Spherical kinematics in 3-dimensional generalized space
| Autor: | Erhan Ata, Umit Ziya Savcı |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Mathematical analysis 02 engineering and technology Kinematics Space (mathematics) 01 natural sciences 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Rodrigues equation 020201 artificial intelligence & image processing 010307 mathematical physics Orthogonal matrix Unit (ring theory) Mathematics Euler parameters |
| Zdroj: | International Journal of Geometric Methods in Modern Physics. 18:2150033 |
| ISSN: | 1793-6977 0219-8878 |
| DOI: | 10.1142/s021988782150033x |
| Popis: | In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of an orthogonal matrix in 3-dimensional generalized space [Formula: see text]. It is shown that unit generalized quaternion, which is defined by the generalized Euler parameters, corresponds to a rotation in [Formula: see text] space.We found that the rotation in matrix equation forms using matrix form of the generalized quaternion product. Besides, in [Formula: see text] space, we obtained the rotations determined by the unit quaternions and unit split quaternions, which are special cases of generalized quaternions for [Formula: see text] in 3-dimensional Eulidean space [Formula: see text] in 3-dimensional Lorentzian space [Formula: see text] respectively. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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