Dual transformations and quaternions
Copyright policy )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 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.
- Ankara University Turkey
- Aksaray University Turkey
Lorentzian space, Kinematics, Rotation Matrix, quaternion, Lorentzian Space, Local differential geometry of Lorentz metrics, indefinite metrics, dual quaternion, Matrices over special rings (quaternions, finite fields, etc.), Dual Quaternion, Dual Transformation, Quaternion, Applications of differential geometry to physics, Differential geometric aspects in kinematics, kinematics, Structure and representation of the Lorentz group, Matrix Lie algebras, dual transformation, Non-Euclidean differential geometry, rotation matrix
Lorentzian space, Kinematics, Rotation Matrix, quaternion, Lorentzian Space, Local differential geometry of Lorentz metrics, indefinite metrics, dual quaternion, Matrices over special rings (quaternions, finite fields, etc.), Dual Quaternion, Dual Transformation, Quaternion, Applications of differential geometry to physics, Differential geometric aspects in kinematics, kinematics, Structure and representation of the Lorentz group, Matrix Lie algebras, dual transformation, Non-Euclidean differential geometry, rotation matrix
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