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Assuming two given time-independent Newtonian systems of the same dimensions, each of the two systems including its own given set of time-independent generalized Poisson Brackets and a time-independent Hamiltonian, there always locally exists a one-to-one function from variables of one system to the variables of the other system, such that it transforms equations of motion of the first system into equations of motion of the second system, the Poisson Brackets of the first system into the Poisson Brackets of the second system, and the Hamiltonian of the first system into the Hamiltonian of the second system.

One interpretation of the above is that all mechanical systems of the same dimension are locally identical, and the variety of systems we observe in the real world is due only to the fact that we use different systems of variables when making our observations.


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