What We See: The Velocities
The actual linear and angular velocities of the disks are easily experimented. Virtual velocities are velocities we may think of. Some virtual velocities cannot be actual velocities, for instance in case of impenetrability of the disks. The set of the vir
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Michel Frémond
Virtual Work and Shape Change in Solid Mechanics
Springer Series in Solid and Structural Mechanics Volume 7
Series editors Michel Frémond, Roma, Italy Franco Maceri, Roma, Italy
More information about this series at http://www.springer.com/series/10616
Michel Frémond
Virtual Work and Shape Change in Solid Mechanics
123
Michel Frémond Department of Civil Engineering and Computer Science University of Rome “Tor Vergata” Rome Italy
ISSN 2195-3511 ISSN 2195-352X (electronic) Springer Series in Solid and Structural Mechanics ISBN 978-3-319-40681-7 ISBN 978-3-319-40682-4 (eBook) DOI 10.1007/978-3-319-40682-4 Library of Congress Control Number: 2016945146 © 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
Mechanics is the science of motion: It predicts the motion we see with our eyes. Motion is involved in most scientific activities and in most engineering work. The importance of this topic has resulted in an axiomatization of mechanics and to have mathematics together with experiments to be tools widely used. There is a large variety of motions we see with our eyes: the motion of the floor of a room, the motion of the grains of a sand pile, the motion of a debris flow, the motion of galaxies, etc. The elements which are used by engineers and scientists to describe them may seem different. But these theories have in common the concepts to describe the motion. The equations of motion are either simple or very sophisticated. The sophistication may result from the need to define and quantify precisely together the shape of the system which is considered and the evolution of this shape, i.e., the shape change or the deformation of the system, and the velocity of deformation. A tool to introduce the mechanical effects of the evolution of the shape of
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