Theory of Oscillations, Sergey Viktorovich Eliseev; Andrey Vladimirovich E
Автор: Vistnes, Arnt Inge Название: Physics of oscillations and waves ISBN: 3319723138 ISBN-13(EAN): 9783319723136 Издательство: Springer Рейтинг: Цена: 10480.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this textbook a combination of standard mathematics and modern numerical methods is used to describe a wide range of natural wave phenomena, such as sound, light and water waves, particularly in specific popular contexts, e.g.
Описание: 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.
Описание: This book book presents theoretical studies of spontaneous symmetry breaking effects along with experimental findings, chiefly for Bose-Einstein-Condensates with self-repulsive nonlinearity, as well as for photorefractive media in optics.
Описание: Contains 32 selected papers that cover: non-linear oscillations of beams, plates, vehicles, and other dynamic systems; analysis and control of non-linear systems; non-linear waves; dynamics of offshore structures; system identification; and, mathematical and numerical methods for investigating non-linear systems.
Автор: Luis T. Aguilar; Igor Boiko; Leonid Fridman; Rafae Название: Self-Oscillations in Dynamic Systems ISBN: 3319233025 ISBN-13(EAN): 9783319233024 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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
Автор: Elena V. Grigorieva; Sergey A. Kaschenko Название: Asymptotic Representation of Relaxation Oscillations in Lasers ISBN: 3319428594 ISBN-13(EAN): 9783319428598 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors.With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others.The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Автор: Viacheslav Karmalita Название: Digital Processing of Random Oscillations ISBN: 3110625008 ISBN-13(EAN): 9783110625004 Издательство: Walter de Gruyter Рейтинг: Цена: 16727.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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)+ ?_0^2 X(t)=E(t), where ?0 = 2?/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 ? = 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 ? and ?0. The proposed approach allows researchers to replace traditional subjective techniques by a formal processing procedure providing efficient estimates with analytically defined statistical uncertainties.
Автор: V. Silberschmidt; Agnessa Kovaleva Название: Optimal Control of Mechanical Oscillations ISBN: 3642084761 ISBN-13(EAN): 9783642084768 Издательство: Springer Рейтинг: Цена: 23757.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory.
Автор: Fitzpatrick, Richard (the University Of Texas, Austin, Usa) Название: Oscillations and waves an introduc ISBN: 1138479713 ISBN-13(EAN): 9781138479715 Издательство: Taylor&Francis Рейтинг: Цена: 12707.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Emphasizing physics over mathematics, this popular, classroom-tested text helps advanced undergraduates acquire a sound physical understanding of wave phenomena. This second edition contains new widgets, animations in Python, and exercises, as well as updated chapter content throughout.
Описание: The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015.
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