Dynamics of a tethered satellite system

There are differences in the dynamic equations of motion of the Tethered Satellite System (TSS) used in the analysis of various papers. We present a detailed derivation of equations of motion for the simplest possible TSS which is composed of two point mass and massless rigid tether as a typical TSS model. Applying general vector differential equation of relative motion for a point mass and carefully defining needed coordinate systems and coordinate transformations, the equations of motion of a tethered subsatellite having a general path were obtained. With the assumption of a massless and rigid tether, the new dynamic equations describe the behavior of the TSS exactly. In this paper, tether force and engine thrust are included into the analysis. The results from this approach has more high order terms but can be simplified to those of the previous research in which approximate kinetic energy was found and Lagrange's method was used to derive equations. This fact proves the validity of the derived results.