Titlebook: Nonlinear Dynamical Systems in Engineering; Some Approximate App Vasile Marinca,Nicolae Herisanu Book 2011 Springer-Verlag Berlin Heidelber

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https://doi.org/10.1007/978-3-642-22735-6Harmonic balance; Krylov and Bogolyubov method of; Lindstedt-Poincaré; Multiple scales; auxiliary funct

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Introduction,Most nonlinear phenomena are models of our real-life problems. The world around us is inherently nonlinear. A vast body of scientific knowledge has developed over a long period of time, devoted to a description of natural phenomena.

DEVIL

,Perturbation Method: Lindstedt-Poincaré,We seek an expansion that is valid for small but finite amplitude motions. It is convenient to introduce a small, dimensionless parameter e which is of the order of the amplitude of the motion and can be used as a crutch, or a bookkeeping device, in obtaining the approximate solution [22,33–35].

interior

The Method of Harmonic Balance,This method may be used to determine the approximate periodic solutions of nonlinear differential equations. If a periodic solution does exist, it may be sought in the form of a Fourier series, whose coefficients are determined by requiring the series to satisfy the equation of motion.

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高射炮

Condescending

Optimal Parametric Iteration Method,The most common and most widely studied methods for determining analytical approximate solutions of a nonlinear dynamical system are iteration methods.

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