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.     

Capabilities of Kinematically Regular Satellite Systems with Symmetry Groups of the Second Type in the Problem of Continuous Single Coverage of the Earth

The problem of a continuous single coverage of the Earth by systems of satellites in circular orbits of equal radii is considered. The results of calculating the characteristics of kinematically regular systems consisting of 6 to 60 satellites and possessing symmetry groups of the second type are presented. It is shown that, when the number of satellites varies from 20 to 38 inclusive, the best systems of this class surpass all currently known systems with respect to their characteristics.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 215–223.Original Russian Text Copyright © 2005 by Mozhaev.     

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

In a previous paper [1], as a result of group-theoretic decomposition, one of the problems of the optimization of the flexible correction process was reduced to a series of subproblems. In this paper, the analytical solutions to these subproblems are obtained by the sweep method. A series of other similar problems with different variants of flexibility is also considered; the decomposition of these problems is performed, and their analytical solutions are presented. It is shown for some numerical examples that flexible corrections require essentially lower fuel consumption than the rigid correction, where all parameters characterizing the absolute motion of a satellite system are corrected to their nominal values.