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Informationen zum Autor Professor Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville. He is an international renowned figure in the area of nonlinear dynamics and mechanics. For about 30 years, Dr. Luo's contributions on nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems, (ii) Dynamical systems synchronization, (iii) Analytical solutions of periodic and chaotic motions in nonlinear dynamical systems, (iv) The theory for stochastic and resonant layer in nonlinear Hamiltonian systems, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 13 monographs and over 200 peer-reviewed journal and conference papers. His new research results are changing the traditional thinking in nonlinear physics and mathematics. Dr. Luo has served as an editor for the Journal "Communications in Nonlinear Science and Numerical simulation", book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control. Klappentext Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysisComprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications.Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be extended to discontinuous dynamics. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systemsVibro-impact Dynamics:* Presents mapping dynamics to determine bifurcation and chaos in vibro-impact systems* Offers two simple vibro-impact systems with comprehensive physical interpretation of complex motions* Uses the theory for discontinuous dynamical systems on time-varying domains, to investigate the Fermi-oscillatorEssential reading for graduate students, university professors, researchers and scientists in mechanical engineering. Zusammenfassung This book establishes vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. Inhaltsverzeichnis Preface Chapter 1 Introduction 1 1.1. Discrete and discontinuous systems 1 1.1.1 Discrete dynamical systems 2 1.1.2 Discontinuous dynamical systems 4 1.2 Fermi oscillator and impact problems 8 1.3 book layout 10 References 12 Chapter 2 Nonlinear Discrete Systems 19 2.1 Defintions 19 2.2 Fixed points and stability 21 2.3 Stability switching theory 34 2.4. Bifurcation theory 50 References 59 Chapter 3 Complete Dynamics and Fractality 61 3.1 Complete dynamics of discrete systems 61 3.2 Routes to chaos 69 3.2.1 One-dimensional maps 69 3.2.2 Two-dimensional maps 73 3.3 Complete Dynamics of Henon map 75 3.4 Simliarity and Multifractals 81 3.4.1 Similar Structures in period doubling 81 3.4.2 Fractality of chaos via PD bifurcation 86 3.4.3 An example 86 3.5 Complete dynamics of Logistic map 93 References...
