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

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The discussion clarifies that in the context of the Euler-Lagrange equations, "stationarity" refers to the condition where the action, defined as s = ∫ L dt, is at a stationary point, typically a minimum. This is established by setting the variation of the action to zero, which leads to the derivation of the Euler-Lagrange equations. The concept emphasizes that the integral of the Lagrangian function L is not constant but rather optimized along the path taken by the particle.

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What does it mean when it says "the integral of the Lagrange equation is stationary for the path followed by the particle"?
 
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Is it just saying that the integral is a constant?
 
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.
 
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.
 

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