Multiplicative hyperbolic split quaternions and generating rotation matrices

Abstract

With the help of split quaternions, rotational motion in Lorentz space can be studied. This rotation corresponds to the rotations on the hyperboloids. The aim of this study is to define and examine hyperbolic rotations in the new geometry space. We describe new quaternions that are called multiplicative hyperbolic split quaternions, in this study. We also defined the geometric hyperbolic scalar product and geometric hyperbolic vector product to be able to study hyperbolical rotations. So, we define geometric hyperbolical rotation matrices. Then, it is also shown visually by giving a few examples through the MAPLE program. Finally, we give geometrical inter- presentations of the results in the multiplicative hyperboloidal split quaternion that come up with these results.