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Mathematical Problems in Engineering
Volume 2012, Article ID 239357, 32 pages
http://dx.doi.org/10.1155/2012/239357
Research Article

Application of the Hori Method in the Theory of Nonlinear Oscillations

Departamento de Matemática, Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP, Brazil

Received 12 November 2011; Accepted 25 January 2012

Academic Editor: Antonio F. Bertachini A. Prado

Copyright © 2012 Sandro da Silva Fernandes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some remarks on the application of the Hori method in the theory of nonlinear oscillations are presented. Two simplified algorithms for determining the generating function and the new system of differential equations are derived from a general algorithm proposed by Sessin. The vector functions which define the generating function and the new system of differential equations are not uniquely determined, since the algorithms involve arbitrary functions of the constants of integration of the general solution of the new undisturbed system. Different choices of these arbitrary functions can be made in order to simplify the new system of differential equations and define appropriate near-identity transformations. These simplified algorithms are applied in determining second-order asymptotic solutions of two well-known equations in the theory of nonlinear oscillations: van der Pol equation and Duffing equation.