Classical and algebraic Hamiltonian with su(3) symmetry

We use Gelfand-Zetlin patterns to obtain the coherent state for an arbitrary symmetric irreducible representation of su(3). The semiclassical evolution of a dynamical system whose Hamiltonian contains the Casimir operators of both su(2) and so(3) subalgebras is investigated, and it is concluded that the presence of a common operator in the subalgebras induces integrability despite the absence of dynamical symmetry.