Stability Theory


Stability Theory
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Stability Theory


Stability Theory
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Author : Horst Leipholz
language : en
Publisher: Springer
Release Date : 1987-03

Stability Theory written by Horst Leipholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03 with Science categories.


There have been great advances in theory of stability in recent decades due to the requirements of control theory and flight mechanics, for example. We need only mention the theory of A. M. Lyapunov. A number of specialists have given a very mathematical and abstract description of the Lyapunov stability theory which resulted in a 'stability theory of motion' applicable to the kinetics of rigid bodies and systems. The stability theory of elastomechanics was developed independently. However, there have been a number of important developments in recent years, also with respect to this theory, dealing with the following problems: The concept of the 'follower forces', non-conservative loads, respectively, has been introduced in aeroelasticity. A number of prob­ lems in elastic kinetics that involve pulsating loads or periodically varying parameters has led to new stability questions. So-called 'kinetic' methods have become necessary in elastomechnics in order to determine the stability bound­ aries. An evaluation of the stability criteria of elastostatics, which have been assumed to be generally valid, has shown that they can only be applied to a limited number of problems under special assumptions. The transition from stability to instability is a kinetic process in elastomechanics. Therefore, the most general and most certain method of determining stability is the kinetic stability criterion even if in special cases the classical stability criteria of elastostatics may remain valid. This will be discussed in detail in Section 2. 3.



Stability Theory Of Dynamical Systems


Stability Theory Of Dynamical Systems
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Author : N.P. Bhatia
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-10

Stability Theory Of Dynamical Systems written by N.P. Bhatia 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 2002-01-10 with Science categories.


Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."



Ordinary Differential Equations And Stability Theory


Ordinary Differential Equations And Stability Theory
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Author : David A. Sanchez
language : en
Publisher: Courier Dover Publications
Release Date : 2019-09-18

Ordinary Differential Equations And Stability Theory written by David A. Sanchez and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Mathematics categories.


This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.



Stability Theory Of Differential Equations


Stability Theory Of Differential Equations
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Author : Richard Bellman
language : en
Publisher: Courier Corporation
Release Date : 2013-02-20

Stability Theory Of Differential Equations written by Richard Bellman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.


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.



An Introduction To Stability Theory


An Introduction To Stability Theory
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Author : Anand Pillay
language : en
Publisher: Courier Corporation
Release Date : 2013-05-17

An Introduction To Stability Theory written by Anand Pillay and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-17 with Mathematics categories.


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.



Dynamical Systems Stability Theory And Applications


Dynamical Systems Stability Theory And Applications
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Author : Nam P. Bhatia
language : en
Publisher: Springer
Release Date : 2006-11-14

Dynamical Systems Stability Theory And Applications written by Nam P. Bhatia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.




Fundamentals Of Stability Theory


Fundamentals Of Stability Theory
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Author : John T. Baldwin
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02

Fundamentals Of Stability Theory written by John T. Baldwin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.


This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.



Stability Theory And The Existence Of Periodic Solutions And Almost Periodic Solutions


Stability Theory And The Existence Of Periodic Solutions And Almost Periodic Solutions
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Author : T. Yoshizawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stability Theory And The Existence Of Periodic Solutions And Almost Periodic Solutions written by T. Yoshizawa 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.


Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost periodic solutions. The author hopes that these notes will also serve as an introduction to stability theory. These notes contain stability theory by Liapunov's second method and somewhat extended discussion of stability properties in almost periodic systems, and the existence of a periodic solution in a periodic system is discussed in connection with the boundedness of solutions, and the existence of an almost periodic solution in an almost periodic system is considered in con nection with some stability property of a bounded solution. In the theory of almost periodic systems, one has to consider almost periodic functions depending on parameters, but most of text books on almost periodic functions do not contain this case. Therefore, as mathemati cal preliminaries, the first chapter is intended to provide a guide for some properties of almost periodic functions with parameters as well as for properties of asymptotically almost periodic functions. These notes originate from a seminar on stability theory given by the author at the Mathematics Department of Michigan State Univer sity during the academic year 1972-1973. The author is very grateful to Professor Pui-Kei Wong and members of the Department for their warm hospitality and many helpful conversations. The author wishes to thank Mrs.



Advances In Stability Theory At The End Of The 20th Century


Advances In Stability Theory At The End Of The 20th Century
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Author : A.A. Martynyuk
language : en
Publisher: CRC Press
Release Date : 2002-10-03

Advances In Stability Theory At The End Of The 20th Century written by A.A. Martynyuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-03 with Mathematics categories.


This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first



Introduction To The Theory Of Stability


Introduction To The Theory Of Stability
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Author : Evgeniĭ Alekseevich Barbashin
language : en
Publisher:
Release Date : 1970

Introduction To The Theory Of Stability written by Evgeniĭ Alekseevich Barbashin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Differential equations categories.