SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E42 Kula, Levent; Yayli, Yusuf;
We review the algebraic structure of and show that has a scalar product that allows as to identify it with semi Euclidean . We show that a pair q and p of unit split quaternions in determines a rotation . Moreover, we prove that is a product of rotations in a pair of orthogonal planes in . To do that we call upon one tool from the theory of second ordinary differential equations.
hyperbolic number;split quaternion;generalized inverse;rotation;timelike plane of index 1;timelike plane of index 2;spacelike plane;