Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium

We study the fast rotational motion of a dynamically nonsymmetric satellite about the center of mass under the action of the gravitational torque and the drag torque. Orbital motions with arbitrary eccentricity are assumed to be given. The drag torque is assumed to be a linear function of the angular velocity. The system obtained after the averaging over the Euler-Poinsot motion is studied. We discover the following phenomena: the modulus of the angular momentum and the kinetic energy decrease, and there exist quasistationary regimes of motion (along the polhodes). The orientation of the angular momentum vector in the orbital frame of reference is determined. The general case is studied numerically, and an analytic study is performed in a neighborhood of the axial rotation and in the case of small dissipation.