A study of the evolution of satellite's rotations in the orbit plane

A spinning mode is analyzed for orientation of an Earth low orbit artificial satellite. In this mode, a satellite rotates around its principal central axis of the minimal moment of inertia, which swings near the normal to the orbital plane. The satellite angular rate is a few times greater than the orbital mean motion. The equations of satellite attitude motion are written taking into account the gravitational and restoring aerodynamic torques. The equations contain a small parameter, which characterizes asymmetry of the satellite tensor of inertia and aerodynamic torque. Using small parameter method and numerically, the two-dimensional integral manifold of the equations is constructed which describes quasi steady satellite rotations closed to the cylindrical precession of appropriate symmetrical satellite in the gravitational field. Such quasi steady rotations could be considered to be undisturbed motions in spinning mode. The investigation of the integral manifold consists in numerical solution of a periodical boundary value problem for the auxiliary differential system and numerical computation of quasi steady satellite rotations by the multi-revolution method. The possibility is demonstrated for construction of quasi steady rotations by minimizing the special quadratic functional.