Any action for N interacting particles can be made invariant under gauged Galilean transformations, producing a simple Hamiltonian with first-class constraints.
Classical Mechanics without Absolute Space
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A relative mechanics with no absolute space is shown to be equivalent to Newtonian mechanics applied in a universe of zero net angular momentum. Closed spaces in General Relativity have no angular momentum and shrivel to one point as the mass-energy contained tends to zero, so obeying Mach's principle on the origin of inertia.
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Note About Relational Mechanics of General Forms of Particle Actions
Any action for N interacting particles can be made invariant under gauged Galilean transformations, producing a simple Hamiltonian with first-class constraints.