Методы математической физики - 28 стр.

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ЯрГУ | Ярославль

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E
k
=
1
2
`
Z
0
ρ(x) [u
t
(x, t)]
2
dx .
t = t
0
u(x, t
0
) = u
0
(x)
u(x, 0) = 0 u(x, t
0
) = u
0
(x)
dx
T
0
u
x
(x+dx, t)−T
0
u
x
(x, t) = T
0
u
x
(x + dx, t) − u
x
(x, t)
dx
dx = T
0
u
xx
dx .
dt u
t
dt
dt
dA =
`
Z
0
T
0
u
xx
u
t
dx
dt .
`
Z
0
u
xx
u
t
dx =
`
Z
0
u
t
∂
∂x
µ
∂u
∂x
dx = u
t
u
x
¯
¯
¯
¯
`
0
−
`
Z
0
u
x
u
xt
dx =
= u
t
u
x
¯
¯
¯
¯
`
0
−
`
Z
0
u
x
∂
∂t
u
x
dx = u
t
u
x
¯
¯
¯
¯
`
0
−
1
2
d
dt
`
Z
0
(u
x
)
2
dx .
T
0
u
x
|
0
x = 0 u
t
dt
x = 0 dt
x = `
dA =
−
1
2
d
dt
`
Z
0
T
0
(u
x
)
2
dx
dt = −dE
p
.

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