Chaotic Vibrations

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.

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.