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: 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: 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: 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: Anatoly A. Martynyuk Publisher: Birkhäuser ISBN: 3319422138 Category : Mathematics Languages : en Pages : 233
Book Description
This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.
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: Teodor M. Atanackovic Publisher: World Scientific ISBN: 9810230540 Category : Technology & Engineering Languages : en Pages : 441
Book Description
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Author: Vangipuram Lakshmikantham Publisher: Birkhäuser ISBN: 3319272004 Category : Mathematics Languages : en Pages : 339
Book Description
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
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: Jurgen Moser Publisher: Princeton University Press ISBN: 1400882699 Category : Science Languages : en Pages : 216
Book Description
For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.
Author: Wolfgang Hahn
Author: David R. Merkin
Author: A M Lyapunov
Author: Clive L. Dym
Author: Anatoly A. Martynyuk
Author: Brian Straughan
Author: Teodor M. Atanackovic
Author: Vangipuram Lakshmikantham
Author: D. D. Joseph
Author: Jurgen Moser