The features of mathematical models of controlled motion of a spacecraft with a solar sail, which take into account the translational and rotational motion of all parts of the structure, are considered. Equations for motion in a photogravitational field are used on the basis of the two-body problem, taking into account perturbations, or a more general model of the bounded three-body problem. The gravitational field is supplemented by the field of light pressure forces, which makes it possible to simulate real dynamics processes. When approximating the system of equations of perturbed motion for different orbits and parameters of the main bodies, control capabilities and stability conditions of motion are obtained at the specified orbits, as well as in the vicinity of libration points. Stability of orientation or rotation relative to the center of mass is provided by the moment of light pressure forces on the elements of the sail system or additional actions of special engines.