Multifrequency Oscillations Of Nonlinear Systems

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Multifrequency Oscillations Of Nonlinear Systems

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Author : Anatolii M. Samoilenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11

Multifrequency Oscillations Of Nonlinear Systems written by Anatolii M. Samoilenko 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 2006-04-11 with Mathematics categories.

In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations. In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied. This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.

Multifrequency Oscillations Of Nonlinear Systems

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Author : Anatolii M. Samoilenko
language : en
Publisher:
Release Date : 2014-01-15

Multifrequency Oscillations Of Nonlinear Systems written by Anatolii M. Samoilenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Applied Asymptotic Methods In Nonlinear Oscillations

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Author : Yuri A. Mitropolsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Applied Asymptotic Methods In Nonlinear Oscillations written by Yuri A. Mitropolsky 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 2013-03-09 with Technology & Engineering categories.

Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.

Analytical And Approximate Methods For Complex Dynamical Systems

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Author : Alexander Timokha
language : en
Publisher: Springer Nature
Release Date : 2025-03-16

Analytical And Approximate Methods For Complex Dynamical Systems written by Alexander Timokha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-16 with Science categories.

This book presents Analytical and Approximate Methods for Complex Dynamical Systems and introduces ideas of discontinuous mapping treated as complex dynamical systems. Mathematicians of world-recognized Ukrainian scientific schools established by M.Krylov, M.Bogolyubov, Yu.Mitropolskiy, and A.Sharkovsky used to cooperate for writing the collective book whose purpose consists of illustrating a synergy of combining diverse (by idea and technique) constructive analytical and approximate approaches and methods in complex dynamical systems which are herein associated with mathematical models of networks, conflict/economic theories, sloshing, soft matter, and even levitating drops. Readers are facilitated to learn contemporary insights, fundamentals (Parts I and III), applications (Part II), and components of theories of bifurcation, synchronization/self-organization, collective dynamics, chaos, solitons, fractional differential equations, symmetry, reduced order modelling, and many others, that makes the book useful for both graduate and postgraduate students, lecturers, researchers, and even engineers dealing with multidimensional dynamic systems.

Applied Methods In The Theory Of Nonlinear Oscillations

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Author : Vi︠a︡cheslav Mikhaĭlovich Starzhinskiĭ
language : en
Publisher:
Release Date : 1980

Applied Methods In The Theory Of Nonlinear Oscillations written by Vi︠a︡cheslav Mikhaĭlovich Starzhinskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Differential equations categories.

Dynamical Systems And Methods

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Author : Albert C. J. Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-30

Dynamical Systems And Methods written by Albert C. J. Luo 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 2011-09-30 with Technology & Engineering categories.

Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers: Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics, mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies and nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator. This book is useful to scholars, researchers and advanced technical members of industrial laboratory facilities developing new tools and products.

Theory Of Oscillations

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Author : Vladimir Ivanovich Zubov
language : en
Publisher: World Scientific
Release Date : 1999

Theory Of Oscillations written by Vladimir Ivanovich Zubov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

This monograph deals with the controlled/non-controlled nonlinear systems of differential equations. A mathematical apparatus is developed to construct stationary conditions and to carry out studies on the behaviour of integral curves in the neighbourhood of such conditions.Considerable coverage is given to existence and methods of finding periodic orbits and almost-periodic solutions, as well as to the description of the class of ergodic recurrent motions. There is further treatment of the perturbation method and the theory of time-independent and periodic perturbations in particular.The theory developed here is applied to the construction and investigation of the neigbourhood of time-independent conditions for nonlinear systems of automatic control, and the control of charged particle beam in magnetic field. Some other specific problems are also solved such as after effect systems and orbit quantization.

The Behaviour Of Nonlinear Vibrating Systems

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Author : Wanda Szemplinska
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-06-30

The Behaviour Of Nonlinear Vibrating Systems written by Wanda Szemplinska 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 1990-06-30 with Technology & Engineering categories.

The purpose of this book is to provide students, practicing engineers and scientists with a treatment of nonlinear phenomena occurring in physical systems. Although only mechanical models are used, the theory applies to all physical systems governed by the same equations, so that the book can be used to study nonlinear phenomena in other branches of engineering, such as electrical engineering and aerospace engineering, as well as in physics. The book consists of two volumes. Volume I is concerned with single degree-of-freedom systems and it presents the fundamental concepts of nonlinear analysis. Both analytical methods and computer simulations are included. The material is presented in such a manner that the book can be used as a graduate as well as an undergraduate textbook. Volume II deals with multi-degree-of-freedom systems. Following an introduc tion to linear systems, the volume presents fundamental concepts of geometric theory and stability of motion of general nonlinear systems, as well as a concise discussion of basic approximate methods for the response of such systems. The material represents a generalization of a series of papers on the vibration of nonlinear multi-degree-of-freedom systems, some of which were published by me and my associates during the period 1965 - 1983 and some are not yet published.

Analytical Methods In Nonlinear Oscillations

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Author : Ebrahim Esmailzadeh
language : en
Publisher: Springer
Release Date : 2018-06-29

Analytical Methods In Nonlinear Oscillations written by Ebrahim Esmailzadeh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-29 with Technology & Engineering categories.

This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range of applications including mechanical and electrical oscillators, micro/nano resonators and sensors, and also modelling of global warming, epidemic diseases, sociology, chemical reactions, biology and ecology.

Communications In Difference Equations

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Author : Saber N. Elaydi
language : en
Publisher: CRC Press
Release Date : 2000-07-06

Communications In Difference Equations written by Saber N. Elaydi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-06 with Mathematics categories.

This collection of carefully refereed and edited papers were originally presented at the Fourth International Conference on Difference Equations held in Poznan, Poland. Contributions were from a diverse group of researchers from several countries and featured discussions on the theory of difference equations, open problems and conjectures, as well as related applications. Whether new to the area of research, or a veteran, this volume will be a valuable resource on the recent advances in the field of difference equations.