Сягло И.С. Теоретическая механика
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~r = ~r
0
+
~
V t, t = t
0
.
~r
~v = ~v
0
+
~
V .
~v ~v
0
~w = ~w
0
m~w
0
=
~
f.
d
dt
(m~v) =
~
f.
~p = m~v
d~p
dt
=
˙
~p =
~
f.
~r
˙
~
M =
~
K,
~
M = [~r×~p]
~
K = [~r ×
~
f]
d~r
d~r
dt
= ~v
d(
mv
2
2
) = dT =
~
fd~r.
T =
1
2
mv
2
~
fd~r d~r
~
fd~r = f
x
dx + f
y
dy + f
z
dz = −dU,
E = T + U = .
f
x
= −
∂f
∂x
, f
y
= −
∂f
∂y
, f
z
= −
∂f
∂z
.
m
a
~w
a
=
~
f
ext
a
+
X
b6=a
~
f
int
ab
.
a, b
~
f
int
ba
a
b
d
dt
X
a
(m
a
~v
a
) =
X
a
~
f
ext
a
+
X
a
X
b6=a
~
f
int
ab
.
~
P =
X
a
(m
a
~v
a
) =
X
a
~p
a
d
~
P
dt
=
X
a
~
f
ext
a
.
d
~
M
a
dt
= ~r
a
×
~
f
ext
a
+
X
b6=a
~r
a
×
~
f
int
ba
.
d
~
M
dt
=
~
K
ext
,
~
M =
X
a
~
M
a
=
X
a
~r
a
× ~p
a
,
~
K
ext
=
X
a
~
K
ext
a
=
X
a
~r
a
×
~
f
ext
a
,
~
M
~
K
ext
d(
X
a
m
a
v
2
a
2
) = dT =
X
a
~
f
ext
a
d~r
a
+
X
a
X
b6=a
~
f
int
ba
d~r,
T =
P
a
1
2
m
a
v
2
a
E = T + U(~r
a
) = .
a
f
xa
= −
∂f
∂x
a
, f
ya
= −
∂f
∂y
a
, f
za
= −
∂f
∂z
a
,
a
~
V
~
V
a
~v
a
= ~v
0
a
+
~
V .
~
P =
~
P
0
+ µ
~
V , µ =
X
a
m
a
.
~
P
0
~
P
0
~
V =
1
µ
X
a
m
a
~v
a
=
d
dt
(
1
µ
X
a
m
a
~r
a
).
~
R =
1
µ
X
a
m
a
~r
a
.
~
R
~
P = µ
~
V ,
µ
˙
~
V =
X
a
~
f
ext
a
.