Spacecraft flights using light pressure energy are no longer a fantasy, but a reality of the near future. Such spaceships can be used to fly to large and small planets, to meet with asteroids and comets, to perform special tasks in the vicinity of the Sun or near the Earth. Of particular interest are the unique capabilities of such devices in remote areas of the Solar system, even near the solar corona. Here, the solar sail can simultaneously play the role of a power plant and a reliable screen, which protects the main instrument compartment from overheating. There is also the possibility of creating heliosynchronous orbits located lower than conventional gravitational orbits. The solar sail can be used to launch the spacecraft into geosynchronous orbit, the plane of which parallel to the equator plane and has non-zero latitude. In the orbits of these latitudes it is possible to create new systems to accommodate satellite systems. One of the important tasks is to create a space solar screen located near the Lagrange point L1 of the Sun-Earth system. This can help compensate for the greenhouse effect and control the global temperature of the Earth. Several such projects have already been published. New technologies will bring visible benefits based on the direct use of an unlimited source of solar energy. This article deals with mathematical models of the dynamics of a spacecraft with the solar sail. Control of the translational orbital motion, the transition to a given orbit and the rotation of the entire apparatus occurs by means of the orientation of the sail relative to the flow of sunlight. For these purposes, it is possible to change the properties, size and position of the sail. The behavior of solutions in the vicinity of the equilibrium or stationary motion is taken into account. The change of stability of the equations describing the perturbed processes is taken into account.