The problems of spacecrafts with a solar sail-controlled motion lead to the study of mathematical models for translational orbital motion and for the spaceship rotation about the mass center in photogravitational fields. There are opportunities to choose the optimal maneuvering conditions to realize orbital motion or to move to a given orbit point. The realization of the given optimal sail orientation about the sunlight flow allows to obtain motions in the vicinity of a possible relative equilibrium or stationary state. This realization also takes into account the stability change according to the process models with perturbations. For the motion control, we can change the properties, dimensions, or location of sail system elements. The spacecraft flights using light pressure are already a reality. Such space sailing ships may soon be used to fly to the big and small planets, for asteroids and comets meeting, to form special motion conditions in the vicinity of the Sun or the Earth. New technologies will bring visible benefits for solving complex problems, based on the direct use of practically unlimited source of solar energy.

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.