Euler-Lagrange equation
（ plural ）
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(mechanics, analytical mechanics) 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.
Euler-Lagrange equation
The Euler-Lagrange equation determines the equations of motion for a system described by a given Lagrangian.
The Euler-Lagrange equation determines the equations of motion for a system described by a given Lagrangian.
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