The Solution of Some Problems of Optimizing the Processes of a Flexible Correction of Motion of Satellite Systems: I

The first of a series of problems of the optimization of correction of satellite systems, moving over near-circular orbits, is considered. The correction is accomplished by means of low-thrust engines and is supposed to be flexible, where only the parameters of the relative motion of satellites must be corrected. The problem has a large dimension, but is invariant with respect to renumbering of satellites. This allows us to decompose the problem, i.e., to find new variables, linearly dependent on old ones, in which the problem breaks down into a series of independent subproblems of low dimension. The decomposition is accomplished by means of the technique 1] based on the theory of linear representations of groups.