Euler-Lagrange equation (English, noun)
expansion: Euler-Lagrange equation (plural Euler-Lagrange equations)
Senses:
topics: engineering
mechanical-engineering
mechanics
natural-sciences
physical-sciences
qualifier: analytical mechanics
glosses: A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action.
Forms:
form: Euler-Lagrange equations
tags: plural