Clifford Algebras Geometric Modelling and Chain Geometries with Appl
After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of
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Daniel Klawitter
Clifford Algebras Geometric Modelling and Chain Geometries with Application in Kinematics Foreword by Prof. Dr. Gunter Weiss
Dr. Daniel Klawitter Dresden, Germany
Dissertation TU Dresden, 2014
ISBN 978-3-658-07617-7 DOI 10.1007/978-3-658-07618-4
ISBN 978-3-658-07618-4 (eBook)
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. Library of Congress Control Number: 2014953940 Springer Spektrum © Springer Fachmedien Wiesbaden 2015 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Spektrum is a brand of Springer DE. Springer DE is part of Springer Science+Business Media. www.springer-Spektrum.de
To my parents, Manuela and Burghard
Foreword What is the right mathematical model to a real phenomenon of our world? Do there exist criteria whether a model can be called elegant as well as practically efficient? These questions will surely be answered differently by e.g. a pure mathematician on the one hand and an engineer on the other. But both will have to start with abstracting real world phenomena to objects of a more or less platonic world. In this idealized world one constructs the ” structured geometric image ” of real world processes and objects in consideration. Thus, on the way to const
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