Euler-Lagrange equation

名词noun

1. 1(mechanics, analytical mechanics) A differential equation which describes a function 𝐪(t) which describes a stationary point of a functional, S(𝐪)=∫L(t,𝐪(t),𝐪˙(t))dt, which represents the action of 𝐪(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L∂𝐪=ddt∂L∂𝐪˙ and its solution for 𝐪(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action.