(iii) The discovery of the conjugate variables (Eq. 101 and Eq. 102) in terms of the generalized Euler angles in spin coherent state , which leads to the corresponding EOMs with these variables (Eq. 109). It turns out that this set of conjugate variables plays a similar role in the SU (N ) mapping formalism (see Eq. 103 and Eq. 104) as the action-angle variable play in the MMST formalism (see Eq. 126 and Eq. 127a).