AccScience Publishing / IJOCTA / Volume 11 / Issue 1 / DOI: 10.11121/ijocta.01.2021.00855
RESEARCH ARTICLE

Obtaining triplet from quaternions

Ali Atasoy1* Yusuf Yaylı2*
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1 Keskin Vocational School, Kırıkkale University, Turkey
2 Department of Mathematics, Ankara University, Turkey
IJOCTA 2021, 11(1), 109–113; https://doi.org/10.11121/ijocta.01.2021.00855
Submitted: 24 August 2019 | Accepted: 10 May 2020 | Published: 28 January 2021
© 2021 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

In this study, we obtain triplets from quaternions. First, we obtain triplets from real  quaternions. Then, as an application of this, we obtain dual triplets from the dual  quaternions. Quaternions, in many areas, it allows ease in calculations and  geometric representation. Quaternions are four dimensions. The triplets are in  three dimensions. When we express quaternions with triplets, our study is  conducted even easier. Quaternions are very important in the display of rotational  movements. Dual quaternions are important in the expression of screw  movements. Reducing movements from four dimensions to three dimensions  makes our study easier. This simplicity is achieved by obtaining triplets from  quaternions.

Keywords
Dual quaternion
Real quaternion
Triplet
Rotation
Screw operator
Conflict of interest
The authors declare they have no competing interests.
References

[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.

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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing