The $\xi$-compensator method in hydrodynamics

Some aspects of the Hamiltonian formalism for the dynamics of an irdaomogeneous incompressible fluid relating to methods of calculating the Poisson brackets in definite problems are considered. As an example, the Poisson bracket of local velocities is calculated. The computational technique is based on the method of $\xi$-compensators. It is shown that a previously established expression for this Poisson bracket can indeed be obtained from the general expression for $\{F,G\}$ by the $\xi$-compensator method.