What does virtual displacement mean in Lagrange equations?

[wormhole]

hey, all

i'm now studiynd analytical mechanics and the subject is Langrange equations. What i can't grasp is the meaning of virtual displacement term.

The formal definition says that:
it's a small displacement of particle with agreement to constraints in such a way that no time passes and uknown forces don't change. The displacement itself has no relation to actual particle path.

there are two places where i get confused:

1) the definition itself when it says that "no time passes"

2) the actual calculation of virtual displacement where i don't understand the reason why the differentiation is done only with respect to generalized coordinates (q) and time is ignored...

Xj - cartezian coordinates
delta(Xj) - virtual displacement of Xj
Qk - generalized coordinates

 

[turin]

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