The quaternions are the second "number system" other than the real numbers ever discovered, and the first to be found by a deliberate search. Their immediate predecessor was the field of complex numbers, formed by adjoining an imaginary unit, the...

In mathematics, quaternions are a non-commutative extension of complex numbers. They were first described by the Irish mathematician, Sir William Rowan Hamilton, in 1843 and applied to mechanics in three-dimensional space. At first, quaternions were...

Smooth motion generation is an important issue in the computer animation and virtual reality (VR) area. In general, the motion of a rigid body consists of translation and orientation. The former is described by a space curve in 3-dimensional Euclidean space, while the latter...

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics. In particular, it is shown that Q-connexion (with quaternion...