  We theoretically and numerically investigate spin waves that occur in systems
of classical magnetic dipoles that are arranged at the vertices of a regular
polygon and interact solely via their magnetic fields. There are certain
limiting cases that can be analyzed in detail. One case is that of spin waves
as infinitesimal excitations from the system's ground state, where the
dispersion relation can be determined analytically. The frequencies of these
infinitesimal spin waves are compared with the peaks of the Fourier transform
of the thermal expectation value of the autocorrelation function calculated by
Monte Carlo simulations. In the special case of vanishing wave number an exact
solution of the equations of motion is possible describing synchronized
oscillations with finite amplitudes. Finally, the limiting case of a dipole
chain with $N\longrightarrow \infty$ is investigated and completely solved.
