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Introduction to Nonlinear Oscillations by Vladimir I. Nekorkin Pdf
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.
Analysis and Damping Control of Power System Low-frequency Oscillations by Haifeng Wang,Wenjuan Du Pdf
This book presents the research and development results on power systems oscillations in three categories of analytical methods. First is damping torque analysis which was proposed in 1960’s, further developed between 1980-1990, and widely used in industry. Second is modal analysis which developed between the 1980’s and 1990’s as the most powerful method. Finally the linearized equal-area criterion analysis that is proposed and developed recently. The book covers three main types of controllers: Power System Stabilizer (PSS), FACTS (Flexible AC Transmission Systems) stabilizer, and ESS (Energy Storage Systems) stabilizer. The book provides a systematic and detailed introduction on the subject as the reference for industry applications and academic research.
Mixed Mode Oscillations (MMOs) by Zdzislaw Trzaska Pdf
This book aims to present a survey of a large class of nonlinear dynamical systems exhibiting mixed-mode oscillations (MMOs). It is a sort of a guide to systems related to MMOs that features material from original research papers, including the author’s own studies. The material is presented in seven chapters divided into sections. Usually, the first sections are of an introductory nature, explain phenomena, and exhibit numerical results. More advanced investigations are presented in the subsequent sections. Coverage includes * Dynamic behavior of nonlinear systems, * Fundamentals of processes exhibiting MMOs,* Mechanism and function of an structure of MMOs patterns, * Analysis of MMOs in electric circuits and systems, * MMOs in chemistry, biology, and medicine, * MMOs in mechanics and transport vehicles, * MMOs in fractional order systems. This is the first extensive description of these topics and the interpretation of analytical results and those obtained from computer simulations with the MATLAB environment. The book provides the readers with better understanding of the nature of MMOs, richness of their behaviors, and interesting applications.
Magnetic Oscillations in Metals by D. Shoenberg Pdf
It is just over 80 years ago that a striking oscillatory field dependence was discovered in the magnetic behaviour of bismuth at low temperatures. This book was first published in 1984 and gives a systematic account of the nature of the oscillations, of the experimental techniques for their study and of their connection with the electronic structure of the metal concerned. Although the main emphasis is on the oscillations themselves and their many peculiarities, rather than on the theory of the electronic structure they reveal, sufficient examples are given in detail to illustrate the kind of information that has been obtained and how this information agrees with theoretical prediction.
Collective Oscillations in a Plasma by A. I. Akhiezer,I. A. Akhiezer,R. V. Polovin Pdf
International Series of Monographs in Natural Philosophy: Collective Oscillations in a Plasma, Volume 7 presents specific topics within the general field of radio waves propagation. This book contains five chapters that address the theory of linear oscillations in a plasma, the spectra of the eigen oscillations, and the mechanism of high-frequency heating. The opening chapters deal with the self-consistent fields; development of initial perturbation; dispersion permittivity tensor of a plasma in a magnetic field; effect of thermal motion of particles on low-frequency resonances; excitation of oscillations by modulated azimuthal currents; and cyclotron damping of low-frequency oscillations. The next chapters describe the nature of beam instability, the fluctuations in a free equilibrium plasma, and the current causing scattered waves. A study of the probability of scattering is presented. The concluding chapters are devoted to the scattering of electromagnetic waves in a plasma-beam system and the coefficient of reflection determination. The book can provide useful information to scientists, physicists, students, and researchers.
Nonlinear Oscillations by Ali H. Nayfeh,Dean T. Mook Pdf
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.
Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov
Author : Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov Publisher : Walter de Gruyter GmbH & Co KG Page : 460 pages File Size : 46,6 Mb Release : 2017-04-10 Category : Mathematics ISBN : 9783110382723
Oscillations and Resonances by Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov Pdf
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
Waves and oscillations permeate virtually every field of current physics research, are central to chemistry, and are essential to much of engineering. Furthermore, the concepts and mathematical techniques used for serious study of waves and oscillations form the foundation for quantum mechanics. Once they have mastered these ideas in a classical context, students will be ready to focus on the challenging concepts of quantum mechanics when they encounter them, rather than struggling with techniques. This lively textbook gives a thorough grounding in complex exponentials and the key aspects of differential equations and matrix math; no prior experience is assumed. The parallels between normal mode analysis, orthogonal function analysis (especially Fourier analysis), and superpositions of quantum states are clearly drawn, without actually getting into the quantum mechanics. An in-depth, accessible introduction to Hilbert space and bra-ket notation begins in Chapter 5 (on symmetrical coupled oscillators), emphasizing the analogy with conventional dot products, and continues in subsequent chapters. Connections to current physics research (atomic force microscopy, chaos, supersolids, micro electro-mechanical systems (MEMS), magnetic resonance imaging, carbon nanotubes, and more) are highlighted in the text and in end-of-chapter problems, and are frequently updated in the associated website. The book actively engages readers with a refreshing writing style and a set of carefully applied learning tools, such as in-text concept tests, "your turn" boxes (in which the student fills in one or two steps of a derivation), concept and skill inventories for each chapter, and "wrong way" problems in which the student explains the flaw in a line of reasoning. These tools promote self-awareness of the learning process. The associated website features custom-developed applets, video and audio recordings, additional problems, and links to related current research. The instructor-only part includes difficulty ratings for problems, optional hints, full solutions, and additional support materials.
Massive Neutrinos: Flavor Mixing Of Leptons And Neutrino Oscillations by Harald Fritzsch Pdf
Since the discovery of neutrino oscillations neutrino physics has become an interesting field of research in physics. They imply that neutrino must have a small mass and that the neutrinos, coupled to the charged leptons, are mixtures of the mass eigenstates, analogous to the flavor mixing of the quarks. The mixing angles for the quarks are small, but for the leptons two of the mixing angles are large. The masses of the three neutrinos must be very small, less than 1 eV, but from the oscillation experiments we only know the mass differences — the absolute masses are still unknown. Also we do not know, if the masses of the neutrinos are Dirac masses, as the masses of the charged leptons and of the quarks, or whether they are Majorana masses.In this volume, an overview of the present state of research in neutrino physics is given by well-known experimentalists and theorists. The contents — originated from talks and discussions at a recent conference addressing some of the most pressing open questions in neutrino physics — range from the oscillation experiments to CP-violation for leptons, to texture zero mass matrices and to the role of neutrinos in astrophysics and cosmology.
Inverse Problems in the Theory of Small Oscillations by Vladimir Marchenko,Victor Slavin Pdf
Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finite-difference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered.