Cell-to-Cell Mapping A Method of Global Analysis for Nonlinear Syste
For many years, I have been interested in global analysis of nonlinear systems. The original interest stemmed from the study of snap-through stability and jump phenomena in structures. For systems of this kind, where there exist multiple stable equilibriu
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c.s. Hsu
Cell-to-Cell Mapping A Method of Global Analysis for Nonlinear Systems With 125 Illustrations
Springer Science+Business Media, LLC
C. S. Hsu Department of Mechanical Engineering University of California Berkeley, CA 94720 U.S.A.
Editors F.John Courant Institute of Mathematical Sciences New York University New York, NY 10012 U.S.A.
J. E. Marsden Department of Mathematics University of California Berkeley, CA 94720 U.S.A.
L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 U.S.A.
AMS Classification: 58FXX Library of Congress Cataloging-in-Publication Data Hsu, e.S. (Chieh Su) Cell-to-cell mapping. (Applied mathematical sciences; v. 64) Bibliography: p. Includes index. 1. Global analysis (Mathematics) 2. Mappings (Mathematics) 3. Nonlinear theories. I. Title. II. Series: Applied mathematical sciences (Springer-Verlag New York Inc.); v. 64. QA1.A647 vol. 64 [QA614] 510 s [514'.74] 87-12776
© 1987 by Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 1987 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher, Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Typeset by Asco Trade Typesetting Ltd., Hong Kong.
987654 32 1 ISBN 978-1-4419-3083-5
ISBN 978-1-4757-3892-6 (eBook)
DOI 10.1007/978-1-4757-3892-6
Preface
For many years, I have been interested in global analysis of nonlinear systems. The original interest stemmed from the study of snap-through stability and jump phenomena in structures. For systems of this kind, where there exist multiple stable equilibrium states or periodic motions, it is important to examine the domains of attraction of these responses in the state space. It was through work in this direction that the cell-to-cell mapping methods were introduced. These methods have received considerable development in the last few years, and have also been applied to some concrete problems. The results look very encouraging and promising. However, up to now, the effort of developing these methods has been by a very small number of people. There was, therefore, a suggestion that the published material, scattered now in various journal articles, could perhaps be pulled together into book form, thus making it more readily available to the general audience in the field of nonlinear oscillations and nonlinear dynamical systems. Conceivably, this might facilitate getting more people interested in worki
