# Euler-Lagrange equation

(Redirected from Euler–Lagrange equation)

## EnglishEdit

### EtymologyEdit

Named after the Swiss mathematician and physicist Leonhard Euler (1707–1783), and the Italian-born French mathematician and astronomer Joseph Louis Lagrange (1736–1813).

### NounEdit

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