About a mode of gravitational orientation of rotating satellite

A spinning mode was analyzed for orientation of an Earth low orbit artificial satellite. In this mode, a satellite rotated around its longitudinal axis (the principal central axis of the minimal moment of inertia) swinging near the normal to the orbital plane. The satellite angular rate was equal a few tenth of degree per second in this mode. The equations of satellite attitude motion were written taking into account a gravitational and restoring aerodynamic torques as well as a dissipative torque of eddy currents produced by the Earth magnetic field. The equations contained a small parameter, which characterized asymmetry of the satellite tensor of inertia and non-gravitational torques. Using small parameter method and numerically, the two-dimensial integral manifold of the equations was constructed which described quasi steady satellite rotations closed to the cylindrical precession of appropriate asymmetrical satellite in the gravitational field. Such quasi steady rotations could be considered to be nominal motions in spinning mode.