The Method of Normal Forms
2nd Edition
Published on 24. August 2011
XII, 330 pages
978-3-527-63577-1 (ISBN)
Description
In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability.
The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging.
The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas.
Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging.
The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas.
Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
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The Method of Normal Forms 2e
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08/2011
Wiley-VCH
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The Method of Normal Forms
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Person
Ali Hasan Nayfeh received his B.S. on engineering science and his M.S. and PhD in aeronautics and astronautics from Stanford University. He established and served as Dean of the College of Engineering, Yarmouk University, Jordan from 1980-1984. He is currently University Distinguished Professor of Engineering at Virginia Polytechnic Institute and State University. He is the Editor of Wiley Series in Nonlinear Science and editor in Chief of Nonlinear Dynamics and the Journal of Vibration and Control.
Prof. Nayfeh is a fellow of the American Physical Society (APS), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Mechanical Engineers (ASME), the Society of Design and Process Science, and the American Academy of Mechanics (AAM). He holds honrary doctorates from Marine Technical University, Russia, Technical University of Munich, Germany, and Politechnika Szczecinsksa, Poland.
Prof. Nayfeh received AIAA's Pendray Aerospace Literature Award in 1995; ASME's J. P. Den Hartog Award in 1997; the Frank J. Maher Award for Excellence in Engineering Education in 1997; ASME's Lyapunov Award in 2005; the Virginia Academy of Science's Life Achievement in Science Award in 2005; the Gold Medal of Honor from the Academy of Trans-Disciplinary Learning and Advanced Studies in 2007; and the Thomas K. Caughey Dynamics Award in 2008.
Prof. Nayfeh is a fellow of the American Physical Society (APS), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Mechanical Engineers (ASME), the Society of Design and Process Science, and the American Academy of Mechanics (AAM). He holds honrary doctorates from Marine Technical University, Russia, Technical University of Munich, Germany, and Politechnika Szczecinsksa, Poland.
Prof. Nayfeh received AIAA's Pendray Aerospace Literature Award in 1995; ASME's J. P. Den Hartog Award in 1997; the Frank J. Maher Award for Excellence in Engineering Education in 1997; ASME's Lyapunov Award in 2005; the Virginia Academy of Science's Life Achievement in Science Award in 2005; the Gold Medal of Honor from the Academy of Trans-Disciplinary Learning and Advanced Studies in 2007; and the Thomas K. Caughey Dynamics Award in 2008.
Content
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
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
