The usual way to derive Hamilton's equations is to perform Legendre transformation of the Lagrangian and then use the stationarity principle. However, this procedure seems a little artificial to me from a "physical" perspective, because in this case the integrand of the action is basically a rewritten Lagrangian, and it appears to be impossible to conceive the former without considering the latter first. Lagrange's approach, on the other hand, is fully self-sufficient. My question is, is there some way to derive Hamilton's equations from a number of general ideas completely independently?
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