Chaotic vibrations (混沌振动：科学家与工程师应用概述)
发布日期:2007-04-28 浏览次
[内容简介]
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.
[目次]
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 Poincare 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.
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