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Stability of Motion

  • Book
  • © 1967

Overview

Authors:
  1. Wolfgang Hahn

    1. Technische Hochschule Graz, Graz, Austria

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 138)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Generalities

    • Wolfgang Hahn
    Pages 1-8

  3. Linear Functional Equations with Constant Coefficients

    • Wolfgang Hahn
    Pages 9-55

  4. The Equilibrium of Autonomous Differential Equations

    • Wolfgang Hahn
    Pages 56-92

  5. The Direct Method of Liapunov

    • Wolfgang Hahn
    Pages 93-165

  6. The Direct Method for General Motions

    • Wolfgang Hahn
    Pages 166-224

  7. The Converse of the Stability Theorems

    • Wolfgang Hahn
    Pages 225-256

  8. Stability Properties of Ordinary Differential Equations

    • Wolfgang Hahn
    Pages 257-284

  9. Linear Differential Equations

    • Wolfgang Hahn
    Pages 285-329

  10. The Liapunov Expansion Theorem

    • Wolfgang Hahn
    Pages 330-341

  11. The Critical Cases for Differential Equations

    • Wolfgang Hahn
    Pages 342-352

  12. Periodic and Almost Periodic Motions

    • Wolfgang Hahn
    Pages 353-431

  13. Back Matter

    Pages 432-448
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Keywords

About this book

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.

Authors and Affiliations

  • Technische Hochschule Graz, Graz, Austria

    Wolfgang Hahn

Bibliographic Information

  • Book Title: Stability of Motion

  • Authors: Wolfgang Hahn

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-50085-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1967

  • Softcover ISBN: 978-3-642-50087-9Published: 18 May 2012

  • eBook ISBN: 978-3-642-50085-5Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 448

  • Number of Illustrations: 35 b/w illustrations

  • Topics: Mathematics, general

  • Industry Sectors: Engineering, IT & Software

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