Euler-Lagrange equation

English

Etymology

Named after the Swiss mathematician and physicist Template:W (1707–1783), and the Italian-born French mathematician and astronomer Template:W (1736–1813).

Noun

1. Template:Lb A differential equation which describes a function $𝐪(t)$ which describes a stationary point of a functional, $S(𝐪)=\int L(t,𝐪(t),\dot{𝐪}(t))dt$, which represents the action of $𝐪(t)$, with $L$ representing the Lagrangian. The said equation (found through the calculus of variations) is $\frac{\partial L}{\partial 𝐪}=\frac{d}{dt}\frac{\partial L}{\partial \dot{𝐪}}$ and its solution for $𝐪(t)$ represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action.