Euler-Lagrange equation

noun

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.

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Meanings

nounEuler-Lagrange equation (plural Euler-Lagrange equations)

plural Euler-Lagrange equations

  1. analytical mechanicsengineeringA 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.

Origin

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

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Cite this entry
APA

Euler-Lagrange equation. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Euler-Lagrange%20equation

MLA

“Euler-Lagrange equation.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Euler-Lagrange%20equation. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Euler-Lagrange equation,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Euler-Lagrange%20equation.

Source: Euler-Lagrange equation on Wiktionary, CC BY-SA 4.0.