[PDF] Analytical Methods In Nonlinear Oscillations eBook

Author : Ebrahim Esmailzadeh
Publisher : Springer
Page : 296 pages
File Size : 34,89 MB
Release : 2018-06-29
Category : Technology & Engineering
ISBN : 9402415424

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This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range of applications including mechanical and electrical oscillators, micro/nano resonators and sensors, and also modelling of global warming, epidemic diseases, sociology, chemical reactions, biology and ecology.

Author : Livija Cveticanin
Publisher : Springer
Page : 241 pages
File Size : 37,44 MB
Release : 2014-05-22
Category : Science
ISBN : 3319052721

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This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Author : John Guckenheimer
Publisher : Springer Science & Business Media
Page : 475 pages
File Size : 36,68 MB
Release : 2013-11-21
Category : Mathematics
ISBN : 1461211409

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An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Author : Vladimir I. Nekorkin
Publisher : John Wiley & Sons
Page : 264 pages
File Size : 34,55 MB
Release : 2015-04-01
Category : Science
ISBN : 3527685421

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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.

Author : Chu-Hui He
Publisher : Frontiers Media SA
Page : 132 pages
File Size : 11,90 MB
Release : 2023-11-24
Category : Science
ISBN : 2832539637

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The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.

Author : Ali H. Nayfeh
Publisher : Wiley-VCH
Page : 720 pages
File Size : 24,10 MB
Release : 1995-03-22
Category : Science
ISBN : 9780471121428

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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.

Author : Jack K. Hale
Publisher : Courier Dover Publications
Page : 193 pages
File Size : 32,57 MB
Release : 2015-03-24
Category : Mathematics
ISBN : 0486803260

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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 : Ivana Kovacic
Publisher : Springer Nature
Page : 278 pages
File Size : 35,71 MB
Release : 2020-08-14
Category : Technology & Engineering
ISBN : 3030531724

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This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations.