Averaging technique in the problem of satellite attitude stabilization in indirect position in the orbital reference frame with the use of Lorentz torque

A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem the Lorentzian stabilization orbital coordinate system indirect equilibrium position solved under conditions perturbing effect gravitational torque. To solve this problem, which characterized by incomplete control, method averaging differential equations developed. Using original construction unsteady Lyapunov function, we obtain sufficient for asymptotic stability programmed motion mode form constructive inequalities with respect to control parameters.