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Clifford Algebras: Geometric Modelling and Chain Geometries with Application in Kinematics - Softcover
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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 MAPPINGS FOR SPECIAL CAYLEY-KLEIN GEOMETRIES ARE DEVELOPED. THESE MAPPINGS ALLOW A DESCRIPTION OF EXISTING KINEMATIC MAPPINGS IN A UNIFYING FRAMEWORK.
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“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 mappings ... . I find this book a great accomplishment and definitely recommend it.” (Eduardo A. Notte Cuello, Mathematical Reviews, May, 2016)
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 mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework.
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- VerlagSpringer Spektrum
- Erscheinungsdatum2014
- ISBN 10 3658076178
- ISBN 13 9783658076177
- EinbandTapa blanda
- Anzahl der Seiten236
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Clifford Algebras : Geometric Modelling and Chain Geometries with Application in Kinematics
Verlag:
Springer Fachmedien Wiesbaden
(2014)
ISBN 10: 3658076178
ISBN 13: 9783658076177
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Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework. Artikel-Nr. 9783658076177
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