Методы математической физики - 27 стр.

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x
2
Z
x
1
ρ(x) [u
t
(x, t
2
) u
t
(x, t
1
)] dx =
=
t
2
Z
t
1
T
0
[u
x
(x
2
, t) u
x
(x
1
, t)] dt +
t
2
Z
t
1
f
0
(t) dt .
x
1
x
0
0 x
2
x
0
+0
t
2
Z
t
1
{T
0
[u
x
(x
0
+ 0, t) u
x
(x
0
0, t)] + f
0
(t)}dt = 0 ,
u
x
(x
0
+ 0, t) u
x
(x
0
0, t) =
1
T
0
f
0
(t) .
u
x
(0, `)
(0, x
0
) (x
0
, `) u
x
u(x
0
+ 0, t) = u(x
0
0, t) ,
E = E
k
+E
p
dx dm =
ρ dx
1
2
dm v
2
=
1
2
ρ(x) dx (u
t
)
2
.