Geometric Mechanics
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters ar
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Waldyr Muniz Oliva
Geometric Mechanics
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Author Waldyr Muniz Oliva CAMGSD, Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa, Portugal E-mail: [email protected], [email protected]
Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 70Hxx, 70G45, 37J60 ISSN 0075-8434 ISBN 3-540-44242-1 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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 New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 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: 10891039
41/3142/du-543210 - Printed on acid-free paper
To my wife Angela for inspiration and constant support
Preface
This book was based on notes which were prepared as a guide for lectures of one semester course on Geometric Mechanics. They were written inside the level of a master course. I started some years ago teaching them at the “Instituto de Matem´atica e Estat´istica” of the “Universidade de S˜ ao Paulo”, and, more recently, at the “Instituto Superior T´ecnico” of the “Universidade T´ecnica de Lisboa”. The spectrum of participants of such a course ranges usually from young Master students to Phd students. So, it is always very difficult to decide how to organize all material to be taught. I decided that the expositions should be self contained, so some subjects that one expects to be interesting for someone, result, often, tedious for others and frequently unreachable for a few ones. In any case, for young researchers interested in differential geometry and or dynamical systems, it is basic and fundamental to see the foundations and the development of classical subjects like Newtonian and Relativistic Mechanics. I wish to thank a number of colleagues from several different Institutions as well as Master and PhD studen
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