A different approach to rotational motion with high dimensional algebras

In this study, the rotational part of rotational and translational movements, which are frequently encountered in many parts of science and engineering applications, is discussed in detail. In this context, the rotation event is handled with topics such as Euler angles, Cayley-Klein and Euler parameters, Rodrigues formula, de Moivre formula an one example problem associated with this rotation has been examined with these methods. In addition; by considering the solutions of real, complex and dual quaternion algebras, 2×2 and 4×4 matrix representations for real quaternions and 2×2, 4×4 and 8×8 matrix representations for complex and dual quaternions, which are isomorphic and different representations, are illustrated separately onto the same example. 8×8 matrix representations have been presented for the first time in the literature, revealing that there are different and alternative representations for a simple rotation operation. In this way, it has been shown that the same rotation operation is provided with 24 different methods and the results are the same.