On Electrodynamic Attitude Stabilization of a Spacecraft in the Natural Magneto-Velocity Coordinate System

A spacecraft with electrodynamic attitude control system in a low Earth orbit is under consideration. The problem of the spacecraft attitude stabilization is studied in the natural magneto-velocity coordinate system associated with the geomagnetic induction and Lorentz force. The nonlinear stability analysis based on the Lyapunov direct method is applied in the problem. A rigorous mathematical justification is proposed, which makes it possible to obtain specific estimates for the control parameters that provide a solution to the problem of spacecraft attitude stabilization without any limitations on the Earth’s magnetic field model. With the aid of the proposed Lyapunov function, sufficient conditions for the asymptotic stability of the spacecraft equilibrium position are derived. These conditions are formulated in terms of explicit and simple inequalities on the control parameters. Thus, a constructive approach to the design of stabilizing electrodynamic attitude control in the natural magneto-velocity coordinate system is formulated.