Lagrange's Equations: Know When to Use Each

[Isaac0427]

Lagrange's equation of the first kind gives us ∂L/∂q-(d/dt)(∂L/∂q^.)=Q and the Euler-Lagrange equations give us ∂L/∂q-(d/dt)(∂L/∂q^.)=0 (I know the equations are not perfectly written but you get the point). How do you know which one to use?

 

[Incand]

The second one only account for conservative forces. When you have forces that ain't conservative the right side is the sum of these forces.
(Assuming I understood your notation correctly, been a long time since I did this)

Edit: maybe someone else can give their input, after checking it again I suspect I may have give you a (way) too simplistic answer.