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Introduction to Mechanics of Particles and Systems

Introduction to Mechanics of Particles and Systems

Costas J. Papachristou

Introduction to Mechanics of Particles and Systems

123

Costas J. Papachristou Department of Physical Sciences Hellenic Naval Academy Piraeus, Greece

ISBN 978-3-030-54270-2 ISBN 978-3-030-54271-9 https://doi.org/10.1007/978-3-030-54271-9

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Newtonian Mechanics is, traditionally, the first stage of “initiation” of a college student into Physics. It is perhaps the only truly autonomous subject area of Physics, in the sense that it can be taught as a self-contained entity without the need for support from other areas of physical science. This textbook is based on lecture notes (originally in Greek) used by this author in his two-semester course of introductory Mechanics, taught at the Hellenic Naval Academy (the Naval Academy of Greece). It is evident that no serious approach to Mechanics (at least at the university level) is possible without the support of higher Mathematics. Indeed, the central law of Mechanics, Newton’s Second Law, carries a rich mathematical structure being both a vector equation and a differential equation. An effort is thus made to familiarize the student from the outset with the use of some basic mathematical tools, such as vectors, differential operators, and differential equations. To this end, the first chapter contains the elements of vector analysis that will be needed in the sequel, while the Mathematical Supplement constitutes a brief introd