Лекции по векторному и тензорному анализу. Лосик М.В. - 7 стр.

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СГУ им. Чернышевского | Саратов

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Рубрика: 

d
dt
(~a(t) +
~
b(t))
(t
0
) = ~a
0
(t
0
) +
~
b
0
(t
0
)
d
dt
(k(t)~a(t))
(t
0
) = k
0
(t
0
)~a(t
0
) + k(t
0
)~a
0
(t
0
)
d
dt
(~a(t),
~
b(t))
(t
0
) = (~a
0
(t
0
),
~
b(t
0
)) + (~a(t
0
),
~
b
0
(t
0
))
d
dt
[~a(t),
~
b(t)]
(t
0
) = [~a
0
(t
0
),
~
b(t
0
)] + [~a(t
0
),
~
b
0
(t
0
)]
d
dt
(~a(t),
~
b(t),~c(t))
(t
0
) = (~a
0
(t
0
),
~
b(t
0
),~c(t
0
)) + (~a(t
0
),
~
b
0
(t
0
),~c(t
0
)) +
(~a(t
0
),
~
b(t
0
),~c
0
(t
0
))
u(t)
t
0
~a(u) u
0
=
u(t
0
) ~a(u(t)) t
0
d
dt
(~a(u(t))
(t
0
) = ~a
0
(u
0
)u
0
(t
0
).
~a(u(t))
~a(u(t))(a
x
(u(t)), a
y
(u(t)), a
z
(u(t))) a
x
(u) a
y
(u) a
z
(u)
~a(u)
O ~r(t)
~r(t) O
~r(t)
~r(t) ~r(t)
~r(t) ~r = ~r(t)
t

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