最終更新日：2025/11/29
(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.
音声機能が動作しない場合はこちらをご確認ください
正解を見る
Euler-Lagrange equation
編集履歴（0）
元となった辞書の項目
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。
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.
（ plural ）
