  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
$\textrm{SU}(2^{n})$.
