What Does Stationarity Mean in the Context of the Euler-Lagrange Equations?

[TheDoorsOfMe]

What does it mean when it says "the integral of the Lagrange equation is stationary for the path followed by the particle"?

 

[TheDoorsOfMe]

Is it just saying that the integral is a constant?

 

[MaceLee]

I would assume it means that the action $$s = \int Ldt$$ is a stationary point (i.e. a min most likely as the action is minimised in real systems).

You might want to wait for some confirmation however as I haven't studied Lagrangian mechanics in too much depth.

 

[Cyosis]

A stationary point is a point where the derivative of a function is 0. To obtain the Euler-Lagrange equations we set the variation of the action to 0.