Singularity And Dynamics On Discontinuous Vector Fields

Author : Albert C.J. Luo
Publisher : Elsevier
ISBN 13 : 0080480934
Total Pages : 311 pages
Book Rating : 4.30/5 ( download)

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Download or read book Singularity and Dynamics on Discontinuous Vector Fields written by Albert C.J. Luo and published by Elsevier. This book was released on 2006-07-07 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones’ thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics. Challenging continuous Newton's dynamics Original theory and seeds of new researches in the field Wide spectrum of applications in science and engineering Systematic presentation and clear illustrations

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 364222461X
Total Pages : 700 pages
Book Rating : 4.14/5 ( download)

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Download or read book Discontinuous Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2012-04-07 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Discontinuous Dynamical Systems” presents a theory of dynamics and flow switchability in discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics of dynamical system networks. The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems. The theory of bouncing flows to boundaries, edges and vertexes in discontinuous dynamical systems with multi-valued vector fields is described in the book as a “billiard” theory of dynamical system networks. The theory of dynamical system interactions in discontinued dynamical systems can be used as a general principle in dynamical system networks, which is applied to dynamical system synchronization. The book represents a valuable reference work for university professors and researchers in applied mathematics, physics, mechanics, and control. Dr. Albert C.J. Luo is an internationally respected professor in nonlinear dynamics and mechanics, and he works at Southern Illinois University Edwardsville, USA.

Author : Albert C. J. Luo
Publisher : Springer
ISBN 13 : 3319174223
Total Pages : 266 pages
Book Rating : 4.28/5 ( download)

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Download or read book System Dynamics with Interaction Discontinuity written by Albert C. J. Luo and published by Springer. This book was released on 2015-07-08 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 3642002536
Total Pages : 234 pages
Book Rating : 4.33/5 ( download)

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Download or read book Discontinuous Dynamical Systems on Time-varying Domains written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2009-11-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.54/5 ( download)

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Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : Albert C. J. Luo
Publisher : John Wiley & Sons
ISBN 13 : 1118402901
Total Pages : 269 pages
Book Rating : 4.00/5 ( download)

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Download or read book Vibro-impact Dynamics written by Albert C. J. Luo and published by John Wiley & Sons. This book was released on 2013-01-25 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis Comprehensive 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 systems Vibro-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-oscillator Essential reading for graduate students, university professors, researchers and scientists in mechanical engineering.

Author : Brandon C. Gegg
Publisher : Springer Science & Business Media
ISBN 13 : 1441998012
Total Pages : 187 pages
Book Rating : 4.19/5 ( download)

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Download or read book Machine Tool Vibrations and Cutting Dynamics written by Brandon C. Gegg and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Machine Tool Vibrations and Cutting Dynamics” covers the fundamentals of cutting dynamics from the perspective of discontinuous systems theory. It shows the reader how to use coupling, interaction, and different cutting states to mitigate machining instability and enable better machine tool design. Among the topics discussed are; underlying dynamics of cutting and interruptions in cutting motions; the operation of the machine-tool systems over a broad range of operating conditions with minimal vibration and the need for high precision, high yield micro- and nano-machining.

Author : Albert C. J. Luo
Publisher : World Scientific
ISBN 13 : 9812771123
Total Pages : 461 pages
Book Rating : 4.24/5 ( download)

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Download or read book Global Transversality, Resonance and Chaotic Dynamics written by Albert C. J. Luo and published by World Scientific. This book was released on 2008 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n -dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. Sample Chapter(s). Chapter 1: Introduction (1,196 KB). Contents: Differential Geometry of Flows; Global Transversality in Continuous Dynamical Systems; Chaotic Layer Dynamics; Two-Dimensional Stochastic Layers; Stochasticity in Resonant Separatrix Layers; Nonlinear Dynamics on an Equi-energy Surface; Stability and Grazing in Dissipative Systems; Global Dynamics in Two-Dimensional Dynamical Systems; Flow Switchability in Discontinuous Dynamical Systems. Readership: Mathematicians, physicists, researchers and engineers in mechanical engineering and electrical engineering as well as university professors and students.

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 1461415233
Total Pages : 500 pages
Book Rating : 4.37/5 ( download)

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Download or read book Regularity and Complexity in Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-07-12 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
ISBN 13 : 3642140033
Total Pages : 504 pages
Book Rating : 4.37/5 ( download)

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Download or read book Fractional Dynamics written by Vasily E. Tarasov and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.