Sinossi
The present book deals with the issues of stability of Motion which most often are encountered in the analysis of scientific and technical problems. There are many comprehensive monographs on the theory of stability of motion, with each one devoted to a separate complicated issue of the theory. The main advantage of this book, however, is its simple yet simultaneous rigorous presentation of the concepts of the theory, which often are presented in the context of applied problems with detailed examples demonstrating effective methods of solving practical problems.
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Contenuti
1 Formulation of the Problem.- 1.1 Basic Definitions.- 1.2 Equations of Perturbed Motion.- 1.3 Examples of Derivation of Equations of a Perturbed Motion.- 1.4 Problems.- 2 The Direct Liapunov Method. Autonomous Systems.- 2.1 Liapunov Functions. Sylvester’s Criterion.- 2.2 Liapunov’s Theorem of Motion Stability.- 2.3 Theorems of Asymptotic Stability.- 2.4 Motion Instability Theorems.- 2.5 Methods of Obtaining Liapunov Functions.- 2.6 Application of Liapunov’s Theorem.- 2.7 Application of Stability Theorems.- 2.8 Problems.- 3 Stability of Equilibrium States and Stationary Motions of Conservative Systems.- 3.1 Lagrange’s Theorem.- 3.2 Invertibility of Lagrange’s Theorem.- 3.3 Cyclic Coordinates. The Routh Transform.- 3.4 Stationary Motion and Its Stability Conditions.- 3.5 Examples.- 3.6 Problems.- 4 Stability in First Approximation.- 4.1 Formulation of the Problem.- 4.2 Preliminary Remarks.- 4.3 Main Theorems of Stability in First Approximation.- 4.4 Hurwitz’s Criterion.- 4.5 Examples.- 4.6 Problems.- 5 Stability of Linear Autonomous Systems.- 5.1 Introduction.- 5.2 Matrices and Basic Matrix Operations.- 5.3 Elementary Divisors.- 5.4 Autonomous Linear Systems.- 5.5 Problems.- 6 The Effect of Force Type on Stability of Motion.- 6.1 Introduction.- 6.2 Classification of Forces.- 6.3 Formulation of the Problem.- 6.4 The Stability Coefficients.- 6.5 The Effect of Gyroscopic and Dissipative Forces.- 6.6 Application of the Thomson-Tait-Chetaev Theorems.- 6.7 Stability Under Gyroscopic and Dissipative Forces.- 6.8 The Effect of Nonconservative Positional Forces.- 6.9 Stability in Systems with Nonconservative Forces.- 6.10 Problems.- 7 The Stability of Nonautonomous Systems.- 7.1 Liapunov Functions and Sylvester Criterion.- 7.2 The Main Theorems of the Direct Method.- 7.3 Examples of Constructing Liapunov Functions.- 7.4 System with Nonlinear Stiffness.- 7.5 Systems with Periodic Coefficients.- 7.6 Stability of Solutions of Mathieu-Hill Equations.- 7.7 Examples of Stability Analysis.- 7.8 Problems.- 8 Application of the Direct Method of Liapunov to the Investigation of Automatic Control Systems.- 8.1 Introduction.- 8.2 Differential Equations of Perturbed Motion of Automatic Control Systems.- 8.3 Canonical Equations of Perturbed Motion of Control Systems.- 8.4 Constructing Liapunov Functions.- 8.5 Conditions of Absolute Stability.- 9 The Frequency Method of Stability Analysis.- 9.1 Introduction.- 9.2 Transfer Functions and Frequency Characteristics.- 9.3 The Nyquist Stability Criterion for a Linear System.- 9.4 Stability of Continuously Nonlinear Systems.- 9.5 Examples.- 9.6 Problems.- References.
Product Description
Book by Merkin David R
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Introduction to the theory of stability. With 94 illustrations. Translated and edited by Fred F. Afagh and Andrei L. Smirnov / Texts in applied mathematics ; volume 24
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New York ; Berlin ; Singspore ; Tokyo ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara : Springer, 1997
ISBN 10: 0387947612
ISBN 13: 9780387947617
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 348 pp. Englisch. Codice articolo 9780387947617
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Springer New York, Springer US Nov 1996, 1996
ISBN 10: 0387947612
ISBN 13: 9780387947617
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Buch. Condizione: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 348 pp. Englisch. Codice articolo 9780387947617
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Buch. Condizione: Neu. Introduction to the Theory of Stability | David R. Merkin | Buch | xx | Englisch | 1996 | Springer | EAN 9780387947617 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Codice articolo 102203860
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