Dual Split Quaternions and Chasles’ Theorem in 3-Dimensional Minkowski Space $${\mathbb{E}^{3}_{1}}$$ E 1 3

Abstract

In 1831, Michel Chasles proved the existence of a fixed line under a general displacement in \({\mathbb{R}^3}\). The fixed line called the screw axis of displacement was obtained by McCharthy in [10]. The purpose of this paper is to develop the method which is given for the pure rotation in [14], and thus to obtain the screw axis of spatial displacement in 3-dimensional Minkowski space. Firstly, we give a relation between dual vectors and lines in \({\mathbb{E}^{3}_{1}}\), characterize the screw axis. Also, we discuss the dual split quaternion representation of a spatial displacement.