Лекции по векторному и тензорному анализу. Лосик М.В. - 53 стр.

UptoLike

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СГУ им. Чернышевского | Саратов

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Рубрика: 

(~e
u
, grad a
u
) + a
u
div ~e
u
=
1
H
u
∂a
u
∂u
+
a
u
H
u
H
v
H
w
∂(H
v
H
w
)
∂u
=
1
H
u
H
v
H
w
∂(a
u
H
v
H
w
)
∂u
.
u v w
(~e
v
, grad a
v
) + a
v
div ~e
v
=
1
H
u
H
v
H
w
∂(a
v
H
u
H
w
)
∂v
,
(~e
w
, grad a
w
) + a
w
div ~e
w
=
1
H
u
H
v
H
w
∂(a
w
H
u
H
v
)
∂w
.
div~a =
1
H
u
H
v
H
w
∂(a
u
H
v
H
w
)
∂u
+
∂(a
v
H
u
H
w
)
∂v
+
∂(a
w
H
u
H
v
)
∂w
.
[grad a
u
, ~e
u
] + a
u
rot ~e
u
.
[grad a
u
, ~e
u
] + a
u
rot ~e
u
= [grad a
u
, ~e
u
] +
a
u
H
u
[grad H
u
, ~e
u
] =
[grad a
u
+
a
u
H
u
~e
u
] =
1
H
u
[grad (a
u
H
u
), ~e
u
].
u v w
[grad a
v
, ~e
v
] + a
v
rot ~e
v
=
1
H
v
[grad (a
v
H
u
), ~e
v
],
[grad a
w
, ~e
w
] + a
w
rot ~e
w
=
1
H
w
[grad (a
w
H
w
), ~e
w
].
rot~a =
1
H
u
[grad (a
u
H
u
), ~e
u
]+
1
H
v
[grad (a
v
H
u
), ~e
v
] +
1
H
w
[grad (a
w
H
w
), ~e
w
].

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