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Frequency Methods In Oscillation Theory
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Book Synopsis Frequency Methods in Oscillation Theory by : Gennady Leonov
Download or read book Frequency Methods in Oscillation Theory written by Gennady Leonov and published by . This book was released on 2014-01-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Frequency Methods in Oscillation Theory by : G.A. Leonov
Download or read book Frequency Methods in Oscillation Theory written by G.A. Leonov and published by Springer. This book was released on 1996 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Frequency Methods in Oscillation Theory by : G.A. Leonov
Download or read book Frequency Methods in Oscillation Theory written by G.A. Leonov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Physical Fundamentals of Oscillations by : Leonid Chechurin
Download or read book Physical Fundamentals of Oscillations written by Leonid Chechurin and published by Springer. This book was released on 2018-04-16 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces possibly the most compact, simple and physically understandable tool that can describe, explain, predict and design the widest set of phenomena in time-variant and nonlinear oscillations. The phenomena described include parametric resonances, combined resonances, instability of forced oscillations, synchronization, distributed parameter oscillation and flatter, parametric oscillation control, robustness of oscillations and many others. Although the realm of nonlinear oscillations is enormous, the book relies on the concept of minimum knowledge for maximum understanding. This unique tool is the method of stationarization, or one frequency approximation of parametric resonance problem analysis in linear time-variant dynamic systems. The book shows how this can explain periodic motion stability in stationary nonlinear dynamic systems, and reveals the link between the harmonic stationarization coefficients and describing functions. As such, the book speaks the language of control: transfer functions, frequency response, Nyquist plot, stability margins, etc. An understanding of the physics of stability loss is the basis for the design of new oscillation control methods for, several of which are presented in the book. These and all the other findings are illustrated by numerical examples, which can be easily reproduced by readers equipped with a basic simulation package like MATLAB with Simulink. The book offers a simple tool for all those travelling through the world of oscillations, helping them discover its hidden beauty. Researchers can use the method to uncover unknown aspects, and as a reference to compare it with other, for example, abstract mathematical means. Further, it provides engineers with a minimalistic but powerful instrument based on physically measurable variables to analyze and design oscillatory systems.
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 Oscillation Theory of Two-Term Differential Equations by : Uri Elias
Download or read book Oscillation Theory of Two-Term Differential Equations written by Uri Elias and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.
Book Synopsis Further Insights into Oscillation Theory by : Nikolai Verichev
Download or read book Further Insights into Oscillation Theory written by Nikolai Verichev and published by Cambridge Scholars Publishing. This book was released on 2021-07-27 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.
Author :Yuri A. Mitropolsky Publisher :Springer Science & Business Media ISBN 13 :9780792345299 Total Pages :232 pages Book Rating :4.3/5 (452 download)
Book Synopsis Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type by : Yuri A. Mitropolsky
Download or read book Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 1997-04-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of partial differential equations is a wide and rapidly developing branch of contemporary mathematics. Problems related to partial differential equations of order higher than one are so diverse that a general theory can hardly be built up. There are several essentially different kinds of differential equations called elliptic, hyperbolic, and parabolic. Regarding the construction of solutions of Cauchy, mixed and boundary value problems, each kind of equation exhibits entirely different properties. Cauchy problems for hyperbolic equations and systems with variable coefficients have been studied in classical works of Petrovskii, Leret, Courant, Gording. Mixed problems for hyperbolic equations were considered by Vishik, Ladyzhenskaya, and that for general two dimensional equations were investigated by Bitsadze, Vishik, Gol'dberg, Ladyzhenskaya, Myshkis, and others. In last decade the theory of solvability on the whole of boundary value problems for nonlinear differential equations has received intensive development. Significant results for nonlinear elliptic and parabolic equations of second order were obtained in works of Gvazava, Ladyzhenskaya, Nakhushev, Oleinik, Skripnik, and others. Concerning the solvability in general of nonlinear hyperbolic equations, which are connected to the theory of local and nonlocal boundary value problems for hyperbolic equations, there are only partial results obtained by Bronshtein, Pokhozhev, Nakhushev.
Book Synopsis Integration on Infinite-Dimensional Surfaces and Its Applications by : A. V. Uglanov
Download or read book Integration on Infinite-Dimensional Surfaces and Its Applications written by A. V. Uglanov and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), stochastic processes, approximation of functions, and calculus of variation on a Banach space, are treated in detail. Audience: This book will be of interest to specialists in functional analysis, and those whose work involves measure and integration, probability theory and stochastic processes, partial differential equations and mathematical physics.
Book Synopsis Introduction to Vertex Operator Superalgebras and Their Modules by : Xiaoping Xu
Download or read book Introduction to Vertex Operator Superalgebras and Their Modules written by Xiaoping Xu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices. Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.
Book Synopsis Advanced Manufacturing Processes by : Volodymyr Tonkonogyi
Download or read book Advanced Manufacturing Processes written by Volodymyr Tonkonogyi and published by Springer Nature. This book was released on 2020-03-27 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a timely yet comprehensive snapshot of innovative research and developments in the area of manufacturing. It covers a wide range of manufacturing processes, such as cutting, coatings, and grinding, highlighting the advantages provided by the use of new materials and composites, as well as new methods and technologies. It discusses topics in energy generation and pollution prevention. It shows how computational methods and mathematical models have been applied to solve a number of issues in both theoretical and applied research. Based on selected papers presented at the Grabchenko’s International Conference on Advanced Manufacturing Processes (InterPartner-2019), held in Odessa, Ukraine on September 10-13, 2019, this book offers a timely overview and extensive information on trends and technologies in the area of manufacturing, mechanical and materials engineering. It is also intended to facilitate communication and collaboration between different groups working on similar topics, and to offer a bridge between academic and industrial researchers.
Book Synopsis Convex and Starlike Mappings in Several Complex Variables by : Sheng Gong
Download or read book Convex and Starlike Mappings in Several Complex Variables written by Sheng Gong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies this topic. It gathers together, and presents in a unified manner, the current state of affairs for convex and starlike biholomorphic mappings in several complex variables. The majority of the results presented are due to the author, his co-workers and his students. Audience: This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable.
Author :D. Przeworska-Rolewicz Publisher :Springer Science & Business Media ISBN 13 :9780792349747 Total Pages :376 pages Book Rating :4.3/5 (497 download)
Book Synopsis Logarithms and Antilogarithms by : D. Przeworska-Rolewicz
Download or read book Logarithms and Antilogarithms written by D. Przeworska-Rolewicz and published by Springer Science & Business Media. This book was released on 1998-03-31 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume proposes and explores a new definition of logarithmic mappings as invertible selectors of multifunctions induced by linear operators with domains and ranges in an algebra over a field of characteristic zero. Amongst the applications of logarithmic and antilogarithmic mappings are the solution of linear and nonlinear equations in algebras of square matrices. Some results may also provide numerical algorithms for the approximation of solutions. This book will be of interest to research mathematicians and other scientists of other disciplines whose work involves the solution of equations.
Book Synopsis A Least Squares Method for the Reduction of Free-oscillation Data by : Phillip R. Wilcox
Download or read book A Least Squares Method for the Reduction of Free-oscillation Data written by Phillip R. Wilcox and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Digital Processing of Random Oscillations by : Viacheslav Karmalita
Download or read book Digital Processing of Random Oscillations written by Viacheslav Karmalita and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the autoregressive method for digital processing of random oscillations. The method is based on a one-to-one transformation of the numeric factors of the Yule series model to linear elastic system characteristics. This parametric approach allowed to develop a formal processing procedure from the experimental data to obtain estimates of logarithmic decrement and natural frequency of random oscillations. A straightforward mathematical description of the procedure makes it possible to optimize a discretization of oscillation realizations providing efficient estimates. The derived analytical expressions for confidence intervals of estimates enable a priori evaluation of their accuracy. Experimental validation of the method is also provided. Statistical applications for the analysis of mechanical systems arise from the fact that the loads experienced by machineries and various structures often cannot be described by deterministic vibration theory. Therefore, a sufficient description of real oscillatory processes (vibrations) calls for the use of random functions. In engineering practice, the linear vibration theory (modeling phenomena by common linear differential equations) is generally used. This theory’s fundamental concepts such as natural frequency, oscillation decrement, resonance, etc. are credited for its wide use in different technical tasks. In technical applications two types of research tasks exist: direct and inverse. The former allows to determine stochastic characteristics of the system output X(t) resulting from a random process E(t) when the object model is considered known. The direct task enables to evaluate the effect of an operational environment on the designed object and to predict its operation under various loads. The inverse task is aimed at evaluating the object model on known processes E(t) and X(t), i.e. finding model (equations) factors. This task is usually met at the tests of prototypes to identify (or verify) its model experimentally. To characterize random processes a notion of "shaping dynamic system" is commonly used. This concept allows to consider the observing process as the output of a hypothetical system with the input being stationary Gauss-distributed ("white") noise. Therefore, the process may be exhaustively described in terms of parameters of that system. In the case of random oscillations, the "shaping system" is an elastic system described by the common differential equation of the second order: X ̈(t)+2hX ̇(t)+ ω_0^2 X(t)=E(t), where ω0 = 2π/Т0 is the natural frequency, T0 is the oscillation period, and h is a damping factor. As a result, the process X(t) can be characterized in terms of the system parameters – natural frequency and logarithmic oscillations decrement δ = hT0 as well as the process variance. Evaluation of these parameters is subjected to experimental data processing based on frequency or time-domain representations of oscillations. It must be noted that a concept of these parameters evaluation did not change much during the last century. For instance, in case of the spectral density utilization, evaluation of the decrement values is linked with bandwidth measurements at the points of half-power of the observed oscillations. For a time-domain presentation, evaluation of the decrement requires measuring covariance values delayed by a time interval divisible by T0. Both estimation procedures are derived from a continuous description of research phenomena, so the accuracy of estimates is linked directly to the adequacy of discrete representation of random oscillations. This approach is similar a concept of transforming differential equations to difference ones with derivative approximation by corresponding finite differences. The resulting discrete model, being an approximation, features a methodical error which can be decreased but never eliminated. To render such a presentation more accurate it is imperative to decrease the discretization interval and to increase realization size growing requirements for computing power. The spectral density and covariance function estimates comprise a non-parametric (non-formal) approach. In principle, any non-formal approach is a kind of art i.e. the results depend on the performer’s skills. Due to interference of subjective factors in spectral or covariance estimates of random signals, accuracy of results cannot be properly determined or justified. To avoid the abovementioned difficulties, the application of linear time-series models with well-developed procedures for parameter estimates is more advantageous. A method for the analysis of random oscillations using a parametric model corresponding discretely (no approximation error) with a linear elastic system is developed and presented in this book. As a result, a one-to-one transformation of the model’s numerical factors to logarithmic decrement and natural frequency of random oscillations is established. It allowed to develop a formal processing procedure from experimental data to obtain the estimates of δ and ω0. The proposed approach allows researchers to replace traditional subjective techniques by a formal processing procedure providing efficient estimates with analytically defined statistical uncertainties.
Book Synopsis Signals, Oscillations, and Waves by : D. E. Vakman
Download or read book Signals, Oscillations, and Waves written by D. E. Vakman and published by Artech House Publishers. This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fortify your knowledge of the amplitudes and frequencies associated with analytic signals and waves, and understand their role in the solution of difficult engineering and physical problems with this practical new book. It shows you how to employ one universal new method in solving challenging engineering problems related to signal processing, wave propagation, electrical and electronics engineering, mechanical and seismic oscillations, acoustics, and other areas. In clear, easy-to-understand language, and with the help of more than 1000 equations, the author illustrates how this practical approach is used to work out both new and classic problems more accurately than traditional methods.
Book Synopsis Inverse Problems in the Theory of Small Oscillations by : Vladimir Marchenko
Download or read book Inverse Problems in the Theory of Small Oscillations written by Vladimir Marchenko and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.