To the substantiation of a numerical-analytical method for revealing secular resonances - Popandopulo, N. A. (Russian physics journal)
Results of the substantiation of a numerical-analytical method for determining secular frequencies in the process of revealing secular resonances in the dynamics of circumplanetary objects are presented. The presented method combines two approaches: the traditional analytical approach and the numerical one. Each of the approaches has its own special features. The analytical approach is not suitable for large eccentricities, since it uses formulas obtained for small eccentricities, and the formulas that implement the numerical approach have irremovable singularities for small eccentricities and orbital inclinations. Since a special feature of the influence of secular resonances is the increase in the eccentricities from zero values to values close to unity, combining these two approaches makes it possible to obtain reliable results. This is confirmed by examples of investigation of the influence of secular resonances on the dynamics of circumlunar objects.