TY - GEN
T1 - On the matrix algebra realization of the theory of biquaternions
AU - Ge, Q. J.
N1 - Publisher Copyright:
© 1994 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1994
Y1 - 1994
N2 - This paper describes a matrix algebra presentation of Clifford's theory of biquaternions. We examine 4×4 skewsymmetric matrices and use their exponentials to relate quaternions to equal-angle double rotations in Euclidean four-space E4. We show how double rotations in E4expressed in terms of plane coordinates lead to elliptic biquaternions in both Pliicker and Study forms and present the fundamental Pliicker and Study conditions that govern the biquaternions. Finally, we show that a spatial displacement in E3in terms of parabolic biquaternions (or dual quaternions) is a limiting case of a double rotation in E4in terms of elliptic biquaternions.
AB - This paper describes a matrix algebra presentation of Clifford's theory of biquaternions. We examine 4×4 skewsymmetric matrices and use their exponentials to relate quaternions to equal-angle double rotations in Euclidean four-space E4. We show how double rotations in E4expressed in terms of plane coordinates lead to elliptic biquaternions in both Pliicker and Study forms and present the fundamental Pliicker and Study conditions that govern the biquaternions. Finally, we show that a spatial displacement in E3in terms of parabolic biquaternions (or dual quaternions) is a limiting case of a double rotation in E4in terms of elliptic biquaternions.
UR - https://www.scopus.com/pages/publications/85103568084
U2 - 10.1115/DETC1994-0221
DO - 10.1115/DETC1994-0221
M3 - Conference contribution
AN - SCOPUS:85103568084
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 425
EP - 432
BT - 23rd Biennial Mechanisms Conference
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1994 Design Technical Conferences, DETC 1994, collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium
Y2 - 11 September 1994 through 14 September 1994
ER -