Cayley Formula, Euler Parameters and Rotations in 3-Dimensional Lorentzian Space

In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of an orthogonal matrix in 3-dimensional generalized space [Formula: see text]. It is shown that unit generalized quaternion, which is defined by the generalized Euler parameters, corresponds to a rotation in [Formula: see text] space.We found that the rotation in matrix equation forms using matrix form of the generalized quaternion product. Besides, in [Formula: see text] space, we obtained the rotations determined by the unit quaternions and unit split quaternions, which are special cases of generalized quaternions for [Formula: see text] in 3-dimensional Eulidean space [Formula: see text] in 3-dimensional Lorentzian space [Formula: see text] respectively.

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Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

Advances in Applied Clifford Algebras ◽

10.1007/s00006-011-0318-0 ◽

2011 ◽

Vol 22 (4) ◽

pp. 1081-1091 ◽

Cited By ~ 6

Author(s):

Osman Keçilioğlu ◽

Siddika Özkaldi ◽

Halit Gündoğan

Keyword(s):

Timelike Vector ◽

Lorentzian Space ◽

3 Dimensional ◽

Screw Motion

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On the explicit characterization of spherical curves in 3-dimensional Lorentzian space L3

Journal of Inverse and Ill-Posed Problems ◽

10.1163/156939403770862794 ◽

2003 ◽

Vol 11 (4) ◽

pp. 389-397

Author(s):

K. Ilarslan ◽

C. Camci ◽

H. Kocayigit ◽

H. H. Hacisalihoglu

Keyword(s):

Lorentzian Space ◽

3 Dimensional ◽

Explicit Characterization

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On the explicit characterization of spherical curves in 3-dimensional Lorentzian space

Journal of Inverse and Ill-Posed Problems ◽

10.1515/156939403770862794 ◽

2003 ◽

Vol 11 (4) ◽

pp. 389-397

Author(s):

K. Ilarslan ◽

C. Camci ◽

H. Kocayigit ◽

H. H. Hacisalihoglu

Keyword(s):

Lorentzian Space ◽

3 Dimensional ◽

Explicit Characterization

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On Harmonic Curvatures of Null Curves of the AW(k)-Type in Lorentzian Space

Zeitschrift für Naturforschung A ◽

10.1515/zna-2008-5-603 ◽

2008 ◽

Vol 63 (5-6) ◽

pp. 248-252 ◽

Cited By ~ 5

Author(s):

Mihriban Külahcı ◽

Mehmet Bektaş ◽

Mahmut Ergüt

Keyword(s):

Lorentzian Space ◽

3 Dimensional ◽

Null Curves

We investigate null curves of the AW(k)-type (1 ≤ k ≤ 3) in the 3-dimensional Lorentzian space, L3, and give curvature conditions of these curves by using the Cartan frame. Moreover, we study harmonic curvatures of curves of AW(k)-type and show that if the α Frenet curve is of type AW(1), then α is a null helix.

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