The Application of Euler-Rodrigues Formula over Hyper-Dual Matrices


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RAMİS Ç., YAYLI Y., Zengin I.

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.