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The Landau-Lifshitz (LL) equations may be derived using the formalism of SU (2) coherent states. For many spin systems, such as those possessing strong onsite anisotropy and spin greater than ½, it is more appropriate to take a classical limit based on coherent states of SU (N), where N> 2. The resulting generalization of the LL equations are naturally derived in the Heisenberg picture, setting up a correspondence between quantum observables and classical variables. We show that one may instead develop an equivalent Schrödinger dynamics directly on coherent states. This formulation involves fewer variables than the Heisenberg approach and possesses a global Hamiltonian structure. The latter fact enables the application of energy-preserving geometric integration schemes. The dynamics may also be coupled to a thermal bath, resulting in a generalization of the stochastic LL equations. Sunny, a software …