  Two dimensional (2D) classical system of dipole particles confined by a
quadratic potential is studied. For clusters of N < 81 particles ground state
configurations and appropriate eigenfrequencies and eigenvectors for the normal
modes are found. Monte Carlo and molecular dynamic methods are used to study in
detail the order - disorder transition (the "melting" of clusters). In
mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower
temperatures an intershell orientational disordering of pairs of shells takes
place; at higher temperatures the intershell diffusion sets in and the shell
structure disappears. In "macroscopic" clusters (N > 37) an orientational
"melting" of only the outer shell is possible. The most stable clusters (having
both maximal lowest nonzero eigenfrequencies and maximal temperatures of total
melting) are that of completed crystal shells which are concentric groups of
nodes of 2D hexagonal lattice with a number of nodes placed in the center of
them. The study of different quantities shows that the melting temperature is a
nonmonotonic function of the number of particles in the system. The dynamical
equilibrium between "solidlike" and "orientationally disordered" forms of
clusters is considered.
