On Rotation About Lightlike Axis in Three-Dimensional Minkowski Space

Abstract

We obtain matrix of the rotation about arbitrary lightlike axis in three-dimensional Minkowski space by deriving the Rodrigues’ rotation formula and using the corresponding Cayley map. We prove that a unit timelike split quaternion q with a lightlike vector part determines rotation R q about lightlike axis and show that a split quaternion product of two unit timelike split quaternions with null vector parts determines the rotation about a spacelike, a timelike or a lightlike axis. Finally, we give some examples.