  In this letter we present a general classification of integrable models of
identical classical spins coupled via the isotropic Heisenberg Hamiltonian. Our
constructive proof of integrability provides a solution scheme for the
equations describing the time evolution of each spin. We show that for a broad
class of Heisenberg couplings, it is possible to solve the equations of motion
iteratively by building a hierarchy of spins, each of which precesses about the
composite spin of the previous level. This leads to the identification of the
frequencies of precession at each level.
