Abstract
The equations governing the time evolution of an ideal fluid in material coordinates are expressed as an unconstrained canonical Hamiltonian system. The incompressibility of the flow is consequent upon certain first integrals of the motion. The variable conjugate to the configuration field is not the usual linear momentum, but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure. The definition of the Hamiltonian involves a minimization with respect to this auxiliary field. The method of derivation may be generally applied to obtain unconstrained Hamiltonian descriptions of Lagrangian field equations subject to pointwise constraints.
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