Download or read book Asymptotic Methods in the Theory of Non linear Oscillations written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and published by CRC Press. This book was released on 1961 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Non linear Oscillations written by N. N. Bogoliubov and published by . This book was released on 1961 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Nonlinear Oscillations written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and published by . This book was released on 1955 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic methods in the theory of non linear oscillations written by Nikolaj N. Bogoljubov and published by . This book was released on 1985 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Non linear Oscillations written by and published by . This book was released on 1961 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Non linear Oscillations written by IUril Alekseevich Mitropol'skii and published by . This book was released on 1961 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Nonlinear Oscillations written by Central Intelligence Agency and published by Hassell Street Press. This book was released on 2021-09-09 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Asymptotic Methods for Relaxation Oscillations and Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Download or read book Introduction to Nonlinear Oscillations written by Vladimir I. Nekorkin and published by John Wiley & Sons. This book was released on 2015-04-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Application of Asymptotic Methods of the Theory of Nonlinear Oscillations to the Problem of Wave Propagation written by I. F. Budagyan and published by . This book was released on 1966 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Asymptotic Methods in Nonlinear Oscillations written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Methods in Nonlinear Wave Theory written by Alan Jeffrey and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oscillations and Resonances written by Sergey G. Glebov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators
Download or read book Introduction to Nonlinear Oscillations written by Vladimir I. Nekorkin and published by John Wiley & Sons. This book was released on 2016-05-02 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Approaches in Nonlinear Dynamics written by Jan Awrejcewicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.
Download or read book Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems. The contents are divided into six chapters. Chapter 1 presents a study of periodic solutions for nonlinear systems of evolution equations including differential equations with lag, systems of neutral type, various classes of nonlinear systems of integro-differential equations, etc. A numerical-analytic method for the investigation of periodic solutions of these evolution equations is presented. In Chapters 2 and 3, problems concerning the existence of periodic and quasiperiodic solutions for systems with lag are examined. For a nonlinear system with quasiperiodic coefficients and lag, the conditions under which quasiperiodic solutions exist are established. Chapter 4 is devoted to the study of invariant toroidal manifolds for various classes of systems of differential equations with quasiperiodic coefficients. Chapter 5 examines the problem concerning the reducibility of a linear system of difference equations with quasiperiodic coefficients to a linear system of difference equations with constant coefficients. Chapter 6 contains an investigation of invariant toroidal sets for systems of difference equations with quasiperiodic coefficients. For mathematicians whose work involves the study of oscillating systems.
Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.
