Resonant rotations of satellite in polar orbit in magnetic and gravitational fields

A second order differential equation is written for the planar rotations of a satellite about a center of mass in an elliptical polar orbit subjected to both gravitational and magnetic forces with the true anomaly as the independent variable. It is assumed in the solution that the permanent magnetic moment is directed along the axis of the satellite corresponding to the moment of inertia, the axis forming an angle with the current radius vector. The Earth's magnetic field is a dipole field with the dipole axis coinciding with the Earth's axis of rotation. The main resonances of the orientation of the satellite in absolute space, the current radius vector of the orbit and the current magnetic line of force are analyzed to demonstrate the feasibility of strict and stable orientation of the satellite with respect to these three orientations. It is possible to completely compensate eccentric oscillations of the satellite by the magnetic field. The special case of a circular orbit is analyzed in considerable detail, showing the magnetic field ranges for which stable solutions exist.