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Clifford Algebras

Geometric Modelling and Chain Geometries with Application in Kinematics

  • Book
  • © 2015

Overview

Authors:
  1. Daniel Klawitter

    1. TU Dresden Institut für Geometrie, Dresden, Germany

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  • Publication in the field of mathematical science
  • Includes supplementary material: sn.pub/extras

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About this book

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 projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic map**s for special Cayley-Klein geometries are developed. These map**s allow a description of existing kinematic map**s in a unifying framework.

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Table of contents (3 chapters)

  1. Front Matter

    Pages 1-18
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  2. Models and Representations

    • Daniel Klawitter
    Pages 5-99

  3. Chain Geometry over Clifford Algebras

    • Daniel Klawitter
    Pages 101-180

  4. Kinematic Map**s for Spin Groups

    • Daniel Klawitter
    Pages 181-199

  5. Back Matter

    Pages 201-216
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Reviews

“Clifford and geometrical algebras are powerful calculation tools that unify geometric concepts from different algebraic structures built over time … . In this book, the author makes use of this powerful mathematical tool, specifically Clifford algebras and their Spin and Pin groups, to unify different kinematic map**s … . I find this book a great accomplishment and definitely recommend it.” (Eduardo A. Notte Cuello, Mathematical Reviews, May, 2016)

Authors and Affiliations

  • TU Dresden Institut für Geometrie, Dresden, Germany

    Daniel Klawitter

About the author

Daniel Klawitter is a scientific assistant at the Institute of Geometry at the Technical University of Dresden, Germany.

Bibliographic Information

  • Book Title: Clifford Algebras

  • Book Subtitle: Geometric Modelling and Chain Geometries with Application in Kinematics

  • Authors: Daniel Klawitter

  • DOI: https://doi.org/10.1007/978-3-658-07618-4

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden 2015

  • Softcover ISBN: 978-3-658-07617-7Published: 10 November 2014

  • eBook ISBN: 978-3-658-07618-4Published: 29 October 2014

  • Edition Number: 1

  • Number of Pages: XVIII, 216

  • Number of Illustrations: 8 b/w illustrations, 10 illustrations in colour

  • Topics: Geometry, Algebraic Geometry, Computational Mathematics and Numerical Analysis

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