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

Year 2022, Volume: 15 Issue: 2, 266 - 276, 31.10.2022

Çağla Ramis , Yusuf Yaylı , İrem Zengin

https://doi.org/10.36890/iejg.1127216

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.

Keywords

Dual numbers, hyper-dual numbers, Euler-Rodrigues formula, Euler's theorem

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