A New Approach to Calculation of Secular Frequencies in the Dynamics of Near-Earth Objects in Orbits with Large Eccentricities

摘要

A modified method for identifying and studying secular resonances in the dynamics of near-Earth objects is described. Unlike the traditionally used approach based on approximate analytical formulas for calculating secular frequencies that are valid only for small eccentricities, the proposed method uses exact values obtained in the process of numerical simulation of the motion from the Newton-Euler equations. This technique can be used to analyze the dynamics of objects with any arbitrary eccentricities of the orbits, but its application to the study of the motion along orbits with large or rapidly growing eccentricities is most interesting. Testing is carried out on the example of research of the Lidov-Kozai resonances in the dynamics of near-Earth objects.