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Asymptotic Methods In The Theory Of Nonlinear Oscillations
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Book Synopsis Asymptotic Methods in the Theory of Non-linear Oscillations by : Nikolaĭ Nikolaevich Bogoli︠u︡bov
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:
Book Synopsis Applied Asymptotic Methods in Nonlinear Oscillations by : Yuri A. Mitropolsky
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.
Book Synopsis Asymptotic Methods for Relaxation Oscillations and Applications by : Johan Grasman
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.
Book Synopsis Introduction to Nonlinear Oscillations by : Vladimir I. Nekorkin
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.
Book Synopsis Asymptotic Methods in the Theory of Nonlinear Oscillations by : Nikolaĭ Nikolaevich Bogoli︠u︡bov
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:
Book Synopsis Applied Methods in the Theory of Nonlinear Oscillations by : Vi︠a︡cheslav Mikhaĭlovich Starzhinskiĭ
Download or read book Applied Methods in the Theory of Nonlinear Oscillations written by Vi︠a︡cheslav Mikhaĭlovich Starzhinskiĭ and published by . This book was released on 1980 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical-analytic Methods in the Theory of Boundary-value Problems by : Nikola? Iosifovich Ronto
Download or read book Numerical-analytic Methods in the Theory of Boundary-value Problems written by Nikola? Iosifovich Ronto and published by World Scientific. This book was released on 2000 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory ? namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods.
Book Synopsis Methods Of Qualitative Theory In Nonlinear Dynamics (Part I) by : Leonid P Shilnikov
Download or read book Methods Of Qualitative Theory In Nonlinear Dynamics (Part I) written by Leonid P Shilnikov and published by World Scientific. This book was released on 1998-12-08 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
Book Synopsis Introduction to Nonlinear Oscillations by : Vladimir I. Nekorkin
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.
Book Synopsis Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions by : Igor Andrianov
Download or read book Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions written by Igor Andrianov and published by John Wiley & Sons. This book was released on 2014-02-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary value problems • Introduces modern asymptotic and summation procedures • Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates • Covers statics, dynamics and stability of plates with mixed boundary conditions • Explains links between the Adomian and homotopy perturbation approaches Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.
Book Synopsis Asymptotic Methods for Engineers by : Igor V. Andrianov
Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
Book Synopsis Approximation Procedures in Nonlinear Oscillation Theory by : Nikolai A. Bobylev
Download or read book Approximation Procedures in Nonlinear Oscillation Theory written by Nikolai A. Bobylev and published by Walter de Gruyter. This book was released on 2012-05-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Eduardo V. Teixeira, Free Boundary Problems: A Primer (2018) Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
Book Synopsis Asymptotic Methods in the Theory of Non-linear Oscillations by :
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:
Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst
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.
Book Synopsis Encyclopedia of Ukraine by : Danylo Husar Struk
Download or read book Encyclopedia of Ukraine written by Danylo Husar Struk and published by University of Toronto Press. This book was released on 1993-12-15 with total page 2380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over thirty years in the making, the most comprehensive work in English on Ukraine is now complete: its history, people, geography, economy, and cultural heritage, both in Ukraine and in the diaspora.
Book Synopsis Playing Around Resonance by : Alessandro Fonda
Download or read book Playing Around Resonance written by Alessandro Fonda and published by Birkhäuser. This book was released on 2016-11-11 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.
Book Synopsis Fractional Analysis by : I.V. Novozhilov
Download or read book Fractional Analysis written by I.V. Novozhilov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers methods of approximate analysis of mechanical, elec tromechanical, and other systems described by ordinary differential equa tions. Modern mathematical modeling of sophisticated mechanical systems consists of several stages: first, construction of a mechanical model, and then writing appropriate equations and their analytical or numerical ex amination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it de scribes, as a rule, many unnecessary details that make equations of motion too complicated. As experience and experimental data are accumulated, the researcher considers simpler models and simplifies the equations. Thus some terms are discarded, the order of the equations is lowered, and so on. This process requires time, experimentation, and the researcher's intu ition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admis sibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approxi mate analysis of differential equations. Application of these methods could shorten and formalize the procedure of simplifying the equations and, thus, of constructing approximate motion models. Wide application of the methods into practice is hindered by the fol lowing. 1. Descriptions of various approximate methods are scattered over the mathematical literature. The researcher, as a rule, does not know what method is most suitable for a specific case. 2.
