Virtual differentials approach to Euler-Lagrange eqn - necessary?
I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for E-L. The whole notion of, and justification for, using 'pretend' differentials over a time interval of zero just isn't sinking in with me. And I notice that not all textbook authors invoke it, so I'm wondering how necessary it is, given that Hamilton's principle gets us to E-L just fine.
So, will I ever need this virtual displacement/work approach for something other than a route to E-L, or can I safely wave bye-bye to it?