## Equilibrium with Lagrangians

So let's say we have a mechanical system described by some Lagrangian $L=L(q_i,\dot{q}_i)$, where the qi'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.
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 Recognitions: Gold Member What is the condition for equilibrium in newtonian mechanics?

 Quote by Jorriss What is the condition for equilibrium in newtonian mechanics?
[tex]\frac{\partial V}{\partial x}=0./tex]. I'm having trouble connecting this to Lagrangians though....