The book is part of the series, which began publication in 1975. The collection includes articles on mathematical issues of the theory of stabilization of composite space systems intended for radiophysical, astronomical and other scientific purposes: The dynamics of the double-rotation satellite, its stability, as well as the auto-fluctuation of the stabilization axis. The problem is reduced to the solution of differential equations, in general nonlinear and containing variable parameters. Dynamic processes are evaluated and control laws are built to stabilize the satellite. The book is designed for applied mathematicians, mechanics, astrophysicists working in the field of design and calculation of spacecraft. It can be used by graduate students and students as a teaching aid.