This command should have been in Physics on day one. Being more familiar with functional differentiation, and Physics:-Fundiff was the first Physics command that ever existed, I postponed writing LagrangeEquations year after year. In general, however, functional differentiation is seen as a more advanced topic. So there is now a new command, Physics:-LagrangeEquations, taking advantage of functional differentiation on background, and distributed for everybody using Maple 2022.2 within the Maplesoft Physics Updates. This is the first version of its help page.
Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft