Spinor Model of Generalized Three-dimensional Rotations

Equations of the set of all possible rotations of the three-dimensional space (with both zero and nonzero centers) which translate the given initial point to the final one were obtained using the spinor representation of the orthogonal transformations of rotation. An equation of the plane where the centers of these rotations are situated was obtained. Relations between the elements of the complex unitary matrices of the second order and the real orthogonal rotation matrices of the third order as well as expressions for calculation of the Euler angles from the coordinates of the initial and final rotation points were derived. The latter play an important part in the control of spatial rotations of the mechanical plants.