The Lagrangian Method - Harvard University
scholar.harvard.edu › files › david-morin6.1. THE EULER-LAGRANGE EQUATIONS VI-3 There are two variables here, x and µ. As mentioned above, the nice thing about the La-grangian method is that we can just use eq. (6.3) twice, once with x and once with µ. So the two Euler-Lagrange equations are d dt ‡ @L @x_ · = @L @x =) mx˜ = m(‘ + x)µ_2 + mgcosµ ¡ kx; (6.12) and d dt ‡ @L @µ_ · = @L @µ =) d dt ¡ m(‘ + x)2µ_ ¢