Ebook: Introduction to the Theory of Stability

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.

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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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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.
Content:
Front Matter....Pages i-xx
Introduction....Pages 1-4
Formulation of the Problem....Pages 5-23
The Direct Liapunov Method. Autonomous Systems....Pages 25-74
Stability of Equilibrium States and Stationary Motions of Conservative Systems....Pages 75-101
Stability in First Approximation....Pages 103-132
Stability of Linear Autonomous Systems....Pages 133-158
The Effect of Force Type on Stability of Motion....Pages 159-219
The Stability of Nonautonomous Systems....Pages 221-264
Application of the Direct Method of Liapunov to the Investigation of Automatic Control Systems....Pages 265-287
The Frequency Method of Stability Analysis....Pages 289-306
Back Matter....Pages 307-319

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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.
Content:
Front Matter....Pages i-xx
Introduction....Pages 1-4
Formulation of the Problem....Pages 5-23
The Direct Liapunov Method. Autonomous Systems....Pages 25-74
Stability of Equilibrium States and Stationary Motions of Conservative Systems....Pages 75-101
Stability in First Approximation....Pages 103-132
Stability of Linear Autonomous Systems....Pages 133-158
The Effect of Force Type on Stability of Motion....Pages 159-219
The Stability of Nonautonomous Systems....Pages 221-264
Application of the Direct Method of Liapunov to the Investigation of Automatic Control Systems....Pages 265-287
The Frequency Method of Stability Analysis....Pages 289-306
Back Matter....Pages 307-319
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