Chaotic Vibrations
An Introduction for Applied Scientists and Engineers
Published on 7. June 2004
Book
Paperback/Softback
309 pages
978-0-471-67908-0 (ISBN)
Description
Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.
More details
Edition
1. Auflage
Language
English
Place of publication
Chichester
United Kingdom
Publishing group
John Wiley and Sons Ltd
Target group
Professional and scholarly
Illustrations
Illustrations
Dimensions
Height: 23.7 cm
Width: 15.6 cm
Thickness: 1.5 cm
Weight
485 gr
ISBN-13
978-0-471-67908-0 (9780471679080)
Schweitzer Classification
Person
FRANCIS C. MOON, PhD. Before returning to Cornell in 1975, Professor Moon taught at Princeton University. At Cornell, he spent seven years as chair of the Department of Theoretical and Applied Mechanics and then served as director of the Sibley School of Mechanical and Aerospace Engineering from 1987-1992. He has published nearly 150 technical papers and five books, spanning a wide spectrum of problems in nonlinear dynamics and chaos, dynamics of structures, magneto-mechanical systems, superconducting bearings, magnetic levitation of vehicles, smart structures, and most recently, the history of engineering. Professor Moon is a member of the National Academy of Engineering.
Content
1. Introduction: A New Age of Dynamics.
1.1 What Is Chaotic Dynamics?
1.2 Classical Nonlinear Vibration Theory: A Brief Review.
1.3 Maps and Flows.
2. How to Identify Chaotic Vibrations.
3. A Survey of Systems with Chaotic Vibrations.
3.1 New Paradigms in Dynamics.
3.2 Mathematical Models of Chaotic Physical Systems.
3.3 Physical Experiments in Chaotic Systems.
4. Experimental Methods in Chaotic Vibrations.
4.1 Introduction: Experimental Goals.
4.2 Nonlinear Elements in Dynamical Systems.
4.3 Experimental Controls.
4.4 Phase Space Measurements.
4.5 Bifurcation Diagrams.
4.6 Experimental Poincaré Maps.
4.7 Quantitative Measures of Chaotic Vibrations.
5. Criteria for Chaotic Vibrations.
5.1 Introduction.
5.2 Introduction Empirical Criteria for Chaos.
5.3 Theoretical Predictive Criteria.
5.4 Lyapunov Exponents.
6. Fractal Concepts in Nonlinear Dynamics.
6.1 Introduction.
6.2 Measures of Fractal Dimension.
6.3 Fractal Dimension of Strange Attractors.
6.4 Optical Measurement of Fractal Dimension.
6.5 Fractal Basin Boundaries.
6.6 complex Maps and the Mandelbrot Set.
Appendix A. Glossary of Terms in Chaotic and Nonlinear Vibrations.
Appendix B. Appendix C. Numerical Experiments in Chaos.
Appendix C. Chaotic Toys.
References.
Author Index.
Subject Index.
1.1 What Is Chaotic Dynamics?
1.2 Classical Nonlinear Vibration Theory: A Brief Review.
1.3 Maps and Flows.
2. How to Identify Chaotic Vibrations.
3. A Survey of Systems with Chaotic Vibrations.
3.1 New Paradigms in Dynamics.
3.2 Mathematical Models of Chaotic Physical Systems.
3.3 Physical Experiments in Chaotic Systems.
4. Experimental Methods in Chaotic Vibrations.
4.1 Introduction: Experimental Goals.
4.2 Nonlinear Elements in Dynamical Systems.
4.3 Experimental Controls.
4.4 Phase Space Measurements.
4.5 Bifurcation Diagrams.
4.6 Experimental Poincaré Maps.
4.7 Quantitative Measures of Chaotic Vibrations.
5. Criteria for Chaotic Vibrations.
5.1 Introduction.
5.2 Introduction Empirical Criteria for Chaos.
5.3 Theoretical Predictive Criteria.
5.4 Lyapunov Exponents.
6. Fractal Concepts in Nonlinear Dynamics.
6.1 Introduction.
6.2 Measures of Fractal Dimension.
6.3 Fractal Dimension of Strange Attractors.
6.4 Optical Measurement of Fractal Dimension.
6.5 Fractal Basin Boundaries.
6.6 complex Maps and the Mandelbrot Set.
Appendix A. Glossary of Terms in Chaotic and Nonlinear Vibrations.
Appendix B. Appendix C. Numerical Experiments in Chaos.
Appendix C. Chaotic Toys.
References.
Author Index.
Subject Index.