The Application of Euler-Rodrigues Formula over Hyper-Dual Matrices
INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.15, no.2, pp.266-276, 2022 (ESCI, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 15 Issue: 2
- Publication Date: 2022
- Doi Number: 10.36890/iejg.1127216
- Journal Name: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.266-276
- Keywords: Dual numbers, hyper-dual numbers, Euler-Rodrigues formula, Euler?s theorem, THEOREM, NUMBERS
- Open Archive Collection: AVESIS Open Access Collection
- Ankara University Affiliated: Yes
Abstract
The Lie group over the hyper-dual matrices and its corresponding Lie algebra are first introduced in this study. One of Euler's strategies called the Euler-Rodrigues formula is applied to the matrices of hyper-dual rotations. The fundamental relationship between the hyper-dual numbers and the dual numbers allows us to apply the formula on dual lines and two intersecting real lines in the three dimensional dual and Euclidean spaces, respectively.