For the aims of numerical integration a simplified method to model lunar resonance spin-orbital interaction is developed. In the method orbital equations are integrated separately from rotational ones, but no fictions secular perturbations in. the longitude or node arise.
The data of 11 open star cluster complexes are presented. From the analysis of these data a conclusion is made of a probable existence of a rotating system of the star complexes.
The semianaytical theory of the motion ol the resonant Earth satellite under the inlluence of Sun and Moon is constructed in nonsingular variables by Lie transforms. The explicit expressions tor the general terms of the combined perturbations are obtained up to the third order with resped to C20. The account ol the additional perturbations is exemplified by the calcuiaiion of the corrections due to the precession and the nutation.