File Name: altmann rotations quaternions and double groups .zip
This book investigates the geometry of quaternion and octonion algebras.
Rotations, Quaternions, and Double Groups. Simon L. This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.
Manuscript received May 21, ; final manuscript received September 3, ; published online October 8, Editor: Harry Dankowicz. Pujol, J. October 8, September ; 65 5 : The well-known Rodrigues' equations for the composition of two finite rotations were introduced in without a detailed derivation.
Rotations, quaternions and double groups. By S. ALTMANN. Pp. xiv+ Oxford: Clarendon Press,. Price £ This book is one of the first in the world.
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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Altmann Published Mathematics Mathematics Magazine.
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Information Discussion 0 Files Holdings. Book Title Rotations, quaternions, and double groups Edition Corrected ed. Y : Dover Publ. Series Dover Books on Mathematics Subject code Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the g ISBN print version electronic version.
Benjamin Olinde Rodrigues 6 October — 17 December , more commonly known as Olinde Rodrigues , was a French banker, mathematician , and social reformer. In mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula about series of orthogonal polynomials and the Euler—Rodrigues parameters. Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux. After graduation, Rodrigues became a banker. A close associate of the Comte de Saint-Simon , Rodrigues continued, after Saint-Simon's death in , to champion the older man's socialist ideals, a school of thought that came to be known as Saint-Simonianism. During this period, Rodrigues published writings on politics, social reform, and banking. In he published a result on transformation groups ,  which applied Leonhard Euler 's four squares formula , a precursor to the quaternions of William Rowan Hamilton , to the problem of representing rotations in space.
Bournemouth University, Bournemouth, UK url: www. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act , this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. More than 50 years ago when I was studying to become an electrical engineer, I came across complex numbers, which were used to represent out-of-phase voltages and currents using the j operator. I believe that the letter j was used, rather than i , because the latter stood for electrical current.
Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Visualizing Quaternions A. Hanson; [Bookshelf] Abstract: This book presents the properties of quaternions and their applications. The text is arranged into three parts.
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