Natural Frequencies of a Tethered Satellite System

Abstract

This study investigated the natural frequencies of a tethered satellite system to enhance stability and operational reliability. Tethered satellite systems provide many advantages for space missions but exhibit inherently complex dynamics due to the interaction between rigid-body motions and tether deformation. A dumbbell model was employed to analyze rigid-body dynamics, with eigenvalue analysis used to determine the natural frequencies of orbital and librational motion. Additionally, tether deformation was examined through simulations based on the absolute nodal coordinate formulation (ANCF) and a tensioned beam model, facilitating both analytical and computational assessments of transverse and longitudinal frequencies. The results show that orbital angular velocity and libration frequencies are highly sensitive to system parameters such as tether length, orbital radius, and satellite masses. Furthermore, the transverse and longitudinal natural frequencies of the tether exhibit distinct dependencies, providing critical insights for the design and control of tethered satellite systems. This work bridges a gap in understanding coupled dynamics and offers a systematic framework for calculating natural frequencies, supporting practical implementation in space missions. © 2025 by the authors.