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

ISBN-13: 9783658076177 / Angielski / Miękka / 2014 / 216 str.

Daniel Klawitter

Opis

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.

Recenzje

"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)

Spis treści

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

O autorze

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

Blurb

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.

 Contents

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

Target Groups

• Researchers and students in the field of mathematics, physics, and mechanical engineering

About the Author

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