Abstract: A satellite with a system of three concentric shields for electrostatic protection against cosmic radiation is considered. The interaction of an electric charge with the Earth’s magnetic field leads to the emergence of a Lorentz force torque acting on the rotational motion of the satellite relative to the center of mass. The Lorentz force torque is calculated taking into account the complex shape of the electrostatic protection screens and the geomagnetic field gradient in the volume of the screen. The geomagnetic field is modeled by a direct magnetic dipole. Differential equations of the satellite’s motion about the center of mass are written out and the first integrals of these equations are constructed. Steady-state motions of the satellite are found and sufficient conditions for their stability are obtained.