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The Method of Normal Forms, 2nd, Updated and Enlarged Edition

E-Book

CAD $159.99

The Method of Normal Forms, 2nd, Updated and Enlarged Edition

Ali H. Nayfeh

ISBN: 978-3-527-63577-1 August 2011 342 Pages

Description

In this introductory treatment the author Ali Nayfeh presents different concepts of dynamical systems theory and nonlinear dynamics. He systematically introduces models and techniques and states the relevant ranges of their validity and applicability. The text provides the reader with a clear operational framework instead of focusing on the underlying mathematical rigor. The exposition mainly features examples, which are shown through to their fianl outcome. For most of the examples, the results obtained with the method of normal forms are shown to be equivalent to to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging.

Additions to this new edition concern major topics of current interest. In particular, the author has added three new chapters dedicated to maps, bifurcations of continuous systems, and retarded systems. Especially the latter topic has gained major importance in several applications in mechanics and other areas.

From the contents:

  • SDOF Autonomous Systems
  • Systems of First-Order Equations
  • Maps
  • Bifurcations of Continuous Systems
  • Forced Oscillations of the Duffing Oscillator
  • Forced Oscillations of SDOF Systems
  • Parametrically Excited Systems
  • MDOF Systems with Quadratic Nonlinearities
  • TDOF Systems with Cubic Nonlinearities
  • Systems with Quadratic and Cubis Nonlinearities
  • Retarded Systems
Preface
Introduction
1 SDOF Autonomous Systems
2 Systems of First-Order Equations
3 Maps
4 Bifurcations of Continuous Systems
5 Forced Oscillations of the Duffing Oscillator
6 Forced Oscillations of SDOF Systems
7 Parametrically Excited Systems
8 MDOF Systems with Quadratic Nonlinearities
9 TDOF Systesm with Cubic Nonlinearities
10 Systems with Quadratic and Cubic Nonlinearities
11 Retarded Systems
Bibliography
Subject Index