  We derive the dynamics of several rigid bodies of arbitrary shape in a
2-dimensional inviscid and incompressible fluid, whose vorticity field is given
by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive
the Hamiltonian formulation via symplectic reduction from a canonical
Hamiltonian system. The reduced system is described by a non-canonical
symplectic form, which has previously been derived for a single, circular disk
using heavy differential-geometric machinery in an infinite-dimensional
setting. In contrast, our derivation makes use of the fact that the dynamics of
the fluid, and thus the point vortex dynamics, is determined from first
principles. Using this knowledge we can directly determine the dynamics on the
reduced, finite-dimensional phase space, using only classical mechanics.
Furthermore, our approach easily handles several bodies of arbitrary shapes.
From the Hamiltonian description we derive a Lagrangian formulation, which
enables the system for variational time integrators. We briefly describe how to
implement such a numerical scheme and simulate different configurations for
validation.
