Unit Generalized Quaternions in Spatial Kinematics

Mehdi Jafari


After a review of some fundamental properties of the generalized quaternions, we apply a unit generalized quaternion to rotation in the 3-dimensional space  Also, the angular velocity of this motion is obtained.

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L. Kula., and Y. Yayli, “Split quaternions and rotations in semi-Euclidean space ”, Journal of Korean Math. Soc., vol. 44(6).1313-1327, 2007.

M. Ozdemir, and A.A. Ergin, “Rotations with unit timelike quaternions in Minkowski 3-space”, Journal of geometry and physics 56, pp. 322-336 2006.

J.P. Ward, Quaternions and Cayley numbers algebra and applications, Kluwer Academic Publishers, London, 1997, pp. 213–315.

H. Pottman and J. Wallner, Computational line geometry, Springer-Verlag Berlin Heidelberg New York, 2000, pp. 321–350.

M. Jafari, “Generalized Hamilton operators and Lie groups”, Ph.D. thesis, Ankara University, Ankara, Turkey, 2012.

M. Jafari and Y. Yayli, “Rotation in four dimensions via generalized Hamilton operators”, Kuwait journal of science, vol. 40(1) pp. 67-79, 2013.

W. B. Heard, Rigid body mechanics, Alexandria, Wiley-vch Verlag GmbH, 2006.

A. Karger and J. Novak, Space kinematics and Lie groups. Gordon and Breach science publishers, Now York, 1985.


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