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The Hamiltonian structures of the incompressible ideal fluid, includingentropy advection, and magnetohydrodynamics are investigated by making use ofDirac's theory of constrained Hamiltonian systems. A Dirac bracket for thesesystems is constructed by assuming a primary constraint of constant density.The resulting bracket is seen to naturally project onto solenoidal velocityfields.

On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac's theory of constraints