Geometric Algebra with Applications in Engineering
The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and mor
- PDF / 32,916,837 Bytes
- 389 Pages / 452.96 x 683.15 pts Page_size
- 92 Downloads / 305 Views
Christian Perwass
Geometric Algebra with Applications in Engineering
Geometry and Computing Series Editors Herbert Edelsbrunner Leif Kobbelt Konrad Polthier
Editorial Advisory Board Jean-Daniel Boissonnat Gunnar Carlsson Bernard Chazelle Xiao-Shan Gao Craig Gotsman Leo Guibas Myung-Soo Kim Takao Nishizeki Helmut Pottmann Roberto Scopigno Hans-Peter Seidel Steve Smale Peter Schr¨oder Dietrich Stoyan
Christian Perwass
Geometric Algebra with Applications in Engineering With 62 Figures
123
Dr. habil. Christian Bernd Ulrich Perwaß Department of Computer Science Christian-Albrechts-Universität zu Kiel Germany [email protected]
ISBN 978-3-540-89067-6
e-ISBN 978-3-540-89068-3
Springer Series in Geometry and Computing Library of Congress Control Number: 2008939438 ACM Computing Classification (1998): F.2.2, l.3.5, l.4, G.1.3, l.1.2, G.4, l.2.9 Mathematics Subjects Classification (2000): 14-01, 51-01, 65D, 68U, 53A c 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: deblik, Berlin Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
To Susanne
Preface
Geometry is a pervasive mathematical concept that appears in many places and in many disguises. The representation of geometric entities, of their unions and intersections, and of their transformations is something that we, as human beings, can relate to particularly well, since these concepts are omnipresent in our everyday life. Being able to describe something in terms of geometric concepts lifts a purely formal description to something we can relate to. The application of “common geometrical sense” can therefore be extremely helpful in understanding many mathematical concepts. This is true not only for elements directly related to geometry such as the fundamental matrix, but also for polynomial curves such as Pythagorean hodograph curves, and analysis-related aspects such as the Cauchy–Riemann equations [127], to mention a few examples. An algebra for geometry is therefore a desirable mathematical tool, and indeed many such algebras have been developed. The first ones were probably Grassmann’s algebra of extensive entities, Hamilton’s quaternions, and complex numbers, which were all combined by W. K. Clif
