  The classical spin system consisting of three spins with Heisenberg
interaction is an example of a completely integrable mechanical system. In this
paper we explicitly calculate its time evolution and the corresponding
action-angle variables. This calculation is facilitated by splitting the six
degrees of freedom into three internal and three external variables, such that
the internal variables evolve autonomously. Their oscillations can be
explicitly calculated in terms of the Weierstrass elliptic function. We test
our results by means of an example and comparison with direct numerical
integration. A couple of special cases is analyzed where the general theory
does not apply, including the aperiodic limit case for special initial
conditions. The extension to systems with a time-depending magnetic field in a
constant direction is straightforward.
