Calculus of Variations: Δ-Variation vs. δ- Variation

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Does anybody know what is the formal difference between the Δ -variation and the δ- variation is?

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!
 
on Phys.org
Do you have any specific references for these notations?
 

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