Euler-Lagrange equation

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English[edit]

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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)

  1. (mechanics, analytical mechanics) A differential equation which describes a function \mathbf{q}(t) which describes a stationary point of a functional, S(\mathbf{q}) = \int L(t, \mathbf{q}(t), \mathbf{\dot 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 {\partial L \over \partial \mathbf{q}} = {d \over dt} {\partial L \over \partial \mathbf{\dot 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.