Generalized elliptical quaternions with some applications
TURKISH JOURNAL OF MATHEMATICS, cilt.47, sa.1, ss.351-371, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 47 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.55730/1300-0098.3364
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.351-371
- Akdeniz Üniversitesi Adresli: Evet
Özet
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.