Does partial L/partial q_i = 0 give equilibrium configurations?

[dEdt]

So let's say we have a mechanical system described by some Lagrangian $L=L(q_i,\dot{q}_i)$, where the q_i's are the generalized coordinates of the system. Does the condition
$$\frac{\partial L}{\partial q_i}=0$$
give the equilibrium configurations of the system? Intuitively it seems so, but I can't prove it.

 

[Jorriss]

What is the condition for equilibrium in Newtonian mechanics?

 

[dEdt]

What is the condition for equilibrium in Newtonian mechanics?

$$\frac{\partial V}{\partial x}=0./tex]. I'm having trouble connecting this to Lagrangians though...$$