# Euler–Lagrange equation

Definition from Wiktionary, the free dictionary

## English[edit]

### Etymology[edit]

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

### Noun[edit]

**Euler–Lagrange equation** (*plural* **Euler–Lagrange equations**)

- (mechanics, analytical mechanics) A differential equation which describes a function which describes a stationary point of a functional, , which represents the action of , with representing the Lagrangian. The said equation (found through the calculus of variations) is and its solution for represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action.