An introduction to the theory of resonance systems
Abstract
An asymptotic theory of ordinary differential equations with a small parameter is presented which uses the averaging principle. A method for constructing the first and higher approximations, representing solutions to the generalized KrylovBogoliubov equation, is described in detail, and consecutive algorithms are presented for implementing the method on a computer. The discussion focuses on multifrequency systems with slow and fast phase variables permitting resonance relations between the frequencies. A detailed classification of such systems is given; the averaging method is demonstrated for resonance systems, and various applications of the proposed methods in nonlinear mechanics are examined.
 Publication:

Moscow Izdatel Moskovskogo Universiteta Pt
 Pub Date:
 1987
 Bibcode:
 1987MIzMU....Q....G
 Keywords:

 Asymptotic Series;
 Differential Equations;
 Resonance;
 Algorithms;
 Approximation;
 Average;
 Bogoliubov Theory;
 Hamiltonian Functions;
 Mathematical Models;
 Nonlinear Systems;
 Perturbation Theory;
 Resonant Frequencies;
 Time Response;
 Physics (General)