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Author: Wolfgang Hahn Publisher: Springer Science & Business Media ISBN: 3642500854 Category : Mathematics Languages : en Pages : 459
Book Description
The theory of the stability of motion has gained increasing signifi cance in the last decades as is apparent from the large number of publi cations on the subject. A considerable part of this work is concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering were the ones which first gave the decisin' impetus for the expansion and modern development of stability theory. In comparison with the many single publications, which are num bered in the thousands, the number of books on stability theory, and especially books not \\Titten in Russian, is extraordinarily small. Books which giw the student a complete introduction into the topic and which simultaneously familiarize him with the newer results of the theory and their applications to practical questions are completely lacking. I hope that the book which I hereby present will to some extent do justice to this double task. I haw endeavored to treat stability theory as a mathe matical discipline, to characterize its methods, and to prove its theorems rigorollsly and completely as mathematical theorems. Still I always strove to make reference to applications, to illustrate the arguments with examples, and to stress the interaction between theory and practice. The mathematical preparation of the reader should consist of about two to three years of university mathematics.
Author: Wolfgang Hahn Publisher: Springer Science & Business Media ISBN: 3642500854 Category : Mathematics Languages : en Pages : 459
Book Description
The theory of the stability of motion has gained increasing signifi cance in the last decades as is apparent from the large number of publi cations on the subject. A considerable part of this work is concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering were the ones which first gave the decisin' impetus for the expansion and modern development of stability theory. In comparison with the many single publications, which are num bered in the thousands, the number of books on stability theory, and especially books not \\Titten in Russian, is extraordinarily small. Books which giw the student a complete introduction into the topic and which simultaneously familiarize him with the newer results of the theory and their applications to practical questions are completely lacking. I hope that the book which I hereby present will to some extent do justice to this double task. I haw endeavored to treat stability theory as a mathe matical discipline, to characterize its methods, and to prove its theorems rigorollsly and completely as mathematical theorems. Still I always strove to make reference to applications, to illustrate the arguments with examples, and to stress the interaction between theory and practice. The mathematical preparation of the reader should consist of about two to three years of university mathematics.
Author: A M Lyapunov Publisher: CRC Press ISBN: 9780748400621 Category : Science Languages : en Pages : 284
Book Description
This book makes more widely accessible the text of Lyapunov's major memoir of the general problem of the stability of motion. Translated by A. T. Fuller (University of Cambridge), the work is now available for the first time in the English language, and marked the centenary of the Russian publication in the late 1800s. Including a biography of Lyapunov and a comprehensive bibliography of his work, this excellent volume will prove to be of fundamental interest to all those concerned with the concept of the stability of motion, boundaries of stability, and with nonlinear dynamics.
Author: Brian Straughan Publisher: Springer Science & Business Media ISBN: 0387765433 Category : Technology & Engineering Languages : en Pages : 445
Book Description
This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.
Author: D. D. Joseph Publisher: Springer Science & Business Media ISBN: 364280991X Category : Science Languages : en Pages : 295
Book Description
The study of stability aims at understanding the abrupt changes which are observed in fluid motions as the external parameters are varied. It is a demanding study, far from full grown"whose most interesting conclusions are recent. I have written a detailed account of those parts of the recent theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.
Author: David R. Merkin Publisher: Springer Science & Business Media ISBN: 1461240468 Category : Mathematics Languages : en Pages : 334
Book Description
Many books on stability theory of motion have been published in various lan guages, including English. Most of these are comprehensive monographs, with each one devoted to a separate complicated issue of the theory. Generally, the examples included in such books are very interesting from the point of view of mathematics, without necessarily having much practical value. Usually, they are written using complicated mathematical language, so that except in rare cases, their content becomes incomprehensible to engineers, researchers, students, and sometimes even to professors at technical universities. The present book deals only with those issues of stability of motion that most often are encountered in the solution of scientific and technical problems. This allows the author to explain the theory in a simple but rigorous manner without going into minute details that would be of interest only to specialists. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations. About one fourth of the examples are from various areas of science and technology. Moreover, some of the examples and the problems have an independent value in that they could be applicable to the design of various mechanisms and devices. The present translation is based on the third Russian edition of 1987.
Author: Clive L. Dym Publisher: Courier Dover Publications ISBN: 9780486425412 Category : Structural stability Languages : en Pages : 0
Book Description
An integration of modern work in structural stability theory, this volume focuses on the Koiter postbuckling analyses, with mathematical notions of stability of motion. In relation to discrete and continuous systems, it bases the minimum energy principles for static stability upon the dynamic concepts of stability of motion. It further develops the asymptotic buckling and postbuckling analyses from potential energy considerations, with applications to columns, plates, and arches.
Author: N.N. Moiseyev Publisher: Springer Science & Business Media ISBN: 364286452X Category : Technology & Engineering Languages : en Pages : 358
Book Description
The dynamics of bodies containing fluids is a subject of long-standing im portance in many technical applications. The stability of motion of such bodies, in particular, has been the subject of study by Soviet engineers and applied mathematicians who have brought their fuH powers of analysis to bear on the problem, and have succeeded in developing a very weH-founded body of theory. It is difficult to find a more striking example anywhere of the application of the classical methods of analytical mechanics, together with more modern concepts of stability analysis, in such a comprehensive and elegent form as that presented by Profs. Moiseyev and Rumyantsev. Therefore, it is highly significant that this recent monograph has been trans lated and made available to the English-speaking community. H. NORMAN ABRAMSON San Antonio July, 1967 v Foreword During the last 15-20 years, problems of dynamics of rigid bodies with fluid-filled cavities have increasingly attracted the attention of scientists.
Author: Lawrence Davis Publisher: ISBN: Category : Physics Languages : en Pages : 590
Book Description
"Body Physics was designed to meet the objectives of a one-term high school or freshman level course in physical science, typically designed to provide non-science majors and undeclared students with exposure to the most basic principles in physics while fulfilling a science-with-lab core requirement. The content level is aimed at students taking their first college science course, whether or not they are planning to major in science. However, with minor supplementation by other resources, such as OpenStax College Physics, this textbook could easily be used as the primary resource in 200-level introductory courses. Chapters that may be more appropriate for physics courses than for general science courses are noted with an asterisk symbol (*). Of course this textbook could be used to supplement other primary resources in any physics course covering mechanics and thermodynamics"--Textbook Web page.
Author: Wolfgang Hahn
Author: Wolfgang Hahn
Author: A M Lyapunov
Author: Brian Straughan
Author: D. D. Joseph
Author: Ioėlʹ Gilʹevich Malkin
Author: David R. Merkin
Author: Clive L. Dym
Author: James Clerk Maxwell
Author: N.N. Moiseyev
Author: Lawrence Davis