Viscosity may be added back by using Langevin dynamics instead of Hamiltonian dynamics and choosing an appropriate damping constant for the particular solvent.
Luke's Lagrangian formulation can also be recast into a Hamiltonian formulation in terms of the surface elevation and velocity potential at the free surface.
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-- The first lead sentence should define what it is--> developed in 1959 by Richard Arnowitt, Stanley Deser and Charles W. Misner is a Hamiltonian formulation of general relativity.
In mathematical physics, Liouville made two fundamental contributions: the Sturm–Liouville theory, which was joint work with Charles François Sturm, and is now a standard procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact (also known as Liouville's theorem) that time evolution is measure preserving for a Hamiltonian system.
The most commonly used tools are Lagrangians and Hamiltonians and are used to derive the Einstein field equations.