Generalized elliptical quaternions with some applications
TURKISH JOURNAL OF MATHEMATICS, vol.47, no.1, pp.351-371, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 47 Issue: 1
- Publication Date: 2023
- Doi Number: 10.55730/1300-0098.3364
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Page Numbers: pp.351-371
- Akdeniz University Affiliated: Yes
Abstract
In this article, quaternions, which is a preferred and elegant method for expressing spherical rotations, are generalized with the help of generalized scalar product spaces, and elliptical rotations on any given ellipsoid are examined by them. To this end, firstly, we define the generalized elliptical scalar product space which accepts the given ellipsoid as a sphere and determines skew symmetric matrices, and the generalized vector product related to this scalar product space. Then we define the generalized elliptical quaternions by using these notions. Finally, elliptical rotations on any ellipsoid in the space are examined by using the unit generalized elliptical quaternions. The formulas and results obtained are supported with numerical examples.