Solved Problems in Lagrangian and Hamiltonian Mechanics
The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integ
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Grenoble Sciences Grenoble Sciences pursues a triple aim: to publish works responding to a clearly defined project, with no curriculum or vogue constraints, to guarantee the selected titles’ scientific and pedagogical qualities, to propose books at an affordable price to the widest scope of readers. Each project is selected with the help of anonymous referees, followed by an average one-year interaction between the authors and a Readership Committee whose members’ names figure in the front pages of the book. Grenoble Sciences then signs a co-publishing agreement with the most adequate publisher. Contact: Tel.: (33) (0) 4 76 51 46 95 - Fax: (33) (0) 4 76 51 45 79 E-mail: [email protected] Website: http://grenoble-sciences.ujf-grenoble.fr Scientific Director of Grenoble Sciences: Jean B ORNAREL, Professor at the Joseph Fourier University, Grenoble, France Grenoble Sciences is supported by the French Ministry of Higher Education and Research and the “R´egion Rhˆone-Alpes”. The Solved Problems in Lagrangian and Hamiltonian Mechanics Reading Committee included the following members: Robert ARVIEU, Professor at the Joseph Fourier University, Grenoble, France Jacques MEYER, Professor at the Nuclear Physics Institute, Claude Bernard University, Lyon, France with the contribution of: Myriam REFFAY and Bertrand RUPH The translation of “Probl`emes corrig´es de M´ecanique et r´esum´es de cours. De Lagrange a` Hamilton”, published by Grenoble Sciences in partnership with EDP Sciences, was performed by: Bernard SILVESTRE-BRAC and Anthony John COLE, Senior researcher at the CNRS, Grenoble, France Front cover illustration: composed by Alice GIRAUD
Claude Gignoux · Bernard Silvestre-Brac
Solved Problems in Lagrangian and Hamiltonian Mechanics
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Dr. Claude Gignoux Universit´e Joseph Fourier Lab. Physique Subatomique et Cosmologie CNRS-IN2P3 53 avenue des Martyrs 38026 Grenoble CX France [email protected]
Dr. Bernard Silvestre-Brac Universit´e Joseph Fourier Lab. Physique Subatomique et Cosmologie CNRS-IN2P3 53 avenue des Martyrs 38026 Grenoble CX France [email protected]
ISBN 978-90-481-2392-6 e-ISBN 978-90-481-2393-3 DOI 10.1007/978-90-481-2393-3 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926952 c Springer Science+Business Media B.V. 2009 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
Mechanics is an old science, but it acquired its great reputation at the end of the 17th century, due to Newton’s works. A century later, Euler and, above all, Lagrange renewed it an
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