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Journals / International Electronic Journal of Geometry / 2022 / Volume: 15 Issue: 2

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

Çağla Ramis(NEVSEHIR HACI BEKTAS VELI UNIVERSITY)0000-0002-2809-8324
Yusuf Yaylı(ANKARA UNIVERSITY)0000-0003-4398-3855
İrem Zengin(IZMIR DEMOCRACY UNIVERSITY)0000-0003-1642-5559
Pages
—
Publication Date
2022-10-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Lie group over the hyper-dual matrices and its corresponding Lie algebra are first introduced in this study.
📊
Key Findings & Data:One of Euler's strategies called the Euler-Rodrigues formula is applied to the matrices of hyper-dual rotations.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dual numbers · hyper-dual numbers · Euler-Rodrigues formula

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.

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Cite This Article

Ramis, Ç., Yaylı, Y., Zengin, İ. (2022). The Application of Euler-Rodrigues Formula over Hyper-Dual Matrices. International Electronic Journal of Geometry, Volume: 15 Issue: 2. https://doi.org/10.36890/iejg.1127216

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