The Elements of Mechanics
The word "elements" in the title of this book does not convey the implica tion that its contents are "elementary" in the sense of "easy": it mainly means that no prerequisites are required, with the exception of some basic background in classical physics
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W. Beiglb6ck E. H. Lieb T. Regge W. Thirring Series Editors
Giovann i Gallavotti
The Elements of Mechanics With 53 Illustrations
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Springer·Science+Business Media, LLC
Giovanni Gallavotti Istituto di Matematica Universita degli Studi di Roma 00185, Rome Italy
Editors Wolf BeiglbOck Institut fUr Angewandte Mathematik Universitiit Heidelberg 1m Neuenheimer Feld 5 D-6900 Heidelberg 1 Federal Republic of Germany
Elliott H. Lieb Department of Physics Joseph Henry Laboratories Princeton University P.O. Box 708 Princeton, NJ 08540 U.S.A.
Tullio Regge Istituto de Fisica Teorica Universita di Torino C. so M. d' Azeglio, 46 10125 Torino Italy
Walter Thirring Institut fiir Theoretische Physik der Universitiit Wien Boltzmanngasse 5 A-1090 Wien Austria
Library of Congress Cataloging in Publication Data Gallavotti, Giovanni. The elements of mechanics. (Texts and monographs in physics) Includes bibliographical references and indexes. 1. Mechanics. I. Title. II. Series. QA805.G24 1983 531 83-360
This book was first printed in Italian: Meccanica Elementare. ©1980 Editore Boringhieri, Torino. © 1983 by Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 1983 Softcover reprint of the hardcover 1st edition 1983 All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Science+Business Media, LLC. Typeset by Computype, St. Paul, Minnesota. Printed and bound by R.R. Donnelley & Sons, Harrisonburg, Virginia. 9 8 7 6 5 432 1 ISBN 978-3-662-00733-4 ISBN 978-3-662-00731-0 (eBook) DOI 10.1007/978-3-662-00731-0
A Daniela per amore infinito
Preface
The word "elements" in the title of this book does not convey the implication that its contents are "elementary" in the sense of "easy": it mainly means that no prerequisites are required, with the exception of some basic background in classical physics and calculus. It also signifies "devoted to the foundations". In fact, the arguments chosen are all very classical, and the formal or technical developments of this century are absent, as well as a detailed treatment of such problems as the theory of the planetary motions and other very concrete mechanical problems. This second meaning, however, is the result of the necessity of finishing this work in a reasonable amount of time rather than an a priori choice. Therefore a detailed review of the "few" results of ergodic theory, of the "many" results of statistical mechanics, of the classical theory of fields (elasticity and waves), and of quantum mechanics are also totally absent; they could constitute the subject of two additional volumes on mechanics. This book grew out of several courses on meccanica razionaie, i.e., essentially, theoretical mechanics, which I gave at the University of Rome during the years 1975-1978. The subjects cover a wide range. Chapter 2, for example, could be used in an undergraduate course by students who have had basic training in classical physics; Chapters 3 and 4 could be used in an adv
