A Smooth and Discontinuous Oscillator Theory, Methodology and Applic
This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) osci
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		    Qingjie Cao Alain Léger Marian Wiercigroch
 
 A Smooth and Discontinuous Oscillator Theory, Methodology and Applications
 
 Springer Tracts in Mechanical Engineering Board of editors Seung-Bok Choi, Inha University, Incheon, South Korea Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China Yili Fu, Harbin Institute of Technology, Harbin, P.R. China Carlos Guardiola, Universitat Politècnica de València, València, Spain Jian-Qiao Sun, University of California, Merced, USA
 
 About this Series Springer Tracts in Mechanical Engineering (STME) publishes the latest developments in Mechanical Engineering - quickly, informally and with high quality. The intent is to cover all the main branches of mechanical engineering, both theoretical and applied, including: • • • • • • • • • • • • • • • • •
 
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 Within the scopes of the series are monographs, professional books or graduate textbooks, edited volumes as well as outstanding PhD theses and books purposely devoted to support education in mechanical engineering at graduate and postgraduate levels.
 
 More information about this series at http://www.springer.com/series/11693
 
 Qingjie Cao Alain Léger Marian Wiercigroch •
 
 A Smooth and Discontinuous Oscillator Theory, Methodology and Applications
 
 123
 
 Qingjie Cao School of Astronautics Harbin Institute of Technology Harbin China
 
 Marian Wiercigroch CADR, School of Engineering, King’s College University of Aberdeen Aberdeen UK
 
 Alain Léger Laboratoire de Mécanique et d’Acoustique, CNRS Marseille Cedex 13 France
 
 ISSN 2195-9862 ISSN 2195-9870 (electronic) Springer Tracts in Mechanical Engineering ISBN 978-3-662-53092-4 ISBN 978-3-662-53094-8 (eBook) DOI 10.1007/978-3-662-53094-8 Library of Congress Control Number: 2016947202 © Springer-Verlag Berlin Heidelberg 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 an		
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