Introduction To Lagrangian Dynamics
This volume provides a short summary of the essentials of Lagrangian dynamics for practicing engineers and students of physics and engineering. It examines a range of phenomena and techniques in a style that is compact and succinct, while remaining compre
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Introduction To Lagrangian Dynamics
Introduction To Lagrangian Dynamics
Aron Wolf Pila
Introduction To Lagrangian Dynamics
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Aron Wolf Pila 10 Hatechiyah Street, apt. 2 Kfar Saba, Israel
ISBN 978-3-030-22377-9 ISBN 978-3-030-22378-6 (eBook) https://doi.org/10.1007/978-3-030-22378-6 © Springer Nature Switzerland AG 2020 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. 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
This volume was intended as a short summary of the essentials of Lagrangian dynamics for undergraduate students of physics and engineering. A number of topics have been included in order to make the presentation compact, succinct, as well as comprehensive. The topics include: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k)
A Review of Classical Mechanics Holonomic and Non-holonomic Systems Virtual Work The Principle of D’Alembert for Dynamical Systems The Mathematics of Conservative Forces The Extended Hamilton’s Principle Lagrange’s Equations and Lagrangian Dynamics A Systematic Procedure for Generalized Forces Quasi-coordinates and Quasi-velocities Lagrangian Dynamics with Quasi-coordinates Lagrangian Dynamics with Quasi-coordinates-Prof. Ranjan Vepa’s Approach
An ample number of examples have been included which demonstrate the techniques involved.
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Dedication
This volume is dedicated to my wife, Leah, for the patience, understanding, and love she has shown me from the day we first met. She’s been an inspiration and guiding light throughout my life and, my working career and into our retirement years.
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Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introductory Remarks . . . . . . . .
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