Clifford Algebras: Geometric Modelling and Chain Geometries with Application in Kinematics

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9783658076177: Clifford Algebras: Geometric Modelling and Chain Geometries with Application in Kinematics

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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About the Author:

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

Review:

“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)

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Daniel Klawitter
Verlag: Betriebswirt.-Vlg Gabler Nov 2014 (2014)
ISBN 10: 3658076178 ISBN 13: 9783658076177
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Buchbeschreibung Betriebswirt.-Vlg Gabler Nov 2014, 2014. Taschenbuch. Buchzustand: Neu. Neuware - 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. 216 pp. Englisch. Artikel-Nr. 9783658076177

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