Mathematical models of the dynamics of spacecraft with a solar sail to control translational orbital motion and rotation of the whole structure are provided the stability of the sail orientation relative to the flow of sunlight. The behavior of solutions in a neighborhood of the possible equilibrium or stationary state of motion is taken into account. Change in the stability depending on the tasks and the transformation of equations that describe the perturbed processes is taken into account. It is possible to vary the properties, sizes or locations of the sails to control the motion and for implementation of the orbital motion or to move to the predetermined final orbit. Flights spacecraft using light pressure energy is no longer fantastic, but the reality of the near future. Such cosmic sailboats can be used for flights to the large and small planets, to meet with asteroids and comet, to form a special motion in the neighborhood of the Sun or near the Earth. Of interest are the special features is the unique possibility of functioning in the original solar areas, even near the solar corona, where the sail can simultaneously play the role power plant, but also a reliable screen, which protects against overheating the main instrument compartment. There is also the possibility of creating of the orbits helio-synchronous below than the normal gravitational orbits. Using a solar sail to bring the spacecraft into a geosynchronous orbit and the plane of this orbit that is parallel to the plane of the equator and has a non-zero latitude. At these latitudes, orbits can create new systems to accommodate satellite systems. One of the important problems is the creations of space-based solar shield located near Lagrange point L1 of the Sun – Earth system could be useful to offset the greenhouse effect and to control the Earth global temperature against global warming. Several such projects are already published. New technologies should bring visible benefits, based on the direct use of an unlimited source of solar energy.