We investigate the angular normal modes for small oscillations about anequilibrium of a single-component coulomb cluster confined by a radiallysymmetric external potential to a circle. The dynamical matrix for this systemis a Laplacian symmetrically circulant matrix and this result leads to ananalytic solution for the eigenfrequencies of the angular normal modes. We alsoshow the limiting dependence of the largest eigenfrequency for large numbers ofparticles.
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