Chaotic Motion in Mechanical and Engineering Systems
We start with the definition of a chaotic process by relating the time evolution of a deterministic mechanical system which is governed by Newton’s laws to the stochastic sequence of heads and eagles following from the process of repeatedly tossing a fair
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ENGINEERING APPLICATIONS OF DYNAMICS OF CHAOS
EDITED BY
W. SZEMPLINSKA-STUPNICKA IPPT-PAN, WARSAW H.TROGER
TECHNICAL UNIVERSITY VIENNA
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche.
This volume contains 161 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1991 by Springer-Verlag Wien Originally published by Springer Verlag Wieu-New York in 1991
pp. 279 - 309 and pp. 311 - 325: copyright not transferred.
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their origmal forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-82328-6 DOI 10.1007/978-3-7091-2610-3
ISBN 978-3-7091-2610-3 (eBook)
PREFACE
In the last two decades the new science known as "chaos" has given up deep insights into previously intractable inherently nonlinear, natural phenomena and impacted upon traditional subjects ranging trhough all the physical and biological sciences, many of the social sciences, mathematics and engineering. For an engineer it is a revolutionary idea that systems for which the completely deterministic laws of motion are known can exhibit an enormously complex behaviour, often appearing as if they were evolving under random forces rather than deterministic laws. This computationally and experimentally verified fact has the important consequence that the system behaviour is unpredictable for long times. The new science dealing with such problems requires new methods of analysis. It is of essential imponance to look at chaotic dynamics from the engineering point of view, to see how to detect and quantify chaos with new measures such as fractal dimensions and Lyapunov exponents, how to cope with the sophisticated theoretical and complex computational analysis and how to predict or avoid onset of chaos in mechanical systems. This is an overall aim of this book. The lectures presented here introduce basic concepts of nonlinear dynamics, discuss various routes to chaos and criteria for predicting transition from regular to chaotic motion, develope qualitative topological methods, apply the approximate analytical methods and computational procedures, and finally give a wide review of chaotic problems in engineering oriented mechanical
systems. Moreover also the impact of the concepts of chaos related to the problem of transition to turbulence in fluid mechanics is addressed. The material is selfcontained and does require an advanced knowledge of nonlinear analysis. Of course, some familiarity with classical dynamics, nonlinear oscillations, stability of motion and the theory of ordinary differential equations, as it is p
