|| (1.17) || . ||, || . (1.18) || ||
.
, - , q 1, ,
δ q 2 =0, ,δ q S =0,
, 
,
. (1.23)
Q 1 
. .
|| , || . ,
, (1.24)
|| , | ||
. (1.25)
ϳ (1.24) (1.17) Qj
,
, (1.26)
(n- )
(S-| ).
, , , , (1.22) . . , .
.
1.1. , l (. 1.8).
. г ' ( )
. (1.27)
|| | - . |'| . | | , |'| '.
) ³ , , q 1 =y ( . 1.8).
 ( ').
(1.25),
|
.
, q 1 =y,
Q 1 =P. (1.28)
, [H].
) , , x (q 1 =x). P. ', 
, 
.
, q 1 =x, , δ x . , , x. , ' (1.27),
|
|
|
.
.
, , | q 1 =x,
. (1.29)
|, [H].
(1.29) || , || (1.26)
,
.
, (), ( x ) , , . 1.8 1 2, . P , - P . , ' (1.27).
) , , S=0 1 M 0 1 M. 
. P, (1.19)
,
Q 1, ,
, (1.30)
.
) φ, . δφ φ. O 
( "-" φ ).
.
Q 1, q 1 =φ,
(1.31)
[H].
, 䳺 , . 㳿 .
). , , 䳺, , =-y ( "-" , , y=0 P, , ).
q 1 =y
.
) , x, (x=0), (. 1.8) l -
.
.
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S, S=0, , l .
.
.
) , φ, φ =0, l - .
,
.
|| || || | . || | , |'| || ||.
|
|
|
1.2. (. 1.9) l 1 l 2, M1 2 P 1 =m 1 g P 2 =m 2 g, . 0, - , ' . .
, xy ( z ). φ 1 φ 2 . . . xy
M 1 2 x 1, y 1, x 2, y 2. M 1 2 '
l 1 l 2. г ' :
1) 
,
2) 
,
, . x 1 x 2, x 1 y 1, y 2 y 1, x 2 y 2, φ 1 φ 2 .
Q 1 Q 2, q 1 = φ 1 q 2 = φ 2 .
. (1.26). P 1 P 2. ' , , ', . (1.26) :
,
.
( q 1u q 2 φ 1u φ 2)
,(1.32)
.
(1.32, )
ϳ (1.32), ||:
(1.33) 
. .
Q2. , 
, 
( ) (. 1.10). P2 ( P1 ).
dA2 2   , , . P2  .
δφ 2 Q 2 ,  .
|
P 1 : P 1
 .
,  ,  
|
Q 1. , 
, 
(. 1.11).
 |
1 2 , φ 2 . P 2
( m 1 m 2),
P 1 P 2
.
,
.
. P 1 P 2, , . (1.22) .
, P 1 P 2 
, (. 1.12).
P 1 Δ1
.
|
|
|
|
1.3. P, , (. 1.13). .
. x - . , ( 0 x) (. 1.13, ).
, q 1 = x, , .
. , . , x (. 1.13, ), F .
dx ( x )
||,
.
|| (.1.13, )
,
.
, || ,
. (1.34)
. F , , . (1.22)
.
㳿 . F P (x) (x=0).
()=- Px,
.
( x, F dx ).
,(1.35)
.
.
O x 1 , (. 1.14).
, q 1 = x 1, .
.
|
dx
.
. (1.36)
. 㳿 , F P (x 1 ≠ 0) (x 1 = 0). Px 1. 
.
. (1.37)
.
dz (1.34) (1.36), , Q 1 . 㳿 (1.35), ( (1.37)).
1.4. , . 1.15. P 1 = m 1 g, P 2 = m 2 g, P 3 = m 3 g 1, 2, 3.
, || ||, || . , , .
, q 1, q 2, q 3 (. 1.15, ). , , . .
|
|
|
x 1 ≠ 0, x 2 ≠ 0, x 3 ≠ 0 (. 1.15, )
. , , , .
|| (. 1.15, ) | ||
, 
, 
. (1.38)
 |
|| (. 1,15, ), :
, 
, 
. (1.39)
Q 3. (. 1.15, ), 1 2 , d x 3 ( , x 3). P 3 F 3. 
, 
.
Q 3,
. (1.40)
Q 2. , x 2 δ x 2, (. 1.15, ). F 2, F 3 P 2. δ A 2 δ x 1=0, 
, δ x 3=0
.
ϳ|| , ||,
.(1.41)
Q 1 
, δ x 2=0, δ x 3=0 (. 1.15, ).
,
| | (1.38), (1.39), ||
.
Q 1 δ x 1
. (1.42)
. 㳿 . ' 3, , 㳿
. (1.43)
|| (1.22)
, 
, 
.
,
,
.
, |, || .
|| 111 1.5.
 |
- , . 1.16 . : =r =l, P, 䳺 , M, . 0 , G. .
| .
(0) 0, , , 
. ',
(1.44)
' ', , , () ' (1.44). .
, q=xA,
(1.45)
=q, x B = q, j =q.
, q 1 =φ, , - ( . 1.16). 0, , q 1 =φ ':
, 
, 
, 
, 
,
. (1.46)
, q 1 =φ.
, , . dz , , ' , 0 (X 0, Y 0) G 0, , N .
|
|
|
. (1.47)
(-) , M P 
. (1.47) ' (1.46) 
. (1.46)
.
ϳ δ x B (1.47)
.
, Q 1, q=j,
. (1.48)
, q=x A, (1.47) 
, ' (1.45)
,
.
.1.17 ( x A 0 0 1)
  ,
|
;
,
.
ϳ δx δφ (1.47),
.
, , q=x A,
. (1.49)
