Elementary Stability And Bifurcation Theory
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Elementary Stability And Bifurcation Theory
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Author : Gerard Iooss
language : en
Publisher: Springer
Release Date : 2012-10-08
Elementary Stability And Bifurcation Theory written by Gerard Iooss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-08 with Mathematics categories.
This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.
Elementary Stability And Bifurcation Theory
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Author : G. Iooss
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elementary Stability And Bifurcation Theory written by G. Iooss 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 2013-03-09 with Science categories.
In its most general form bifurcation theory is a theory of equilibrium solutions of nonlinear equations. By equilibrium solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of equilibrium solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broaqest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, econom ists, and others whose work involves understanding equilibrium solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis 1. general enough to apply to the huge variety of applications which arise in science and technology, and 2. simple enough so that it can be understood by persons whose mathe matical training does not extend beyond the classical methods of analysis which were popular in the 19th Century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. It is generally believed that the mathematical theory of bifurcation requires some functional analysis and some of the methods of topology and dynamics.
Elementary Stability And Bifurcation Theory
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Author : Gèerard Iooss
language : en
Publisher:
Release Date : 1990
Elementary Stability And Bifurcation Theory written by Gèerard Iooss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Bifurcation theory categories.
Topics In Stability And Bifurcation Theory
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Author : David H. Sattinger
language : en
Publisher:
Release Date : 1973
Topics In Stability And Bifurcation Theory written by David H. Sattinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Bifurcation theory categories.
Elementary Stability And Bifurcation Theory
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Author : Gerard Iooss
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elementary Stability And Bifurcation Theory written by Gerard Iooss 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 2012-12-06 with Mathematics categories.
This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.
Stability And Bifurcation Of Structures
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Author : Angelo Luongo
language : en
Publisher: Springer Nature
Release Date : 2023-06-27
Stability And Bifurcation Of Structures written by Angelo Luongo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-27 with Technology & Engineering categories.
This book overcomes the separation existing in literature between the static and the dynamic bifurcation worlds. It brings together buckling and post-buckling problems with nonlinear dynamics, the bridge being represented by the perturbation method, i.e., a mathematical tool that allows for solving static and dynamic problems virtually in the same way. The book is organized as follows: Chapter one gives an overview; Chapter two illustrates phenomenological aspect of static and dynamic bifurcations; Chapter three deals with linear stability analysis of dynamical systems; Chapter four and five discuss the general theory and present examples of buckling and post-buckling of elastic structures; Chapter six describes a linearized approach to buckling, usually adopted in the technical literature, in which pre-critical deformations are neglected; Chapters seven to ten, analyze elastic and elasto-plastic buckling of planar systems of beams, thin-walled beams and plate assemblies, respectively; Chapters eleven to thirteen, illustrate dynamic instability phenomena, such as flutter induced by follower forces, aeroelastic bifurcations caused by wind flow, and parametric excitation triggered by pulsating loads. Finally, Chapter fourteen discusses a large gallery of solved problems, concerning topics covered in the book. An Appendix presents the Vlasov theory of open thin-walled beams. The book is devoted to advanced undergraduate and graduate students, as well as engineers and practitioners. The methods illustrated here are immediately applicable to model real problems. The Book Introduces, in a simple way, complex concepts of bifurcation theory, by making use of elementary mathematics Gives a comprehensive overview of bifurcation of linear and nonlinear structures, in static and dynamic fields Contains a chapter in which many problems are solved, either analytically or numerically, and results commented
Practical Bifurcation And Stability Analysis
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Author : Rüdiger Seydel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-14
Practical Bifurcation And Stability Analysis written by Rüdiger Seydel 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 2009-12-14 with Mathematics categories.
Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
Nonlinear Stability And Bifurcation Theory
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Author : Hans Troger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Stability And Bifurcation Theory written by Hans Troger 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 2012-12-06 with Science categories.
Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.
Topics In Bifurcation Theory And Applications
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Author : Grard Iooss
language : en
Publisher: World Scientific
Release Date : 1998
Topics In Bifurcation Theory And Applications written by Grard Iooss and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Technology & Engineering categories.
This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries. The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette-Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.
Stability Bifurcation And Postcritical Behaviour Of Elastic Structures
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Author : M. Pignataro
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Stability Bifurcation And Postcritical Behaviour Of Elastic Structures written by M. Pignataro and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.
A comprehensive and systematic analysis of elastic structural stability is presented in this volume. Traditional engineering buckling concepts are discussed in the framework of the Liapunov theory of stability by giving an extensive review of the Koiter approach. The perturbation method for both nonlinear algebraic and differential equations is discussed and adopted as the main tool for postbuckling analysis. The formulation of the buckling problem for the most common engineering structures - rods and frames, plates, shells, and thin-walled beams, is performed and the critical load evaluated for problems of interest. In many cases the postbuckling analysis up to the second order is presented. The use of the Ritz-Galerkin and of the finite element methods is examined as a tool for approximate bifurcation analysis. The volume will provide an up-to-date introduction for non-specialists in elastic stability theory and methods, and is intended for graduate and post-graduate students and researchers interested in nonlinear structural analysis problems. Basic prerequisites are kept to a minimum, a familiarity with elementary algebra and calculus is all that is required of readers to make use of this book.