Classical Mechanics Hamiltonian and Lagrangian Formalism
The revised edition of this advanced text provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It revi
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Classical Mechanics Hamiltonian and Lagrangian Formalism Second Edition
Classical Mechanics
Alexei Deriglazov
Classical Mechanics Hamiltonian and Lagrangian Formalism
Second Edition
123
Alexei Deriglazov Universidade Federal de Juiz de Fora Dept. of Mathematics Juiz de Fora Minas Gerais Brazil Laboratory of Mathematical Physics Tomsk Polytechnic University Tomsk Russian Federation
ISBN 978-3-319-44146-7 DOI 10.1007/978-3-319-44147-4
ISBN 978-3-319-44147-4 (eBook)
Library of Congress Control Number: 2016955096 1st edition: © Springer-Verlag Berlin Heidelberg 2010 2nd edition: © Springer International Publishing Switzerland 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface to the Second Edition
In the revised and enlarged edition I corrected numerous errors and typos found in the first edition. In the Chaps. 1, 2, 7 and 8 I have made, in the interests of clarity, a large number of small changes. Some sections, which even I myself was not able to understand 5 years after they were written, were rewritten again Several new sections with applications of formalism were added: 1.7.7, 6.9, 8.7.1 and 8.7.2. The main alteration in this edition consists of the incorporation of a new chapter devoted to the description of a relativistic spinning particle in external fields. It can be considered as a non-trivial application of the formalism of constrained systems described in Chap. 8. A review of the achievements in this fascinating area before 1968 can be found in the book of Corben [58]. Contrary to Corben, who discussed the problem on the level of equations of motion, my emphasis has been placed on the Lagrangian and Hamiltonian variational formulations for the description of rotational degrees of freedom and their influence on the trajectory of a spinning body. I present the so-called vector model of spin a
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