Investigation of steady-state motions of Earth artificial satellite in single axis magnetic orientation mode

We investigate the angular motion of an axially symmetric artificial satellite with a permanent magnet in the Earth's magnetic field (EMF). The satellite orbital motion is considered taking into account the influence of the non-centrality of the Earth's gravitational field and the atmosphere drag, IGRF is used as the model of the EMF, the satellite's own magnetic moment is parallel to the axis of symmetry. Steady-state satellite motions are constructed in which this axis forms a small angle with the EMF vector. We approximate such a motion by a sequence of periodic solutions of modified motion equations. These solutions have the orbital period, but the sequence as a whole reproduces almost full spectrum of a steady-state motion including the frequencies relating to the Earth rotation.