# nLab Euler-Lagrange equation

### Context

#### Variational calculus

variational calculus

# Contents

## Idea

In variational calculus the Euler-Lagrange equations of a nonlinear functional arising from transgression of a local Lagrangian density characterize the extrema of that functional, hence its critical locus (the “shell”).

This originates from and is mainly used in physics, specifically in Lagrangian field theory, where the functional in question is the action functional of a physical system, and where its critical points encode the physically realized field histories by the principle of extremal action.

## References

Revised on January 7, 2018 05:09:42 by Urs Schreiber (84.63.72.123)