Institute for High-Performance Computer Systems RAS, Moscow
In this paper a new construction method of the perturbation motion theory of celestial bodies, based on the averaging principle in view of frequency resonances is stated. The first approximation of the assymptotical theory is the exact solution of the dynamics averaging equations, in which are include "secular" and "long-periodic" members in decomposition of perturbation function. The high-degree approximations are the exact solution of a known Krylov-Bogolubov generalized equition. It is shown, that these iterations are expressed in the analytical form by multiple Fourrier series. The mathematical form of the method is those, that it admits the effective computer algorithmization.