# Difference between δ and ∆ variation?

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## Main Question or Discussion Point

what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?

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dextercioby
Homework Helper
Can you point to a reference (book, website) for the „∆-variation”?

vanhees71
what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?
Typically, ##\Delta## is not a variation but an ##\textit{actual}## difference, e.g. ##\Delta f= f(x_2)-f(x_1)##.
Lagrange introduced a special symbol for the process of variation, which he called ##\delta##. Although variation is an infinitesimal change in a similar manner to the ##d## in ##dy## from calculus, it is not the same. It is not an actual infinitesimal change but a virtual change, like a mathematical experiment of some kind, where you're saying to yourself: suppose i were to move "so and so" (some object say) a little bit in that direction, how would "such and such" change. The object isn't actually moving there but you're asking yourself what if it was to move there. Do you see the difference?

jtbell
Mentor
what is the difference between δ- variation and ∆-variation
Typically,
Which is why it is important to give the sourc(es) of where you saw δ-variation and ∆-variation. You can't depend on all textbooks and web sites using the same standard definition.

PhysicsExplorer
what is the difference between δ- variation and ∆-variation in variational principle, used in classical mechanics?

Can't speak for anyone else, but I reserve $$\Delta$$ for changes in the uncertainty, say between time and energy

$$\Delta E \Delta t$$

Technically speaking, there is no difference between this above and

$$\delta E \delta t$$

You could reserve the small delta notation only for small/infinitesimal changes in a system.