Linear Systems and Configuration-Space Decoupling Techniques
The equation of motion of linear systems is one of the most commonly used equations in science and engineering. It has long been recognized that coordinate coupling in linear systems is a considerable barrier to analysis and design. In this context, it is
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ances in the Theory of System Decoupling
Advances in the Theory of System Decoupling
Rubens Gonçalves Salsa Junior • Fai Ma
Advances in the Theory of System Decoupling
Rubens Gonçalves Salsa Junior Aeronautics Institute of Technology S˜ao José dos Campos, S˜ao Paulo, Brazil
Fai Ma University of California at Berkeley Berkeley, CA, USA
ISBN 978-3-030-60845-3 ISBN 978-3-030-60846-0 (eBook) https://doi.org/10.1007/978-3-030-60846-0 © Springer Nature Switzerland AG 2021 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, 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
To my wife, Luiza, and my daughter, Capitu (RGSJ) To Hsing-Ho, Andrew, and Catherine (FM)
Preface
Linear dynamical systems are characterized by a second-order ordinary differential equation with three real coefficient matrices. The classical decoupling problem in vibrations amounts to converting such systems into a form whose coefficients are diagonal. Coordinate decoupling plays a central role not only in vibrations but also in such diverse areas as numerical linear algebra, quantum mechanics, and mathematical economics. In the past 10 years, the method of modal analysis was generalized to decouple practically all linear systems, including those with nonsymmetric coefficient matrices. The extension, called phase synchronization, is based upon compensations for time drifts caused by viscous damping and external excitation. The resulting invertible decoupling transformation is real, non-linear, and time varying. While phase synchronization could be immensely useful, information on this topic is scattered in various journal articles, requiring the interested readers to resort to multiple references to fully understand the methodology. To make things more complicated, diff
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