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This paper introduces and defines the quaternion with a brief insight into its properties and algebra. The main part of this paper is devoted to the derivation of basic equations of the vector rotation around each rotational x, y, z axis. Then, the equations of generalized quaternion rotation and express the general rotation operator is derived. Finally the utilization of equations is demonstrated on a simple example. For purposes of simplicity the quaternions theory is demonstrated around the z -axis by γ angle. For the purpose of this paper, the fact that the subspace of vector quaternions may be regarded as being equivalent to the ordinary is used.

Universal approach to derivation of quaternion rotation formulas