  We analyze the dynamical generation of entanglement in systems of two
interacting spins initially prepared in a product of spin coherent states. For
arbitrary time-independent Hamiltonians, we derive a semiclassical expression
for the purity of the reduced density matrix as function of time. The final
formula, subsidiary to the linear entropy, shows that the short-time dynamics
of entanglement depends exclusively on the stability of trajectories governed
by the underlying classical Hamiltonian. Also, this semiclassical measure is
shown to reproduce the general properties of its quantum counterpart and give
the expected result in the large spin limit. The accuracy of the semiclassical
formula is further illustrated in a problem of phase exchange for two particles
of spin $j$.
