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Methods Of Accelerated Convergence In Nonlinear Mechanics
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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 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 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 2012-08-14 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 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 . This book was released on 1976 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mothods of accelerated convergence in nonlinear mechanics. Bogoliubov by : Nikolai Nicolaevich Bogoliubov
Download or read book Mothods of accelerated convergence in nonlinear mechanics. Bogoliubov written by Nikolai Nicolaevich Bogoliubov and published by . This book was released on 1976 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients by : Yuri A. Mitropolsky
Download or read book Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems. The contents are divided into six chapters. Chapter 1 presents a study of periodic solutions for nonlinear systems of evolution equations including differential equations with lag, systems of neutral type, various classes of nonlinear systems of integro-differential equations, etc. A numerical-analytic method for the investigation of periodic solutions of these evolution equations is presented. In Chapters 2 and 3, problems concerning the existence of periodic and quasiperiodic solutions for systems with lag are examined. For a nonlinear system with quasiperiodic coefficients and lag, the conditions under which quasiperiodic solutions exist are established. Chapter 4 is devoted to the study of invariant toroidal manifolds for various classes of systems of differential equations with quasiperiodic coefficients. Chapter 5 examines the problem concerning the reducibility of a linear system of difference equations with quasiperiodic coefficients to a linear system of difference equations with constant coefficients. Chapter 6 contains an investigation of invariant toroidal sets for systems of difference equations with quasiperiodic coefficients. For mathematicians whose work involves the study of oscillating systems.
Book Synopsis Computational Methods in Nonlinear Structural and Solid Mechanics by : Ahmed K. Noor
Download or read book Computational Methods in Nonlinear Structural and Solid Mechanics written by Ahmed K. Noor and published by Elsevier. This book was released on 2014-05-20 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.
Book Synopsis Asymptotic Methods in Resonance Analytical Dynamics by : Eugeniu Grebenikov
Download or read book Asymptotic Methods in Resonance Analytical Dynamics written by Eugeniu Grebenikov and published by CRC Press. This book was released on 2004-03-02 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.
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 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 Equadiff-91 - International Conference On Differential Equations (In 2 Volumes) by : C Perello
Download or read book Equadiff-91 - International Conference On Differential Equations (In 2 Volumes) written by C Perello and published by World Scientific. This book was released on 1993-05-25 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equadiff-91 stems from the series of conferences initiated by the late Professor Vogel. The first conference Equadiff-70 which was held in Marseille. Since then, similar conferences had been held in Brussels, Florence, Wurzburg as well as Xanthi. The purpose of the Equadiff series of conferences is to present the latest development in the field of differential equations, both ordinary and partial, including their numerical treatment and applications to the mathematics community. These conferences had attracted renowned mathematicians from all over the world to present their studies and findings. The latest conference under the series was Equadiff-91, held in Barcelona. It attracted some 30 renowned mathematicians. Researchers and graduate students of pure and applied mathematics will find this compilation of conference proceedings up-to-date, relevant and insightful.
Download or read book Synergetics written by Hermann Haken and published by Springer Science & Business Media. This book was released on 2004-01-12 with total page 796 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 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.
Book Synopsis Mathematical Aspects of Classical and Celestial Mechanics by : Vladimir I. Arnold
Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.
Book Synopsis Dynamical Systems in Classical Mechanics by : Valeriĭ Viktorovich Kozlov
Download or read book Dynamical Systems in Classical Mechanics written by Valeriĭ Viktorovich Kozlov and published by American Mathematical Soc.. This book was released on 1995 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics.
