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Comprehensive analysis of space debris rotational dynamics is vital for active debris removal missions that require physical capture or de-tumbling of a target. We study the attitude motion of used rocket bodies acknowledgedly belonging to one of the categories of large space debris objects that pose an immediate danger to space operations in low Earth orbits. Particularly, we focus on Sun-synchronous orbits (SSO) with altitudes in the interval 600 ÷ 800 km, where the density of space debris is maximal. Our mathematical model takes into account the gravity gradient torque and the torque due to eddy currents induced by the interaction of conductive materials with the geomagnetic field. Using perturbation techniques and numerical methods we examine the deceleration of the initial fast rotation and the subsequent transition to a relative equilibrium with respect to the local vertical. A better understanding of the latter phase is achieved owing to a more accurate model of the eddy currents torque than in most prior research. We show that SSO precession is also an important factor influencing the motion properties. One of its effects is manifested at the deceleration stage as the angular momentum vector oscillates about the direction to the south celestial pole.