Obtaining triplet from quaternions
Obtaining triplet from quaternions
In this study, we obtain triplets from quaternions. First, we obtain triplets from realquaternions. Then, as an application of this, we obtain dual triplets from the dualquaternions. Quaternions, in many areas, it allows ease in calculations andgeometric representation. Quaternions are four dimensions. The triplets are inthree dimensions. When we express quaternions with triplets, our study isconducted even easier. Quaternions are very important in the display of rotationalmovements. Dual quaternions are important in the expression of screwmovements. Reducing movements from four dimensions to three dimensionsmakes our study easier. This simplicity is achieved by obtaining triplets fromquaternions.
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- [1] Sangwine, S.J., & Bihan, N.L. (2010). Quaternion polar representation with a complex modulus and complex argument inspired by the CayleyDickson form. Advanced Applied Clifford Algebra, (20), 111-120.
- [2] Pfaff, F.R. (2000). A commutative multiplication of number triplets. The American Mathematical Monthly 107(2), 156–162.
- [3] Akyar, B. (2008). Dual quaternions in spatial kinematics in an algebraic sense. Turkish Journal of Mathematics (32), 373–391.
- [4] Dimentberg, F.M. (1965). The screw calculus and its applications in mechanics; Foreign Division Translation FTD-HT-23-1632-67.
- [5] Kula, L., & Yaylı, Y. (2006). A commutative multiplication of dual number triplets. Journal of Science of Dumlupınar University (10), 53-60.
- [6] Hanson, A.J. (2005). Visualizing quaternion, Morgan-Kaufmann, Elsevier.