Spin dynamics of a long tethered sub-satellite system in geostationary orbit

A long tethered sub-satellite system (LTSS) has a promising application for earth observation, which requires that the LTSS spins towards the earth. Due to the long flexible tethers and the spinning of the LTSS, the system exhibits dynamics of high nonlinearity and high complexity. While most previous studies did not consider more than three satellites in a tethered satellite system, the computational method developed in this work allows considering an arbitrary number of satellites as demonstrated by the numerical examples presented. First of all, a nonlinear flexible multibody dynamic model of the spinning LTSS in the orbital coordinate frame is established and the corresponding dynamic analysis is studied. Here, the absolute nodal coordinate formulation (ANCF) and the natural coordinate formulation (NCF) are used to accurately describe the large deformations and large overall motions of the flexible tethers and rigid satellites, respectively. Afterwards, through coordinate transformation, the orbital dynamics of the LTSS is obtained and the effects of Coriolis force, centrifugal force, and gravity gradient are analytically derived. Finally, several numerical examples are presented, and the vibrations and stabilities of the LTSS are analyzed via parameter study. • A spin dynamic model of a long tethered sub-satellite system is established. • The effects of Coriolis and centrifugal forces, gravity gradient are considered. • Vibrations and stabilities of the system is analyzed via parameter study.