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Theory Of Stability Of Motion
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Book Synopsis Stability of Motion by : Wolfgang Hahn
Download or read book Stability of Motion written by Wolfgang Hahn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Stability of Motion by : Ioėlʹ Gilʹevich Malkin
Download or read book Theory of Stability of Motion written by Ioėlʹ Gilʹevich Malkin and published by . This book was released on 1959 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Theory of Stability by : David R. Merkin
Download or read book Introduction to the Theory of Stability written by David R. Merkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis General Problem of the Stability Of Motion by : A M Lyapunov
Download or read book General Problem of the Stability Of Motion written by A M Lyapunov and published by CRC Press. This book was released on 1992-08-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Theory of Stability by : David R. Merkin
Download or read book Introduction to the Theory of Stability written by David R. Merkin and published by Springer. This book was released on 2011-09-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability Theory and Its Applications to Structural Mechanics by : Clive L. Dym
Download or read book Stability Theory and Its Applications to Structural Mechanics written by Clive L. Dym and published by Courier Dover Publications. This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Stability Theory by : Anand Pillay
Download or read book An Introduction to Stability Theory written by Anand Pillay and published by Courier Corporation. This book was released on 2013-05-17 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory treatment covers the basic concepts and machinery of stability theory. Lemmas, corollaries, proofs, and notes assist readers in working through and understanding the material and applications. Full of examples, theorems, propositions, and problems, it is suitable for graduate students in logic and mathematics, professional mathematicians, and computer scientists. Chapter 1 introduces the notions of definable type, heir, and coheir. A discussion of stability and order follows, along with definitions of forking that follow the approach of Lascar and Poizat, plus a consideration of forking and the definability of types. Subsequent chapters examine superstability, dividing and ranks, the relation between types and sets of indiscernibles, and further properties of stable theories. The text concludes with proofs of the theorems of Morley and Baldwin-Lachlan and an extension of dimension theory that incorporates orthogonality of types in addition to regular types.
Book Synopsis Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) by : Junji Kato
Download or read book Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) written by Junji Kato and published by CRC Press. This book was released on 1996-02-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed.
Book Synopsis Theory of Stability of Motion by : I. G. Malkin
Download or read book Theory of Stability of Motion written by I. G. Malkin and published by . This book was released on 1900 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability Theory for Dynamic Equations on Time Scales by : Anatoly A. Martynyuk
Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability Theory of Differential Equations by : Richard Bellman
Download or read book Stability Theory of Differential Equations written by Richard Bellman and published by Courier Corporation. This book was released on 2013-02-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
Book Synopsis Introduction to the Technical Theory of Stability of Motion by : Konstantin Andreevich Karacharov
Download or read book Introduction to the Technical Theory of Stability of Motion written by Konstantin Andreevich Karacharov and published by . This book was released on 1965 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Criteria of stability are established with the help of the differential method both with and without using values of roots of characteristic equation.
Book Synopsis Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) by : Junji Kato
Download or read book Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations) written by Junji Kato and published by Routledge. This book was released on 2019-09-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
Book Synopsis Stability and Wave Motion in Porous Media by : Brian Straughan
Download or read book Stability and Wave Motion in Porous Media written by Brian Straughan and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Certain Problems in the Theory of Stability of Motion in the Whole by : V. A. Pliss
Download or read book Certain Problems in the Theory of Stability of Motion in the Whole written by V. A. Pliss and published by . This book was released on 1958 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability Analysis of Nonlinear Systems by : Vangipuram Lakshmikantham
Download or read book Stability Analysis of Nonlinear Systems written by Vangipuram Lakshmikantham and published by Birkhäuser. This book was released on 2015-12-29 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stable and Random Motions in Dynamical Systems by : Jurgen Moser
Download or read book Stable and Random Motions in Dynamical Systems written by Jurgen Moser and published by Princeton University Press. This book was released on 2016-03-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
