Moon, Francis C. Chaotic Vibrations An Introduction for Applied Scientists and Engineers
1. Edition - June 2004 67.90 Euro 2004. 309 Pages, Softcover - Practical Approach Book - ISBN-10: 0-471-67908-9 ISBN-13: 978-0-471-67908-0 - Wiley-VCH, Berlin
Short description Chaotic oscillations are the emergence of random motions from completely deterministic systems. Such motions had been known in fluid mechanics, but were also observed in low-order mechanical and electrical systems and even in simple one-degree-of-freedom problems. This paperback version of the cloth classic translates 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. It also describes how to perform both computer and physical experiments in chaotic dynamics and contains a list of computer experiments and details for a demonstration experiment on chaotic vibrations.
From the contents 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.
