A Lagrangian and canonical formalism in the hydrodynamics of an incompressible fluid

The geometrical formulation of the variational principle in the hydrodynamics of an incompressible fluid is given. The Lagrange-Euler equations in the language of differential forms are formulated. The canonical formalism in the hydrodynamics in the general framework of multi-phase spaces (4]) is considered and the construction of the phase space for hydrodynamics is given.