  Starting from the equations of rotational hydrodynamics we study the
macroscopic behaviour of a trapped Bose-Einstein condensate containing a large
number of vortices. The stationary configurations of the system, the
frequencies of the collective excitations and the expansion of the condensate
are investigated as a function of the angular velocity of the vortex lattice.
The time evolution of the condensate and of the lattice geometry induced by a
sudden deformation of the trap is also discussed and compared with the recent
experimental results of P. Engels et al., Phys. Rev. Lett. 89, 100403 (2002).
