Last Updated：2025/11/29
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The Euler-Lagrange equation determines the equations of motion for a system described by a given Lagrangian.
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The Euler-Lagrange equation determines the equations of motion for a system described by a given Lagrangian.
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Related words
Euler-Lagrange equation
Noun
(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.
Japanese Meaning
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。
Related Words
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