when using interpolation functions to get the interpolated values of displacement and rotation in Gauss point, we could define two separate equations; one for the displacement and one for the rotation as in the attached photo.

The problem is interpolating the rotation.

Due to the fact that large 3D rotations couldn't be added simply, so it leads to me to use orthogonal rotation matrix R with nine components, but it is hard to define the rotational DOF using using nine components, so we tend to use rotation vector or incremental material rotation vector or incremental spatial rotation vector (three methods).

I am asking which is the best of the three above to interpolate the shape function of rotation.