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4 votes

Applications of Hamiltonian formalism to classical mechanics

E.T. Whittaker's A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge, multiple editions from 1904 onwards) provides applications, particularly to celestial mechanics. R. Abr …
Phil Harmsworth's user avatar
2 votes

Mechanical systems with their configuration space being a Lie group

If one dimensional $n$ body systems fit your definition of a "naturally occurring mechanical system", then the paper by M.A. Olshanetsky and A.M. Perelomov, "Completely Integrable Hamiltonian Systems …
Phil Harmsworth's user avatar