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Clifford Algebras

Geometric Modelling and Chain Geometries with Application in Kinematics

Daniel Klawitter (Autor)

Buch | Softcover

XVIII, 216 Seiten

2014
Springer Fachmedien Wiesbaden GmbH (Verlag)
978-3-658-07617-7 (ISBN)

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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.

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

Models and representations of classical groups.- Clifford algebras, chain geometries over Clifford algebras.- Kinematic mappings for Pin and Spin groups.- Cayley-Klein geometries.

"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)

Erscheint lt. Verlag	10.11.2014
Zusatzinfo	XVIII, 216 p. 18 illus., 10 illus. in color.
Verlagsort	Wiesbaden
Sprache	englisch
Maße	148 x 210 mm
Gewicht	313 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Cayley-Klein Geometries • Clifford algebra model • Euclidean displacements • Euclidean Geometry • hyperquadrics • kinematic mappings
ISBN-10	3-658-07617-8 / 3658076178
ISBN-13	978-3-658-07617-7 / 9783658076177
Zustand	Neuware