On the Matrix Realization of the Theory of Biquaternions
Affiliation:
1. Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, New York 11794-2300
Abstract
This paper describes a matrix algebra realization of Clifford’s theory of biquaternions. By examining 4 × 4 skew-symmetric matrices, the paper shows the connection between infinitesimal screws in elliptic three-space and vector quaternions. By studying the matrix exponential of the skew-symmetric matrices, the paper also shows how finite screws in elliptic three-space lead to matrix realization of quaternions. Finally, it is shown that line transformations in elliptic three-space lead to double quaternions and that a dual quaternion is a limiting case of a double quaternion.
Publisher
ASME International
Subject
Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
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