Generalized Euler angles for a unitary control of the Hamiltonian system

We provide an angular parametrization of the special unitary group $\textrm{SU}(2^{n})$ generalizing Euler angles for $\textrm{SU}(2)$ by successively applying the KAK decomposition. We then determine constraint equations for the parametric curve of generalized Euler angles corresponding to the exponential curve of a given Hamiltonian. The constraint equations are in the form of first-order differential-algebraic equations and resemble Wei-Norman equations of canonical coordinates of the second kind for $\textrm{SU}(2^{n})$.