Asymptotic stability of a satellite with electrodynamic attitude control in the orbital frame

A satellite in a circular near-Earth orbit is under consideration. The three-axis stabilization of the satellite in the orbital coordinate system with the use of electrodynamic attitude control system is studied. No constraints are imposed on the Earth's magnetic field approximation. The gravity gradient disturbing torque acting on the satellite attitude dynamics is taken into account as the largest disturbing torque. With the use of the Lyapunov direct method, conditions under which electrodynamic control solves the problem are obtained. The restrictions on the control parameter values for which one can guarantee the asymptotic stability of the programmed satellite motion are found and represented in an explicit form. Comparison of the results of numerical simulation and analytical investigation demonstrate effectiveness of the proposed approach.