Last edited by Dijind
Saturday, August 1, 2020 | History

5 edition of Rotations, quaternions, and double groups found in the catalog.

Rotations, quaternions, and double groups

by Simon L. Altmann

  • 396 Want to read
  • 39 Currently reading

Published by Dover Publications in Mineola, N.Y .
Written in English

    Subjects:
  • Rotation groups.,
  • Quaternions.,
  • Finite groups.,
  • Representations of groups.

  • Edition Notes

    Originally published: Oxford : Clarendon Press ; New York : Oxford University Press, 1986.

    StatementSimon L. Altmann.
    Classifications
    LC ClassificationsQC174.17.R65 A48 2005
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL3425982M
    ISBN 100486445186
    LC Control Number2005049630

    Rotations, Quaternions, and Double Groups ().pdf writen by Simon L. Altmann: This text presents a consistent description of the geometric and quaternionic treatment of rotation operators. Covers the fundamentals of symmetries, matrices, and groups and presents a primer on rotations and. Geometry of 4D rotations. Four-dimensional rotations are of two types: simple rotations and double rotations. Simple rotations. A simple rotation R about a rotation centre O leaves an entire plane A through O (axis-plane) fixed. Every plane B that is completely orthogonal to A intersects A in a certain point such point P is the centre of the 2D rotation induced by R in B.

    The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. Quaternions were introduced by Hamilton in Important precursors to this work included Euler's four-square identity () and Olinde Rodrigues' parameterization of general rotations by four parameters (), but neither of these writers treated the four-parameter rotations as an algebra. Carl Friedrich Gauss had also discovered quaternions in , but this work was not published until.

    yields the vector v rotated by an angle α around the u axis. The rotation is clockwise if our line of sight points in the direction operation is known as conjugation by q. It follows that quaternion multiplication is composition of rotations, for if p and q are quaternions representing rotations, then rotation (conjugation) by pq is which is the same as rotating (conjugating) by q and. Today, quaternions are of interest to historians of mathematics. Vector analysis performs the daily mathematical routine that could also be done with quaternions. I personally think that there may be 4D roads in physics that can be efficiently traveled only by quaternions, and that is the path which is laid out in these web Size: KB.


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Rotations, quaternions, and double groups by Simon L. Altmann Download PDF EPUB FB2

"Rotations, Quaternions and Double Groups" surveys ALL those topics and more in a fluid, clear and sharp way. In addition, the careful geometric AND algebraic presentation thru-out this fine primer by Simon Altmann is an exemplar of mathematical presentation immediately favoring application via such methods as the very useful Dirac Bra-Ket Cited by: Rotations, Quaternions, and Double Groups (Dover Books on Mathematics) - Kindle edition by Altmann, Simon L.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Rotations, Quaternions, and Double Groups (Dover Books on Mathematics).4/5(15).

Rotations, quaternions, and double groups Simon L. Altmann This detailed monograph treats finite point groups as subgroups of the full rotation group, providing geometrical and topological methods which allow a unique definition of the quaternion parameters for all operations.

This text presents a consistent description of the geometric and quaternionic treatment of rotation operators. Covers the fundamentals of symmetries, matrices, and groups and presents a primer on rotations and rotation matrices.

Also explores rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, more. Quaternions are a simple and powerful tool for handling rotations and double groups.

This book gives a complete treatment of finite point groups as subgroups of the full rotation group and emphasizes geometrical and topological methods which permit a unique definition of the quaternion parameters for all operations of such groups.4/5(13). Rotations, Quaternions, and Double Groups book.

Read 2 reviews from the world's largest community for readers. This text presents a consistent descriptio /5. Buy Rotations, Quaternions, and Double Groups (Dover Books on Mathematics) by Altmann, Simon L (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible orders/5(14). Get free shipping on Rotations, Quaternions, and Double Groups ISBN from TextbookRush at a great price and get free shipping on orders over $35. Double groups are an ad hoc invention of the physicist Hans Bethe who was attempting to distinguish 2π rotations from null rotations for finite rotation groups.

Bethe essentially doubled the number of elements in the finite rotation group and defined a compatible group operation to make the double group well-defined. 4. Rotations and Angular Momentum 5. Tensor Bases: Introduction to Spinors 6. The Bilinear Transformation 7. Rotations and SU(2). The Stereographic Projection 8.

Projective Representations 9. The Geometry of Rotations The Topology of Rotations The Spinor Representations The Algebra of Rotations: Quaternions Double Groups Brand: Dover Publications. The stereographic projection --Projective representations --The geometry of rotations --The topology of rotations --The spinor representations --The algebra of rotations: quaternions --Double groups --The irreducible representations of SO(3) --Examples and applications --Solutions to problems.

adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A. Rotations, Quaternions, and Double Groups. by Simon L. Altmann. Dover Books on Mathematics.

Share your thoughts Complete your review. Tell readers what you thought by rating and reviewing this book. Rate it * You Rated it *Brand: Dover Publications. Rotations, quaternions, and double groups.

[Simon L Altmann] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Book: All Authors / Contributors: Simon L Altmann.

Find more information about: ISBN:. Rotations, Quaternions, and Double Groups by Simon L. Altmann,available at Book Depository with free delivery worldwide/5(8). Rotations, Quaternions and Double Groups ().pdf writen by Simon L. Altmann: Quaternions are a simple and powerful tool for handling rotations and double groups.

This book gives a complete treatment of finite point groups as subgroups of. The history of the incorporation of quaternions and rotation groups into classical physics: mechanics and electromagnetism. The history of the incorporation of quaternions and rotation groups into modern physics: quantum mechanics and relativity theory.

A source book of this kind should be useful to historians of science; asCited by: 2. Buy a cheap copy of Rotations, Quaternions, and Double book by Simon L. Altmann. This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a Free shipping over $Cited by: Rotations, Quaternions, and Double Groups.

Average rating: 0 out of 5 stars Write a review. Simon L Altmann. Walmart # $ $ 99 $ $ Book Format. Select Option. Current selection is: Paperback. Book Format: Paperback. Paperback. Qty: Add to Brand: Simon L Altmann. Description of the book "Rotations, Quaternions, and Double Groups": 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.

Altmann L.S. Rotations, quaternions, and double groups. Notation-conventions-how to use this book Introduction The Rodrigues programme Rotations by 2 Improper point groups The algebra of rotations: quaternions An entertainment on binary rotations The definition of quaternions Inversion of quaternions.Simon L.

Altmann is the author of Rotations, Quaternions, and Double Groups ( avg rating, 8 ratings, 2 reviews, published ), Is Nature Supernatur /5.Rotations, Quaternions, and Double Groups by Simon L. Altmann. ebook. Sign up to save your library. 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.