| Abstract: | Systems in the N.M. Bogolyubov standard form as well as systems with rapid phases are considered. It is proposed to seek the solution in the form of an asymptotic series in a small parameter with coefficients representable in the form of the sum of two functions. The first depends on slow time and is found as the solution of a simpler equation in a finite segment. The second is a trigonometric polynomial of the time (or the angular displacements) with coefficients which depend on the slow time (it is found in an explicit manner). It is convenient to use the results in solving certain problems in celestial mechanics. |
