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Cayley Formula, Euler Parameters and Rotations in 3-Dimensional Lorentzian Space
(Birkhauser Verlag Ag, 2010) Özkaldı, Sıddıka; Gündogan, Halit
In this study, by using Lorentzian matrix multiplication, Cayley formula and Euler parameters of a Lorentzian orthogonal matrix are obtained in Lorentz space L(3). Then, by using Euler parameters of a rotation in a split quaternion, the split quaternion equation of a rotation movement is obtained in the space L(3).
Clifford Product and Lorentzian Plane Displacements In 3-Dimensional Lorentzian Space
(Springer Basel Ag, 2009) Gündogan, Halit; Özkaldı, Sıddıka
In this paper, by defining Clifford algebra product in 3-dimensional Lorentz space, L (3), it is shown that even Clifford algebra of L (3) corresponds to split quaternion algebra. Then, by using Lorentzian matrix multiplication, pole point of planar displacement in Lorentz plane L (2) is obtained. In addition, by defining degenerate Lorentz scalar product for L (3) and by using the components of pole points of Lorentz plane displacement in particular split hypercomplex numbers, it is shown that the Lorentzian planar displacements can be represented as a special split quaternion which we call it Lorentzian planar split quaternion.