Spherical kinematics in 3-dimensional generalized space

İngilizce (OpenAlex)

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.