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Satellite motion control in the vicinity of the libration point with expenditure criteria is considered. Expenditure optimization is natural in the case, where it is necessary to keep mechanical system in the neighborhood of the equilibrium point for a long time. Disturbing factors from time to time distort this system unacceptably far from the equilibrium point, and we need to extinguish these deviations, using fuel or another resource, which reserves are limited. Optimization of the satellite motion control acco...

The problem of quenching small vibrations of a mechanical system near its equilibrium position is considered. A method for finding switching points of piecewise constant control for simultaneous damping of several vibrations of the same frequency is proposed. As an optimized functional "the Expenditure" is considered. The method leads to explicit formulas. All results of research are formulated as the theorem. As an example the problem of stabilizing the spacecraft's rotation axis is considered. The mathematical m...