Two-dimensional formal integral manifolds are constructed for mechanical systems, which motion equations, contain a small parameter. The construction makes use of the Bogolyubov - Mitropolsky method. Such integral manifolds are used to describe two modes of artificial satellite passive single axis orientation. One of them is the gravity gradient orientation mode and the other is the satellite rotation around its axis of the minimal moment of inertia, which makes small oscillation near the normal to the orbital plane. In the first case the small parameter is ratio of satellite minimal and maximal principal central moments of inertia, in the second one it is ratio of difference two biggest principal central moments of inertia to minimal moments of inertia. Gravitational and restoring aerodynamic torque are taken into account in satellite attitude motion equation. The main attention is paid to selection of generating solution and methods of investigation of motion evolution under the action of nonpotential part of the aerodynamic torque.

Theoretical and applied problems of mechanics