Сягло И.С. Теоретическая механика
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T = T
0
+
µV
2
2
+
~
P
0
~
V .
T = T
0
+
µV
2
2
.
T
0
E = E
0
+
µV
2
2
.
0 0
0
¤
¤
¤
¤
¤
¤
¤
¤
¤
¤
¤º
-S
S
S
S
S
S
S
S
S
S
So
~r
a
~r
a
0
~
l
0 0
0
m
a
m
a
~r
a
= ~r
a
0
+
~
l.
~r
a
~
M =
~
M
0
+
~
l ×
~
P .
~
M
0
~
P
~
M =
~
M
0
~r
a
= ~r
a
0
~
M =
~
M
0
+ µ
~
R ×
~
V .
~
M
0
t = 0
x = t
3
+ 2, y = 3 − t
3
x = 3 cos t, y = 3 −sin t
x = 2 cos 2t, y = 3 sin t
x = a cos t
2
, y = a sin t
2
, z = bt
XOY OX
αt (α = )
r = a(1 + t
2
), ϕ = t
r = 2a cos(kt/2), ϕ = kt/2
r = 2a cos
2
(ϕ/2)
r = exp(kϕ) ϕ = bt
r
α
l
~r
a
a
1, 2, . . . , N
3N
k
k
f
i
(~r
a
, t) = 0, i = 1, 2, . . . , k.
k
s = 3N −k
3N
s s
q
i
, (i = 1, 2, . . . , s)
q
i
~r
a
= ~r
a
(q
i
, t).
~v
a
=
˙
~r
a
=
X
i
∂~r
a
∂q
i
˙q
i
+
∂~r
a
∂t
.
~v
a
=
X
i
∂~r
a
∂q
i
˙
q
i
.
˙q
i
~
f
R
a
~
f
A
a
m
a
~w
a
=
~
f
A
a
+
~
f
R
a
.
~
f
A
a
+
~
f
R
a
= 0.