The Euler-Lagrange differential equation is the fundamental equation of calculus of variations. It states that if J is defined by an integral of the form J = integral f(t, y, y^.) d t, where y^. congruent (d y)/(d t), then J has a stationary value if the Euler-Lagrange differential equation (df)/(dy) - d/(d t)((df)/(dy^.)) = 0 is satisfied.

Beltrami identity | brachistochrone problem | calculus of variations | Euler-Lagrange derivative | functional derivative | variation

Joseph-Louis Lagrange | Leonhard Euler