Homogenization in Time of Singularly Perturbed Mechanical Systems
This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in tim
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1687
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1687
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Folkmar Bornemann
Homogenization in Time of Singularly Perturbed Mechanical Systems
Springer
Author Folkmar Bornemann Lehrstuhl fur Numerische Mathematik und WissenschaftIiches Rechnen Technische Universitat Munchen D-80290 Munchen, Germany e-mail: [email protected] Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme Bornemann, Folkmar A.: Homogenization in time of singularly perturbed mechanical systems / Folkmar Bornemann. - Berlin; Heidelberg; New York; Barcelona; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1998 (Lecture notes in mathematics; 1687) ISBN 3-540-64447-4
Mathematics Subject Classification (1991): 34Cxx, 34Exx, 35Qxx, 70Kxx, 81Ql5 ISSN 0075-8434 ISBN 3-540-64447-4 Springer-Verlag Berlin Heidelberg New York 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 any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer- Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10649830 46/3143-543210 - Printed on acid-free paper
in memoriam Alfred Neumann (1902-1982)
Preface Although the title might suggest it differently, this monograph is about a certain method for establishing singular limits rather than about a clearcut class of singularly perturbed problems. Using this particular method I will address in a unified way such diverse topics as the micro-scale justification of the Lagrange-d'Alembert principle and the limit behavior of strong constraining potentials in classical mechanics on the one hand, and the adiabatic theorem of quantum mechanics on the other hand. I am confident that all these topics are cases of a larger class of singularly perturbed mechanical systems that show up rapid micro-scale fluctuations, allowing for the application of the method to be presented. Reflecting this, I have tried to apply the method to each case as directly as possible and refrained from studying an abstract super-class of problems which would leave the cases as mere examples. I believe th
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