Applied Asymptotic Methods In Nonlinear Oscillations

Author : Yuri A. Mitropolsky
Publisher : Springer Science & Business Media
ISBN 13 : 9401588473
Total Pages : 352 pages
Book Rating : 4.78/5 ( download)

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Download or read book Applied Asymptotic Methods in Nonlinear Oscillations written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.

Author : I︠U︡riĭ Alekseevich Mitropolʹskiĭ
Publisher :
ISBN 13 :
Total Pages : 411 pages
Book Rating : 4.22/5 ( download)

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Download or read book Applied Asymptotic Methods in Nonlinear Oscillations written by I︠U︡riĭ Alekseevich Mitropolʹskiĭ and published by . This book was released on 1994 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher : CRC Press
ISBN 13 : 9780677200507
Total Pages : 556 pages
Book Rating : 4.01/5 ( download)

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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:

Author :
Publisher :
ISBN 13 :
Total Pages : 537 pages
Book Rating : 4.61/5 ( download)

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Download or read book Asymptotic Methods in the Theory of Non-linear Oscillations written by and published by . This book was released on 1961 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Johan Grasman
Publisher : Springer Science & Business Media
ISBN 13 : 1461210569
Total Pages : 229 pages
Book Rating : 4.66/5 ( download)

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Download or read book Asymptotic Methods for Relaxation Oscillations and Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. 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. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.

Author : Sergey G. Glebov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110382725
Total Pages : 460 pages
Book Rating : 4.23/5 ( download)

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Download or read book Oscillations and Resonances written by Sergey G. Glebov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Polina S. Landa
Publisher : Springer Science & Business Media
ISBN 13 : 3540452524
Total Pages : 401 pages
Book Rating : 4.22/5 ( download)

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Download or read book Regular and Chaotic Oscillations written by Polina S. Landa and published by Springer Science & Business Media. This book was released on 2012-11-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.

Author : Alan Jeffrey
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.69/5 ( download)

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Download or read book Asymptotic Methods in Nonlinear Wave Theory written by Alan Jeffrey and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ronald E. Mickens
Publisher : CUP Archive
ISBN 13 : 9780521222082
Total Pages : 234 pages
Book Rating : 4.87/5 ( download)

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Download or read book An Introduction to Nonlinear Oscillations written by Ronald E. Mickens and published by CUP Archive. This book was released on 1981 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory account of the equations describing nonlinear oscillations & the methods for solving them.

Author : N. N. Bogoliubov
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.93/5 ( download)

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Download or read book Asymptotic Methods in the Theory of Non-linear Oscillations written by N. N. Bogoliubov and published by . This book was released on 1961 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: