Study of the triple-mass Tethered Satellite System under aerodynamic drag and J2 perturbations

The dynamics of multi-tethered satellite formations consisting of three masses are studied in this paper. The triple-mass triple-tethered satellite system is modeled under the low Earth orbit perturbations of drag and Earth’s oblateness and its equilibrium conditions are derived. It is modeled as three equal end-masses connected by a uniform-mass straight tether. The lengths of tethers are supposed to be constant and in this manner the angles of the plane consisting the masses are taken as the state variables of the system. The governing equations of motion are derived using Lagrangian approach. The aerodynamic drag perturbation is expressed as an external non-conservative force and the Earth oblateness (J2 perturbation) is considered as a term of potential energy. The equilibrium conditions of this system are found and their stability is investigated through the linear stability theory. Then, the results are verified by using a nonlinear simulation for three types of equilibrium conditions.