  The dynamics of N point vortices in a fluid is described by the
Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable
Hamiltonian system for N=2 or 3 but chaotic dynamics for N>3. Here we consider
a generalization of the HK equations to describe the dynamics of magnetic
vortices within a collective-coordinate approximation. In particular, we
analyze in detail the dynamics of a system of three magnetic vortices by a
suitable generalization of the solution for three point vortices in an ordinary
fluid obtained by Groebli more than a century ago. The significance of our
results for the dynamics of ferromagnetic elements is briefly discussed.
