Simple, Double and Isoclinic Rotations with a Viable Algorithm

Year 2020, Volume: 8 Issue: 1, 11 - 24, 20.03.2020

Melek Erdoğdu , Mustafa Özdemir

https://doi.org/10.36753/mathenot.642208

Cited By: 9

Abstract

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.

Keywords

Euclidean Four Space, Rodrigues Rotation Formula, Rotation matrix, Cayley Rotation Formula

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