Virtual differentials approach to Euler-Lagrange eqn - necessary?

fgarnold

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?
Thx.

jasonRF

There is nothing wrong with skipping this if it is your first time through Lagrangian/Hamiltonian dynamics. When I took intermediate mechanics we did not cover the virtual displacement/work stuff. We used what was the standard book at the time - Marion and Thornton - which didn't even cover it. However, the honors version of the course did cover it. I have never learned it, but recently have started to re-learn mechanics just for fun and plan on going through the virtual displacement stuff this time around. It appears that it can be a useful approach to getting a nice physical picture of the forces associated with constraints on a system.

Perhaps one of the many people around here that know much more about this than I do will chime in.

Enjoy,

jason