed by space debris necessitates innovative approaches for its removal. This article presents a comprehensive mathematical modeling and dynamic analysis of a flexible tethered satellite system (FTSS) in the post-capture phase, taking into account nonlinear strain effects for the flexible appendages. The FTSS consists of a rigid central body satellite, two identical flexible panels, and a towing mass that manipulates the satellite through a tether. We develop a detailed dynamic model that accurately represents the system's three-dimensional motion, incorporating the rigid body's 6 degrees of freedom (DOF), the tether's 3 DOF motion, and two modal generalized coordinates for each panel. The extended Hamilton method is employed to derive this model, enabling us to investigate the conditions under which nonlinear strain considerations become critical. The findings of this article reveal that nonlinear strain effects can profoundly impact the system's dynamics under certain geometric and forcing conditions, often overlooked in previous studies. In these scenarios, the panel strains exceed the linear regime, necessitating the use of nonlinear models for accurate representation. This work emphasizes the importance of incorporating nonlinear strain terms in the dynamic analysis of FTSSs, particularly when dealing with large deformations and high-amplitude vibrations encountered in debris removal applications.
Shahbazzadeh et al. (Sun,) studied this question.