What is wrong with the simple localised geometric derivation of the Euler Lagrange equation. As opposed to the standard derivation that Lagrange provided. Sorry I haven't mastered writing mathematically using latex. I will have a look at this over the next few days. More clarification. I seen a simple derivation that looked at the change in position of a length of rope at a single point and the increase in the gradient to the left and decrease of the gradient to the right at the same point, adding up these variations gave a neat and easy derivation of euler lagrange and made the terms make sense What's wrong get with the simple euler derivation. Sorry may have to rewrite this once I have practiced latex.