Physics Help Forum Trying to get my head around the Lagrangian

 Feb 5th 2019, 09:10 PM #1 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 550 Trying to get my head around the Lagrangian In the calculus of variation they set up the problem as action S $S = \int^a_b f [ y(x), y^{ \prime } (x), x ] dx$ where $Y(x) = y(x) + \eta (x)$ and $\eta (x_1)=\eta (x_2) = 0$ In the case of finding the shortest distance between two points this makes sense but in the case of finding the path of least time as in a roller coaster shaped like a e Brachistochrone I am not getting why the case of $\eta (x_1)=\eta (x_2) = 0$ applies? How does this work in that case? __________________ Burn those raisin muffins. Burn 'em all I say.