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.
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Nešović, E. On Rotation About Lightlike Axis in Three-Dimensional Minkowski Space. Adv. Appl. Clifford Algebras 26, 237–251 (2016). https://doi.org/10.1007/s00006-015-0601-6
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DOI: https://doi.org/10.1007/s00006-015-0601-6