Chaotic and Fractal Dynamics : Introduction for Applied Scientists and Engineers
Francis C. Moon
Bok Engelsk 2008 · Electronic books.
| Utgitt | Hoboken : : Wiley, , 2008.
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| Omfang | 1 online resource (538 p.)
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| Opplysninger | Description based upon print version of record.. - CHAOTIC AND FRACTAL DYNAMICS; CONTENTS; Preface; 1 Introduction: A New Age of Dynamics; 1.1 What is Chaotic Dynamics?; Why Fractal Dynamics?; Why Study Chaotic Dynamics?; Sources of Chaos; Where Have Chaotic Vibrations Been Observed?; 1.2 Classical Nonlinear Vibration Theory: A BRIEF REVIEW; Linear vibration Theory; Nonlinear Vibration Theory; Quasiperiodic Oscillators; Dynumics of Lossless or Conservative Systems; Nonlinear Resonance in Conservative Systems; Frequency Spectra of Nonlinear Oscillators; Torus Map; Local Geometric Theory of Dynamics; Bifurcations; Strange Attractors. - 1.3 Maps and FlowsThree Paradigms for Chaos; Henon and Horseshoe Maps; The Lorenz Attractor and Fluid Chaos; Quantum Chaos; Closing Comments; Problems; 2 How to Identify Chaotic Vibrations; Nonlinear System Elements; Random Inputs; Observation of Time History; Phase Plane; Fourier Spectrum and Autocorrelation; Poincare' Maps and Return Maps; Bifurcations: Routes to Chaos; Quasiperiodicity and Mode-Locking; Transient Chaos; Conservative Chaos; Lyapunov Exponents and Fractal Dimensions; Strange-Nonchaotic Motions; Problems; 3 Models for Chaos; Maps and Flows; 3.1 Introduction. - Early Observations of Chaotic Vibrations4.2 Particle and Rigid Body Systems; Multiple- Well Potential Problems; Chaotic Dynamics in the Solar System; Pendulum Problems; Rigid Body Problems; Impact Oscillators; Chaos in Gears and Kinematic Mechanisms; Control System Chaos; 4.3 Chaos in Elastic Systems; Chaos in Elastic Continua; Three-Dimensional Elastica and Strings; 4.4 Flow-induced Chaos in Mechanical Systems; Flow-Induced Elastic Vibrations; 4.5 Inelastic and Geomechanical Systems; Nonlinear Dynamics of Friction Oscillators; Chaos, Fractals, and Surface Machining. - Fracture, Fatique, and Chaos. - Poincare Maps and Bifurcation DiagramsQuantitative Measures of Period Doubling; Scaling Properties of Period-Doubling Maps; Subharmonic Spectra Scaling; Symbol Sequences in Period Doubling; Period Doubling in Conservative Systems; 3.7 The Measure of Chaos; Lyapunov Exponents; Probability Density Function for Maps; Numerical Calculation of PDF; PDF and Lyapunov Exponents; 3.8 3-D Flows; Models and Maps; Lorenz Model for Fluid Convection; Duffing's Equation and the "Japanese Attractor"; A Map from a 4 - 0 Conservative Flow; Problems; 4 Chaos in Physical Systems; 4.1 New Paradigms in Dynamics. - The Geometry of Mappings: Maps on the PlaneImpact Oscillator Maps; Classification of Map Dynamics; Quasiperiodic Motions; Stochastic Orbits; Fractal Orbits; 3.2 Local Stability of 2-D Maps; 3.3 Global Dynamics of 2-D Maps; Linear Transformation; Folding in 2-Maps-Horseshoes; Composition of Maps-Henon Maps; The Horseshoe Map; 3.4 Saddle Manifolds, Tangles, and Chaos; 3.5 From 2-D to 1-D Maps; The Kicked Rotor; Circle Map; The Henon Map; Experimental Evidence for Reduction of 2-D to 1-D Maps; 3.6 Period-Doubling Route to Chaos; Qualitative Features of Period Doubling. - A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.
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| Emner | |
| Sjanger | |
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| ISBN | 0471545716
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