Dual transformations and quaternions

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 inv...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-09, Vol.44 (14), p.10957-10971
Main Authors: Yüca, Gülsüm, Yaylı, Yusuf
Format: Article
Language:English
Subjects:
dual quaternion
dual transformation
Euclidean geometry
Kinematics
Lorentzian space
Matrix representation
quaternion
Quaternions
Robotics
Rotation
rotation matrix
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7459