Chaotic Vibrations: An Introduction for Applied Scientists and Engineers
Chaotic Vibrations: An Introduction for Applied Scientists and Engineers
复制标题
DOI：
10.1115/1.3173762
复制
发表时间：
1988-12
期刊：
影响因子：
--
通讯作者：
F. Moon;E. Dowell;C. Pezeshki
中科院分区：
文献类型：
--
作者：
F. Moon;E. Dowell;C. Pezeshki
1.引言：动力的新时代。1.1什么是混沌动力学？1.2经典非线性振动理论：简要回顾。1.3地图和流程。2.如何识别混沌振动。3.混沌振动系统综述。3.1动力学中的新范式。3.2混沌物理系统的数学模型。3.3混沌系统中的物理实验。4.混沌振动的实验方法。4.1引言：实验目标。4.2动力系统中的非线性元件。4.3实验对照。4.4相空间测量。4.5分叉图。4.6实验庞加莱地图。4.7混沌振动的定量测量。5.混沌振动的判据。5.1引言。5.2介绍混沌的经验标准。5.3理论预测标准。5.4李雅普诺夫指数。6.非线性动力学中的分形概念。6.1引言。6.2分形维的度量。6.3奇异吸引子的分维。6.4分维的光学测量。6.5分形盆地边界。6.6复杂地图和Mandelbrot集。附录A.混沌和非线性振动术语汇编。附录B附录C混沌中的数值实验。附录C混乱的玩具。参考资料。作者索引。主题索引。
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.