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Pertubation Methods with Mathematica

Ali H. Nayfeh
Organization: Virginia Tech
Department: Department of Engineering Science and Mechanics
Char-Ming Chin
Organization: Virginia Tech
Department: Department of Engineering Science and Mechanics
Revision date


Many vibration problems in engineering are nonlinear in nature. The usual linear analysis may be inadequate for many applications. An essential difference in the study of nonlinear systems is that general solutions cannot be obtained by superposition, as in the case of linear systems. Moreover, the nonlinearity brings many new phenomena, which do not occur in linear systems. To study nonlinear systems, one has to learn new mathematical techniques, which have been developed in many branches of applied mathematics, physics, and engineering. In the past several years, a number of powerful computer software packages have been developed that allow one to perform complicated symbolic manipulations. In this book, we use Mathematica's symbolic programming techniques to implement various perturbation methods for studying the dynamics of weakly nonlinear systems. Instead of being burdened by the tedious algebra required to obtain the solutions, Mathematica enables us to focus our attention on understanding the techniques and the physics, thereby free our time for creative thinking.

This is an extensive book on Pertubation methods, in 9 chapters.

The most current version is maintained at the author's webpage, http://www.esm.vt.edu/~anayfeh/

*Mathematics > Calculus and Analysis > Dynamical Systems
*Science > Physics > Wave Motion

Duffing, Lindstedt-Poincaré, Multiple Scales, Method of, Averaging, Forced Oscillations, Euler-Lagrange Equations, Finite Degrees of Freedom, Pertubation Methods


PMmath.zip (420.1 KB) - ZIP archive [for Mathematica 3.0]