Periodic Solutions of Nonlinear Dynamical Systems Numerical Computat
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical
- PDF / 9,260,932 Bytes
- 177 Pages / 468 x 684 pts Page_size
- 98 Downloads / 302 Views
1483
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, ZUrich F. Takens, Groningen
1483
Eduard Reithmeier
Periodic Solutions of Nonlinear Dynamical Systems Numerical Computation, Stability, Bifurcation and Transition to Chaos
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Author Eduard Reithmeier 5134 Etcheverry Hall Department of Mechanical Engineering University of California, Berkeley Berkeley, CA 94720, USA
Cover: Leupold's draft for periodic perpetual motion. From: Jacob Leupold. Theatrum Machinarum Generale. Schauplatz des Grundes mechanischer Wissenschaften. Mathematico und Mechanico der koniglich PreuBischen und Sachsischen Societat der Wissenschaften, vol I, Leipzig, Zunkel, 1724.
Mathematics Subject Classification (1991): 34B15, 34C15, 34C25, 58FlO, 58F14, 58F21
ISBN 3-540-54512-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-54512-3 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991 Printed in Germany
Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper
Preface Watching the cyclic motion of the planets around the sun, the seasons on earth, our biological day and night rythm, the periodicity of life itself (to be born, live and die) are only a few examples showing that we are embedded in and surrounded by cyclic phenomena. In fact, periodic solutions of mathematical models of physical systems arise precisely because we live in a cyclic (or nearly so) world. In studying the extensive literature on periodic and almost periodic solutions of non-linear ODE's, I think the first question comming to mind is why there should be another text on this topic. My reasons for writing are multiple. I suppose anyone who has ever studied the theory of non-linear vibrations was surprised to discover motion readily discernible by us, the periodic motion, is so difficult to investigate analytically highly developed mathematical tools; and in most cases there is no analytical access at all. There is a large number of mathematicans and scientists who developed analytical tools for the investigation of periodic solutions of nonlinear ODE's; indeed, the field is nearly saturated. Hence, the probability is very low of making serious progress in developing further analytical methods. However, the numerical treatment of ODE's reached a very high level in the last two decades,
Data Loading...
