Year 2020, Volume 8 , Issue 1, Pages 11 - 24 2020-03-20

Simple, Double and Isoclinic Rotations with a Viable Algorithm

Melek ERDOĞDU [1] , Mustafa ÖZDEMİR [2]


The main topic of this study is to investigate rotation matrices in four dimensional Euclidean space in two different ways. The first of these ways is Rodrigues formula and the second is Cayley formula.The most important common point of both formulas is the use of skew symmetric matrices. However, depending on the skew symmetric matrix used, it is possible to classify the rotation matrices by both formulas. Therefore, it is also revealed how the rotation matrices obtained by both formulas are classified as simple, double
or isoclinic rotation. Eigenvalues of skew symmetric matrices play the major role in this classification. With the use of all results, it is also seen which skew symmetric matrix is obtained from a given rotation matrix by Rodrigues and Cayley formula, respectively. Finally, an algorithm for classification of rotations is given with the help of the obtained datas and explained with an example.
Euclidean Four Space, Rodrigues Rotation Formula, Rotation matrix, Cayley Rotation Formula
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Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0001-9610-6229
Author: Melek ERDOĞDU (Primary Author)
Country: Turkey


Orcid: 0000-0002-1359-4181
Author: Mustafa ÖZDEMİR

Dates

Publication Date : March 20, 2020

Bibtex @research article { mathenot642208, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {11 - 24}, doi = {10.36753/mathenot.642208}, title = {Simple, Double and Isoclinic Rotations with a Viable Algorithm}, key = {cite}, author = {Erdoğdu, Melek and Özdemi̇r, Mustafa} }
APA Erdoğdu, M , Özdemi̇r, M . (2020). Simple, Double and Isoclinic Rotations with a Viable Algorithm . Mathematical Sciences and Applications E-Notes , 8 (1) , 11-24 . DOI: 10.36753/mathenot.642208
MLA Erdoğdu, M , Özdemi̇r, M . "Simple, Double and Isoclinic Rotations with a Viable Algorithm" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 11-24 <https://dergipark.org.tr/en/pub/mathenot/issue/53229/642208>
Chicago Erdoğdu, M , Özdemi̇r, M . "Simple, Double and Isoclinic Rotations with a Viable Algorithm". Mathematical Sciences and Applications E-Notes 8 (2020 ): 11-24
RIS TY - JOUR T1 - Simple, Double and Isoclinic Rotations with a Viable Algorithm AU - Melek Erdoğdu , Mustafa Özdemi̇r Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.642208 DO - 10.36753/mathenot.642208 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 11 EP - 24 VL - 8 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.642208 UR - https://doi.org/10.36753/mathenot.642208 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes Simple, Double and Isoclinic Rotations with a Viable Algorithm %A Melek Erdoğdu , Mustafa Özdemi̇r %T Simple, Double and Isoclinic Rotations with a Viable Algorithm %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 1 %R doi: 10.36753/mathenot.642208 %U 10.36753/mathenot.642208
ISNAD Erdoğdu, Melek , Özdemi̇r, Mustafa . "Simple, Double and Isoclinic Rotations with a Viable Algorithm". Mathematical Sciences and Applications E-Notes 8 / 1 (March 2020): 11-24 . https://doi.org/10.36753/mathenot.642208
AMA Erdoğdu M , Özdemi̇r M . Simple, Double and Isoclinic Rotations with a Viable Algorithm. Math. Sci. Appl. E-Notes. 2020; 8(1): 11-24.
Vancouver Erdoğdu M , Özdemi̇r M . Simple, Double and Isoclinic Rotations with a Viable Algorithm. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 11-24.
IEEE M. Erdoğdu and M. Özdemi̇r , "Simple, Double and Isoclinic Rotations with a Viable Algorithm", Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, pp. 11-24, Mar. 2020, doi:10.36753/mathenot.642208