English Dictionary

Euler-Lagrange equation

名詞

(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.

日本語の意味

解析力学において、作用（ラグランジアンを用いた積分表現の物理量）が定常値（極値）となる条件を示す微分方程式。 / 変分法に基づいて、ラグランジアンから導出され、粒子や物体の運動軌跡が最小作用の原理を満たすように記述する方程式。

The Euler-Lagrange equation determines the equations of motion for a system described by a given Lagrangian.

オイラー＝ラグランジュ方程式は、与えられたラグランジアンで記述される系の運動方程式を決定する。

意味（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)=∫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 equations （ plural ）