最終更新日：2024/08/03
(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.
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Euler-Lagrange equation
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元となった辞書の項目
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.
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.
