Weakly Nonlinear Systems
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Weakly Nonlinear Systems
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Author : Federico Beffa
language : en
Publisher: Springer Nature
Release Date : 2023-10-26
Weakly Nonlinear Systems written by Federico Beffa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-26 with Technology & Engineering categories.
The open access book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators. The result is a much-simplified notation, free of multiple integrals, a conceptual simplification, and the ability to solve the associated nonlinear differential equations in a purely algebraic way. The representation based on distributions not only becomes manifestly power series alike, but it includes power series as the description of the subclass of memory-less, time-invariant, weakly nonlinear systems. With this connection, many results from the theory of power series can be extended to the larger class of weakly nonlinear systems with memory. As a specific application, the theory is specialised to weakly nonlinear electric networks. The authors show how they can be described by a set of linear equivalent circuits which can be manipulated in the usual way. The authors include many real-world examples that occur in the design of RF and mmW analogue integrated circuits for telecommunications. The examples show how the theory can elucidate many nonlinear phenomena and suggest solutions that an approach entirely based on numerical simulations can hardly suggest. The theory is extended to weakly nonlinear time-varying systems, and the authors show examples of how time-varying electric networks allow implementing functions unfeasible with time-invariant ones. The book is primarily intended for engineering students in upper semesters and in particular for electrical engineers. Practising engineers wanting to deepen their understanding of nonlinear systems should also find it useful. The book also serves as an introduction to distributions for undergraduate students of mathematics.
Weakly Connected Nonlinear Systems
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Author : Anatoly Martynyuk
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Weakly Connected Nonlinear Systems written by Anatoly Martynyuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected
Sinusoidal Analysis And Modeling Of Weakly Nonlinear Circuits
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Author : Donald D. Weiner
language : en
Publisher: Van Nostrand Reinhold Company
Release Date : 1980
Sinusoidal Analysis And Modeling Of Weakly Nonlinear Circuits written by Donald D. Weiner and has been published by Van Nostrand Reinhold Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Technology & Engineering categories.
Nonlinear Systems
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Author : P. G. Drazin
language : en
Publisher: Cambridge University Press
Release Date : 1992-06-26
Nonlinear Systems written by P. G. Drazin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-26 with Mathematics categories.
The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.
Nonlinear Waves And Weak Turbulence
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Author : Vladimir Evgenʹevich Zakharov
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Nonlinear Waves And Weak Turbulence written by Vladimir Evgenʹevich Zakharov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Hamiltonian systems categories.
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms and the inverse scattering method.
Methods Of Nonlinear Analysis
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Author : Pavel Drabek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-28
Methods Of Nonlinear Analysis written by Pavel Drabek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-28 with Mathematics categories.
In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book.
Nonlinear System Theory
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Author : Casti
language : en
Publisher: Academic Press
Release Date : 1985-02-21
Nonlinear System Theory written by Casti and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-02-21 with Computers categories.
Nonlinear System Theory
Mathematical Methods For Scientists And Engineers
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Author : Peter B. Kahn
language : en
Publisher:
Release Date : 1990
Mathematical Methods For Scientists And Engineers written by Peter B. Kahn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Numerical calculations categories.
Part I of this text/reference presents techniques for linear systems with emphasis on asymptotic methods. The development in Part II employs the methods given in the first part and focuses attention on weakly nonlinear oscillatory systems and nonlinear difference equations. The stress is on practical methods, rather than on proof of theorems, and each method is illustrated by examples of applications in the sciences. Presents some numerical and graphical solutions generated by Lotus 1-2-3 and Math CAD.
Nonlinear Flow Phenomena And Homotopy Analysis
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Author : Kuppalapalle Vajravelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-22
Nonlinear Flow Phenomena And Homotopy Analysis written by Kuppalapalle Vajravelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-22 with Mathematics categories.
Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems and often fail when used for problems with strong nonlinearity. “Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer” presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering. Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA.
Normal Modes And Localization In Nonlinear Systems
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Author : Alexander F. Vakakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Normal Modes And Localization In Nonlinear Systems written by Alexander F. Vakakis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ¢n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape ¢n. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.