Fig. 4

The Euler angle. In the three-dimensional space, vector A₀B₀ is rotated to the vector A₁B₁. In order to obtain the Euler angle, the coordinate system is rotated in accordance with the ZYZ format. The blue coordinate system is the initial state XYZ_blue. The XYZ_blue axis is rotated by an angle α around the Z axis to obtain an intermediate coordinate system XYZ_green. Then XYZ_green is rotated around its own Y-axis by an angle β to obtain the intermediate coordinate system XYZ_red, at which time the blue Z-axis moves to the red Z-axis, and the X-axis and Y-axis are on the red plane. Rotate XYZ_red around its Z axis by angle γ to obtain the final coordinate system XYZ_yellow, which is the red coordinate system in this figure. The rotation angle of the vector A₀B₀ to A₁B₁ is (α, β, γ)