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Euler-Lagrange equation

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


Euler-Lagrange equation (plural Euler-Lagrange equations)

  1. (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.