Forced Oscillations Of Multidimensional Highly Nonlinear Systems
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Forced Oscillations Of Multidimensional Highly Nonlinear Systems
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Author : Vladimir Metrikin
language : en
Publisher: Springer Nature
Release Date : 2025-01-31
Forced Oscillations Of Multidimensional Highly Nonlinear Systems written by Vladimir Metrikin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-31 with Science categories.
This book highlights the presentation of methods for studying oscillations under external periodic influence and random changes in parameters in dynamic systems with nonlinearities that have discontinuities and kinks. The analysis of dynamic systems is based on effective approaches and algorithms of the method of point mappings of Poincaré surfaces, developed by the Nizhny Novgorod Scientific School of academician A.A. Andronov. Considerable attention is paid to the study of the general picture of the possible behavior of systems and their use in solving various applied problems. Using specific examples, it is found that this research approach allows not only to advance in the study of known nonlinear features but also to discover new effects and applications. The presentation is illustrated by numerous specific examples of oscillatory strongly nonlinear systems with discontinuous nonlinearities or piecewise-continuous nonlinearities. A separate chapter is devoted to the development and use of the point mapping method for random changes in the parameters of dynamic systems, as well as in dynamic systems subject to external seismic loads. The book is intended for scientists and engineers who are engaged in research and practice activities related to the theory of nonlinear oscillations and its applications, as well as graduate students and senior undergraduate students in relevant majors.
Introduction To Nonlinear Oscillations
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Author : Vladimir I. Nekorkin
language : en
Publisher: John Wiley & Sons
Release Date : 2015-04-01
Introduction To Nonlinear Oscillations written by Vladimir I. Nekorkin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Science categories.
A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.
Nonlinear Oscillations
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Author : Ali H. Nayfeh
language : en
Publisher: John Wiley & Sons
Release Date : 2024-11-12
Nonlinear Oscillations written by Ali H. Nayfeh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-12 with Science categories.
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.
Journal Of The Institution Of Engineers India
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Author :
language : en
Publisher:
Release Date : 2000
Journal Of The Institution Of Engineers India written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Electric engineering categories.
Technical Abstract Bulletin
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Author : Defense Documentation Center (U.S.)
language : en
Publisher:
Release Date : 1964
Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Military art and science categories.
The Shock And Vibration Digest
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Author :
language : en
Publisher:
Release Date : 1981
The Shock And Vibration Digest written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Shock (Mechanics) categories.
Asymptotic Approaches In Nonlinear Dynamics
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Author : Jan Awrejcewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Approaches In Nonlinear Dynamics written by Jan Awrejcewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
How well is Nature simulated by the varied asymptotic models that imaginative scientists have invented? B. Birkhoff [52J This book deals with asymptotic methods in nonlinear dynamics. For the first time a detailed and systematic treatment of new asymptotic methods in combination with the Pade approximant method is presented. Most of the basic results included in this manuscript have not been treated but just mentioned in the literature. Providing a state-of-the-art review of asymptotic applications, this book will prove useful as an introduction to the field for novices as well a reference for specialists. Asymptotic methods of solving mechanical and physical problems have been developed by many authors. For example, we can refer to the excel lent courses by A. Nayfeh [119-122]' M. Van Dyke [154], E.J. Hinch [94J and many others [59, 66, 95, 109, 126, 155, 163, 50d, 59dJ. The main features of the monograph presented are: 1) it is devoted to the basic principles of asymp totics and its applications, and 2) it deals with both traditional approaches (such as regular and singular perturbations, averaging and homogenization, perturbations of the domain and boundary shape) and less widely used, new approaches such as one- and two-point Pade approximants, the distributional approach, and the method of boundary perturbations.
Frequency Methods In Oscillation Theory
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Author : G.A. Leonov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Frequency Methods In Oscillation Theory written by G.A. Leonov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is devoted to nonlocal theory of nonlinear oscillations. The frequency methods of investigating problems of cycle existence in multidimensional analogues of Van der Pol equation, in dynamical systems with cylindrical phase space and dynamical systems satisfying Routh-Hurwitz generalized conditions are systematically presented here for the first time. To solve these problems methods of Poincaré map construction, frequency methods, synthesis of Lyapunov direct methods and bifurcation theory elements are applied. V.M. Popov's method is employed for obtaining frequency criteria, which estimate period of oscillations. Also, an approach to investigate the stability of cycles based on the ideas of Zhukovsky, Borg, Hartmann, and Olech is presented, and the effects appearing when bounded trajectories are unstable are discussed. For chaotic oscillations theorems on localizations of attractors are given. The upper estimates of Hausdorff measure and dimension of attractors generalizing Doudy-Oesterle and Smith theorems are obtained, illustrated by the example of a Lorenz system and its different generalizations. The analytical apparatus developed in the book is applied to the analysis of oscillation of various control systems, pendulum-like systems and those of synchronization. Audience: This volume will be of interest to those whose work involves Fourier analysis, global analysis, and analysis on manifolds, as well as mathematics of physics and mechanics in general. A background in linear algebra and differential equations is assumed.
Introduction To Nonlinear Oscillations
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Author : Vladimir I. Nekorkin
language : en
Publisher: John Wiley & Sons
Release Date : 2016-05-02
Introduction To Nonlinear Oscillations written by Vladimir I. Nekorkin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-02 with Science categories.
A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.
Nonlinear Oscillations And Waves In Dynamical Systems
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Author : Polina Solomonovna Landa
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-02-29
Nonlinear Oscillations And Waves In Dynamical Systems written by Polina Solomonovna Landa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-29 with Mathematics categories.
This volume is an up-to-date treatment of the theory of nonlinear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified point of view. Also, the relation between the theory of oscillations and waves, nonlinear dynamics and synergetics is discussed. One of the purposes of this book is to convince readers of the necessity of a thorough study of the theory of oscillations and waves, and to show that such popular branches of science as nonlinear dynamics, and synergetic soliton theory, for example, are in fact constituent parts of this theory. Audience: This book will appeal to researchers whose work involves oscillatory and wave processes, and students and postgraduates interested in the general laws and applications of the theory of oscillations and waves.