Сягло И.С. Теоретическая механика
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X, Y, Z
p
X
=
X
a
~p
a
∂~r
a
∂X
, p
Y
=
X
a
~p
a
∂~r
a
∂Y
, p
Z
=
X
a
~p
a
∂~r
a
∂Z
.
OX ∆X ∆~r
a
=
~
i∆X
∂~r
a
∂X
=
~
i, p
X
=
X
a
~p
a
~
i =
~
P
~
i = P
X
.
p
X
OX
p
Y
p
Z
~
P
ϕ
ϕ
~
M
m
x = ξη, y =
1
2
(ξ
2
− η
2
).
L =
1
2
m ˙x
2
+
1
2
ma
2
˙y
2
+ c ˙x ˙y −
1
2
kx
2
L =
1
2
m( ˙x
2
+ ˙y
2
) + c(x ˙y − y ˙x) −
1
2
k(x
2
+ y
2
)
L =
1
2
m( ˙x
2
+ ˙y
2
) − eϕ −
e
c
~
A~v
L = −mc
2
r
1 −
v
2
c
2
m
1
|
m
1
m
2
l
|
y
l
1
m
1
l
2
m
2
l =
sin(Ωt)
m
r Ω
|
¸
m
r
|
y
l
1
m
1
l
2
m
2
m
Ω
α
a
m
k
1
, k
2
n
|
k
1
k
2m
α
A B
m
R
α
OX
L =
1
2
m
1
v
2
1
+
1
2
m
2
v
2
2
− U(|~r
2
−~r
1
|).
~
R =
m
1
~r
1
+ m
2
~r
2
m
1
+ m
2
= 0.
~r
~r = ~r
2
−~r
1
.
~r
1
~r
2
~r
~r
1
= −
m
2
~r
m
1
+ m
2
, ~r
2
=
m
1
~r
m
1
+ m
2
.
~r ~v
1
~v
2
~v =
˙
~r
m =
m
1
m
2
m
1
+ m
2
.
~r
L =
1
2
mv
2
− U(r) .
m
~
f = − U = −
dU
dr
~r
r
.
m
m
1
~r
1
= 0 ~r
2
= ~r m = m
2
~
M
~
M = m [~r ×~v] ~r ~v
~
M