Stabilization of an electrically charged spacecraft in the orbital plane

In this paper, the orbital motion of an electrically charged spacecraft in the gravitational and magnetic fields of the Earth is investigated. The straight dipole is considered as a model of the geomagnetic field. The nonlinear autonomous system of differential equations of motion of the spacecraft center of mass in the Cartesian and spherical coordinate systems is derived. The analytical study of the influence of the Lorentz force on the orbital motion of a charged spacecraft is carried out. The approximate solution of the differential system is found. The results of numerical simulation of the spacecraft orbital motion based on the derived system of differential equations are presented. The analytical and numerical solutions are compared. The problem of stabilizing the spacecraft's center of mass in the orbital plane is considered. Feedback control methods based on the use of jet engines are proposed. The technical justification of the proposed control methods is carried out. As a result, stabilization of an electrically charged spacecraft in a small neighbourhood of the plane of the initial orbit is achieved.