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They seem to be used interchangeably. I read somewhere that Δ = δ + Δt*(d/dt) but I have no idea how that is arrived at.

I know that the δ- variation is employed in the calculus of variations and the Δ is used to derive the principle of least action. As I previously understood it, the Δ referred to a "change in" some quantity and the δ corresponds to a inexact differential, but how are they defined in this context of calculus of variations (and the principle of least action)?

Any further insight would be greatly appreciated!!