The Hamiltonian formulation of classical mechanics is such a beautiful way of describing classical motion compared to the Newtonian formulation. See Laundau & Lifschitz book 1! All the Hamilton-Jacobi equations are derived from observing symmetries in space time, even Newton’s 3 principles are derived (F=ma an the rest). All of this has the added benefit of transposing well into quantum mechanics, where forces are anyway replaced with hamiltonians.
For fluid mechanics I don’t know if Hamiltonians are the right formulation.
For fluid mechanics I don’t know if Hamiltonians are the right formulation.