Mechanical Systems, Classical Models Volume II: Mechanics of Discret
This second volume of Mechanical Systems, Classical Models, deals with the dynamics of systems consisting of discrete particles as well as continuous systems. While differences between these models are highlighted, the generality of the proofs and corresp
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MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING Series Editor
Alan Jeffrey
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, in all areas of today's Physical Sciences and Engineering, is well established. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems in modern Physical Sciences and Engineering would otherwise have been impossible. The purpose of the series is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume in the series will provide a detailed introduction to a specific subject area of current importance, and then will go beyond this by reviewing recent contributions, thereby serving as a valuable reference source.
For other titles published in this series, go to www.springer.com/series/7311
Mechanical Systems, Classical Models Volume II: Mechanics of Discrete and Continuous Systems
by
Petre P. Teodorescu Faculty of Mathematics, University of Bucharest, Romania
123
Prof. Dr. Petre P. Teodorescu Str. Popa Soare 38 023984 Bucuresti 20 Romania
Translated into English, revised and extended by Petre P. Teodorescu
© 2002 EDITURA TEHNICÃ This translation of “Mechanical Systems, Classical Models” (original title: Sisteme mecanice. Modele clasice, Published by: EDITURA TEHNICÃ , Bucuresti, Romania, 1984 -2002), First Edition, is published by arrangement with EDITURA TEHNICÃ, Bucharest, RO MANIA.
ISBN: 978-1-4020-8987-9
e-ISBN: 978-1-4020-8988-6
Library of Congress Control Number: 2007943834
c 2009 Springer Science+Business Media B.V. 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. Cover Design: eStudio Calamar S.L. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
Contents
Preface 11. Dynamics of Discrete Mechanical Systems 11.1 Dynamics of Discrete Mechanical Systems with Respect to an Inertial Frame of Reference 11.1.1 Introductory Notions 11.1.2 General Theorems. Conservation Theorems 11.2 Dynamics of Discrete Mechanical Systems with Respect to a Non-inertial Frame of Reference 11.2.1 Motion of a Discrete Mechanical System with Respect to a Koenig Frame of Reference 11.2.2 Motion of a Discrete Mechanical System with Respect to an Arbitrary Non-inertial Frame of Reference
vii 1 1 1 10 50 50 58
12. Dynamics of
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