Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

Abstract

In the present paper we obtain the timelike Euler parameters of a Lorentzian orthogonal matrix in Lorentz space \({L^{3} = \mathbb{R}^{2,1}}\) by using Lorentzian matrix multiplication. Then, by using the timelike Euler parameters of a given rotation in a split quaternion formulation, we produce split quaternion equation of a rotation motion in L3. Moreover the components of a dual split quaternion are obtained by replacing the timelike L-Euler parameters with their split dual versions.