Theory Of Oscillations
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| Author | : A. A. Andronov |
| Publisher | : Elsevier |
| Total Pages | : 848 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 1483194728 |
Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-oscillating systems. This book discusses as well the discontinuous self-oscillations of a symmetrical multi-vibrator neglecting anode reaction. The final chapter deals with the immense practical importance of the stability of physical systems containing energy sources particularly control systems. This book is a valuable resource for electrical engineers, scientists, physicists, and mathematicians.
| Author | : G.A. Leonov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 415 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9400901933 |
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.
| Author | : A. A. Andronov |
| Publisher | : |
| Total Pages | : 358 |
| Release | : 1983 |
| Genre | : Oscillations |
| ISBN | : |
| Author | : A. C. Facundo |
| Publisher | : State University of New York Press |
| Total Pages | : 244 |
| Release | : 2016-09-30 |
| Genre | : Literary Criticism |
| ISBN | : 1438463103 |
Oscillations of Literary Theory offers a new psychoanalytic approach to reading literature queerly, one that implicates queer theory without depending on explicit representations of sex or queer identities. By focusing on desire and identifications, A. C. Facundo argues that readers can enjoy the text through a variety of rhythms between two (eroticized) positions: the paranoid imperative and queer reparative. Facundo examines the metaphor of rupture as central to the logic of critique, particularly the project to undo conventional formations of identity and power. To show how readers can rebuild their relational worlds after the rupture, Facundo looks to the themes of the desire for omniscience, the queer pleasure of the text, loss and letting go, and the vanishing points that structure thinking. Analyses of Nabokov's Lolita, Danielewski's House of Leaves, Findley's The Wars, and Ishiguro's Never Let Me Go are included, which model this new approach to reading.
| Author | : Lynn Erbe |
| Publisher | : Routledge |
| Total Pages | : 504 |
| Release | : 2017-10-02 |
| Genre | : Mathematics |
| ISBN | : 135142632X |
Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.
| 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 | : Daniel B. Forger |
| Publisher | : MIT Press |
| Total Pages | : 369 |
| Release | : 2024-08-06 |
| Genre | : Science |
| ISBN | : 0262552817 |
An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.
| Author | : Jack K. Hale |
| Publisher | : Courier Dover Publications |
| Total Pages | : 193 |
| 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 | : Richard Fitzpatrick |
| Publisher | : CRC Press |
| Total Pages | : 425 |
| Release | : 2018-07-17 |
| Genre | : Science |
| ISBN | : 1351063081 |
Emphasizing physics over mathematics, this popular, classroom-tested text helps advanced undergraduates acquire a sound physical understanding of wave phenomena. This second edition of Oscillations and Waves: An Introduction contains new widgets, animations in Python, and exercises, as well as updated chapter content throughout; continuing to ease the difficult transition for students between lower-division courses that mostly encompass algebraic equations and upper-division courses that rely on differential equations. Assuming familiarity with the laws of physics and college-level mathematics, the author covers aspects of optics that crucially depend on the wave-like nature of light, such as wave optics. Examples explore discrete mechanical, optical, and quantum mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; and electromagnetic waves. The text also introduces the conventional complex representation of oscillations and waves during the discussion of quantum mechanical waves. Features: Fully updated throughout and featuring new widgets, animations, and end of chapter exercises to enhance understanding Offers complete coverage of advanced topics in waves, such as electromagnetic wave propagation through the ionosphere Includes examples from mechanical systems, elastic solids, electronic circuits, optical systems, and other areas
| Author | : Krešimir Veselić |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 215 |
| Release | : 2011-07-09 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 3642213340 |
The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.
