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| Author | : Jack K. Hale |
| Publisher | : Courier Dover Publications |
| Total Pages | : 192 |
| Release | : 2015-03-24 |
| Genre | : Mathematics |
| ISBN | : 0486803260 |
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction provides a unified approach for obtaining periodic solutions to nonautonomous and autonomous differential equations. 1963 edition.
| Author | : P.S Landa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 550 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401587639 |
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
| Author | : Chihiro Hayashi |
| Publisher | : Princeton University Press |
| Total Pages | : 405 |
| Release | : 2014-07-14 |
| Genre | : Science |
| ISBN | : 1400852870 |
This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
| Author | : John Guckenheimer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 475 |
| Release | : 2013-11-21 |
| Genre | : Mathematics |
| ISBN | : 1461211409 |
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
| Author | : Arkadii Kh. Gelig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1461217601 |
There are two main fields of application of pulse-modulated sys tems, communications and control. Communication is not a subject of our concern in this book. Controlling by a pulse-modulated feed attracted our efforts. The peculiarity of this book is that all back the sampled-data systems are considered in continuous time, so no discrete time schemes are presented. And finally, we pay a little at tention to pulse-amplitude modulation which was treated in a vast number of publications. The primary fields of our interest are pulse width, pulse-frequency, and pulse-phase modulated control systems. The study of such systems meets with substantial difficulties. An engineer, who embarks on theoretical investigations of a pulse-mo dulated control, is often embarrassed by the sophisticated mathe matical tools he needs to know. When a mathematician, who looks for practical applications of his mathematical machinery, meets with these systems, he faces a lot of of complicated technical schemes and terms. Probably this is the reason why publications on pulse modu lation are seldom in scientific journals. As for books on this subject (save on amplitude modulation), the significant part of them is in Russian and hardly available for a non-Russian reader.
| Author | : Vladimir I. Nekorkin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 264 |
| Release | : 2015-04-01 |
| Genre | : Science |
| ISBN | : 3527685421 |
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.
| Author | : M.I Rabinovich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 586 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9400910339 |
'Et mai - ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost sheJf next to the dusty canister Iabclled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
| Author | : Alexander Fidlin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2005-12-19 |
| Genre | : Technology & Engineering |
| ISBN | : 3540281169 |
"Nonlinear Oscillations in Mechanical Engineering" explores the effects of nonlinearities encountered in applications in that field. Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused by dry friction and collisions. Another important source of nonlinearity which is covered is that caused by rotating unbalanced parts common in various machines as well as variable inertias occurring in all kinds of crank mechanisms. This book is written for advanced undergraduate and postgraduate students, but it may be also helpful and interesting for both theoreticians and practitioners working in the area of mechanical engineering at universities, in research labs or institutes and especially in the R and D departments within industrial firms.
| Author | : Austin Blaquiere |
| Publisher | : Elsevier |
| Total Pages | : 409 |
| Release | : 2012-12-02 |
| Genre | : Technology & Engineering |
| ISBN | : 0323151663 |
Nonlinear System Analysis focuses on the study of systems whose behavior is governed by nonlinear differential equations. This book is composed of nine chapters that cover some problems that play a major role in engineering and physics. The opening chapter briefly introduces the difference between linear and nonlinear systems. Considerable chapters are devoted to engineering and physics related problems and their applications to particle accelerators, frequency measurements, and masers. Included in these chapters are important practical problems, such as synchronization, stability of systems with periodic coefficients, and effect of random disturbances. The remaining chapters examine random fluctuations of the motion and self-oscillators. This book is intended primarily for engineers and physicists.
| Author | : Ivana Kovacic |
| Publisher | : Springer Nature |
| Total Pages | : 278 |
| Release | : 2020-08-14 |
| Genre | : Technology & Engineering |
| ISBN | : 3030531724 |
This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations.
