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Mothods Of Accelerated Convergence In Nonlinear Mechanics Bogoliubov
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Book Synopsis Averaging Methods in Nonlinear Dynamical Systems by : Jan A. Sanders
Download or read book Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.
Book Synopsis Nonlinear Mechanics, Groups and Symmetry by : Yuri A. Mitropolsky
Download or read book Nonlinear Mechanics, Groups and Symmetry written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.
Download or read book Synergetics written by Hermann Haken and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.
Book Synopsis Methods of Accelerated Convergence in Nonlinear Mechanics by : Nikolaĭ Nikolaevich Bogoli︠u︡bov
Download or read book Methods of Accelerated Convergence in Nonlinear Mechanics written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and published by Springer. This book was released on 1976 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations by : K.D. Elworthy
Download or read book Differential Equations written by K.D. Elworthy and published by Routledge. This book was released on 2017-11-22 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents recent developments in the areas of differential equations, dynamical systems, and control of finke and infinite dimensional systems. Focuses on current trends in differential equations and dynamical system research-from Darameterdependence of solutions to robui control laws for inflnite dimensional systems.
Book Synopsis Advanced Synergetics by : Hermann Haken
Download or read book Advanced Synergetics written by Hermann Haken and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man made. But we often forget that in many cases devices function by means of pro cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz ing systems and man-made devices is not at all rigid.
Book Synopsis Dichotomies and Stability in Nonautonomous Linear Systems by : Yu. A. Mitropolsky
Download or read book Dichotomies and Stability in Nonautonomous Linear Systems written by Yu. A. Mitropolsky and published by CRC Press. This book was released on 2002-10-10 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms, to the solution of this problem. The authors explore the preservation of invariant tori of dynamic systems under perturbation. This volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
Book Synopsis Methods of Accelerated Convergence in Nonlinear Mechanics by : N.N. Bogoljubov
Download or read book Methods of Accelerated Convergence in Nonlinear Mechanics written by N.N. Bogoljubov and published by Springer. This book was released on 2011-11-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with some of the latest results in nonlinear mechanics, obtained recently by the use of a modernized version of Bogoljubov's method of successive changes of variables which ensures rapid convergence. This method visualised as early as 1934 by Krylov and Bogoljubov provides an effective tool for solving many interesting problems of nonlinear mechanics. It led, in particular, to the solution of the problem of the existence of a quasi periodic regime, with the restriction that approximate solutions obtained in the general case involved divergent series. Recently, making use of the research of Kolmogorov and Arno'ld, Bogoljubov has modernised the method of successive substitutions in such a way that the convergence of the corresponding expansions is ensured. This book consists of a short Introduction and seven chapters. The first chapter presents the results obtained by BogoIjubov in 1963 on the extension of the method of successive substitutions and the study of quasi periodic solutions applied to non-conservative systems (inter alia making explicit the dependence of these solutions on the parameter, indicating methods of obtaining asymptotic and convergent series for them, etc.).
Book Synopsis Truly Nonlinear Oscillations by : Ronald E. Mickens
Download or read book Truly Nonlinear Oscillations written by Ronald E. Mickens and published by World Scientific. This book was released on 2010 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of truly nonlinear (TNL) oscillator equations. The volume gives a general overview of the author''s work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply these technique to the field of nonlinear oscillations.
Book Synopsis Statistical Mechanics And The Physics Of Many-particle Model Systems by : Alexander Leonidovich Kuzemsky
Download or read book Statistical Mechanics And The Physics Of Many-particle Model Systems written by Alexander Leonidovich Kuzemsky and published by World Scientific. This book was released on 2017-02-24 with total page 1259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models.This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography.The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.
Book Synopsis Perspectives of Nonlinear Dynamics: Volume 1 by : E. Atlee Jackson
Download or read book Perspectives of Nonlinear Dynamics: Volume 1 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
Download or read book Complex Sciences written by Jie Zhou and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: I was invited to join the Organizing Committee of the First International Conference on Complex Sciences: Theory and Applications (Complex 2009) as its ninth member. At that moment, eight distinguished colleagues, General Co-chairs Eugene Stanley and Gaoxi Xiao, Technical Co-chairs János Kertész and Bing-Hong Wang, Local Co-chairs Hengshan Wang and Hong-An Che, Publicity Team Shi Xiao and Yubo Wang, had spent hundreds of hours pushing the conference half way to its birth. Ever since then, I have been amazed to see hundreds of papers flooding in, reviewed and commented on by the TPC members. Finally, more than 200 contributions were - lected for the proceedings currently in your hands. They include about 200 papers from the main conference (selected from more than 320 submissions) and about 33 papers from the five collated workshops: Complexity Theory of Art and Music (COART) Causality in Complex Systems (ComplexCCS) Complex Engineering Networks (ComplexEN) Modeling and Analysis of Human Dynamics (MANDYN) Social Physics and its Applications (SPA) Complex sciences are expanding their colonies at such a dazzling speed that it - comes literally impossible for any conference to cover all the frontiers.
Book Synopsis Oscillatory Evolution Processes by : Igor Gumowski
Download or read book Oscillatory Evolution Processes written by Igor Gumowski and published by Manchester University Press. This book was released on 1989 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Book Synopsis The Optimal Homotopy Asymptotic Method by : Vasile Marinca
Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Book Synopsis Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems by : Vasile Marinca
Download or read book Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems written by Vasile Marinca and published by Springer Nature. This book was released on 2021-07-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1962 with total page 1116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Subject Catalog by : Library of Congress
Download or read book Subject Catalog written by Library of Congress and published by . This book was released on with total page 1044 pages. Available in PDF, EPUB and Kindle. Book excerpt:
