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Dual transformations and quaternions
Author(s) -
Yüca Gülsüm,
Yaylı Yusuf
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7459
Subject(s) - dual quaternion , quaternion , mathematics , invariant (physics) , rotation matrix , rotation (mathematics) , algebra over a field , matrix representation , kinematics , dual (grammatical number) , euclidean space , space (punctuation) , matrix (chemical analysis) , pure mathematics , geometry , computer science , classical mechanics , art , chemistry , physics , literature , organic chemistry , materials science , composite material , mathematical physics , group (periodic table) , operating system
In this study, we are interested in the way quaternions to represent 3D and 4D rotations in Lorentzian space. We give a new method for obtaining a rotation matrix in Lorentzian space with the help of a unit quaternion. Furthermore, we prove that rotation matrices correspond to a quaternion leave invariant the same axis in Euclidean and Lorentzian space. Then, we introduce a semi‐orthogonal matrix representation of a quaternion curve in 4D space. Moreover, we provide applications and draw their figures to explore visual representations. Finally, due to the importance of the dual space in kinematics, robotics, and other areas related, we carry this work into their dual spaces by using a dual quaternion.