.


:




:

































 

 

 

 





 

. , , , . , , , .

, , .

 

 

137.1.

 

, (. 14.7), : = β1, = β2, = β3, D = β4 (. 14.4).

.

pi qi, (. . 14.4) , ( - ; ):

, (14.91)

s1 s2 , .

1. n = 4, k = 3, r = 1.

2. ( ).

β1' + β2' + β3' + β4' 3600 = 0.

, r = 1.

3. , βi. ,

11 = +1, 21 = +1, 31 = +1, 41 = +1.

aij qi ( 14.5).

. 14.7. .

 

14.4

pi qi
β1 800 16' 44,3" 0,221 4,520
β2 910 45' 00,7" 0,459 2,181
β3 690 25' 56,8" 0,473 2,113
β4 1180 32' 25,2" 0,225 4,452

 

14.5

,

i→ j↓        
  + 1 + 1 + 1 + 1
i 0,221 0,459 0,473 0,225
qi 4,520 2,181 2,113 4,452

 

W1 = [ βi ] 3600 = 3600 00' 07,0" 3600 = + 7".

4. bjj ( ):

, (14.92)

..

. (14.93)

, aij qi, 13,266 k1 + 7 = 0, k1 = - 0,528.

5.

(14.94)

( ):

(14.94): ! ( ). 0,1" .

, . , . , - : . , . , . . , . .

6. :

β1' = 80 16' 44,3" 2,4" = 80 16' 41,9"; β2' = 91 45' 00,7" 1,1" = 91 44' 59,6";

β3' = 69 25' 56,8" 1,2" = 69 25' 55,6"; β4' = 118 32' 25,2" 2,4" = 181 32' 22,8".

: (14.91) ! ( ).

, , .. .

 

 

137.2.

 

1, 2, 3 4 (. 14.8). 9 , . 10, 20 30. . 14.6 , :

 

. 14.8. .

14.6

h, s , p - q -
  +3586 0,84 2,38 0,42
  +2841 1,36 1,47 0,68
  -752 2,15 0,93 1,08
  -1243 0,78 2,56 0,39
  +509 2,63 0,76 1,32
  +5338 2,05 0,98 1,03
  -5863 3,02 0,66 1,51
  +4639 3,44 0,58 1,72
  -3024 2,38 0,84 1,19

se = 2

 

, (14.95)

.

1. n = 9, k = 4, r = 5.

2. r = 5 :

1. h1' + h3' h2' = 0

2. h4' + h5' h3' = 0

3. h6' + h7' + h5' = 0 (14.96)

4. h7' + h8' h9' (HP30 HP20) = 0

5. h1' + h4' + h8' (HP30 HP10) = 0

3. , hi. aij :

11 = +1; 31 = +1; 21 = - 1;

42 = +1; 52 = +1; 32 = - 1;

63 = + 1; 73 = + 1; 53 = + 1;

74 = + 1; 84 = + 1; 94 = - 1;

15 = + 1; 45 = + 1; 85 = +1.

aij qi (. 14.7).

14.7

i j↓                  
  +1 -1 +1            
      -1 +1 +1        
          +1 +1 +1    
              +1 +1 -1
  +1     +1       +1  
qi 0,42 0,68 1,08 0,39 1,32 1,03 1,51 1,72 1,19

( ), (14.96) hi :

W1 = h1 + h3 h2 = 3586 752 2841 = - 7 ;

W2 = h4 + h5 h3 = -1243 + 509 (-752) = +18 ;

W3 = h6 + h7 + h5 = 5338 5863 + 509 = - 16 ;

W4 = h7 + h8 h9 (HP30 HP20) = - 5863 + 4639 (-3024) 1794 = +6 ;

W5 = h1 + h4 + h8 (HP30 HP10) = 3586 1243 + 4639 6965 = +17 .

4. (14.88) bjj :

(14.97)

aij qi (14.97) :

1. 2,18 k1 1,08 k2 + 0,42 k5 7 = 0;

2. -1,08 k1 + 2,79 k2 + 1,32 k3 + 0,39 k5 + 18 = 0;

3. 1,32 k2 + 3,86 k3 + 1,51 k4 16 = 0; (14.98)

4. 1,51 k3 + 4,42 k4 + 1,72 k5 + 6 = 0;

5. 0,42 k1 + 0,39 k2 + 1,72 k4 + 2,53 k5 + 17 = 0.

(14.98) :

k1 = - 2,137; k2 = - 11,552; k3 = +9,606; k4 = -3,882; k5 = -1,945.

(14.98):

1. 2,18 (-2,137) 1,08 (-11,552) + 0,42 (-1,945) 7 = + 0,001;

2. -1,08(-2,137) + 2,79(-11,552) + 1,32(+9,606) + 0,39(-1,945) + 18 = -0,001;

3. 1,32(-11,552) + 3,86(+9,606) + 1,51(-3,882) 16 = - 0,031;

4. 1,51(+9,606) + 4,42(-3,882) + 1,72(-1,945) + 6 = +0,001;

5. 0,42(-2,137) + 0,39(-11,552) + 1,72(-3,882) + 2,53(-1,945) + 17 = -0,001.

3. . . , 1 , .

5. vi, (14.86) . 14.7:

(14.99)

qi, aij kj (14.99) :

1. v1 = 0,42 ∙1∙ (-2,137) + 0,42∙1∙ (-1,945) = - 1,714 = - 2 ;

2. v2 = 0,68 ∙ (-1) ∙ (-2,137) = + 1,453 = + 1 ;

3. v3 = 1,08 ∙ 1 ∙ (2,137) + 1,08 ∙ (-1) ∙ (-11,552) = +10,168 = + 10 ;

4. v4 = 0,39 ∙ 1 ∙ (-11,552) + 0,39 ∙1 ∙ (-1,945) = - 5,264 = - 5 ;

5. v5 = 1,32 ∙1∙ (-11,552) + 1,32 ∙ 1 ∙ (+9,606) = - 2,569 = - 3 ;

6. v6 = 1,03 ∙1 ∙ (+9,606) = + 9,894 = + 10 ;

7. v7 = 1,51 ∙ 1 ∙ (+9,606) + 1,51 ∙1 ∙ (-3,882) = + 8,643 = + 9 ;

8. v8 = 1,72 ∙ 1 ∙ (-3,882) + 1,72 ∙ 1 ∙ (-1,945) = - 10,022 = - 10 ;

9. v9 = 1,19 ∙ (-1) ∙ (-3,882) = + 4,620 = + 5 .

(14.96), ( ):

1. v1 + v3 v2 = - 2 + 10 1 = + 7 (= - W1);

2. v4 + v5 v3 = - 5 3 10 = - 18 (= - W2);

3. v6 + v7 + v5 = +10 + 9 3 = + 16 (= - W3);

4. v7 + v8 v9 = + 9 10 5 = - 6 (= - W4);

5. v1 + v4 + v8 = - 2 5 10 = - 17 (= - W5).

6. (14.96):

h1 '= + 3586 2 = + 3584 ;

h2 '= + 2841 + 1 = + 2842 ;

h3 '= - 752 + 10 = - 742 ;

h4 '= - 1243 5 = - 1248 ;

h5 '= + 509 3 = + 506 ;

h6 '= + 5338 + 10 = + 5348 ;

h7 '= - 5863 + 9 = - 5854 ;

h8 '= + 4639 10 = + 4629 ;

h9 '= - 3024 + 5 = - 3019 .

(14.96) .

1, 2, 3 4:

1 = 10 + h1 ' = 78,336 + 3,584 = 81,920 ;

H2 = HP10 + h2 ' = 78,336 + 2,842 = 81,178 ;

H3 = HP20 h9 ' = 83,507 (- 3,019) = 86,526 ;

H4 = HP30 h8 ' = 85,301 4,629 = 80,672 .

. . , H1 = HP30 h8 ' h4 ' = 85,301 4,629 + 1,248 = 81,920 .

.

 

137.3.

 

, . (. 14.9) [(1), (2), (3)], : , .. .

 

 

. 14.9. .

 

. 14.8, 14.9 14.10 , 1, 2, 3, M, N, MN. ( M N ).

. . - ).

mβ = 2,0". , (ms = 18 = 1,8 ). (pβ = 1; qβ = 1),

14.8

, B C F G
7183,652 8137,565 6124,924 7894,521
Y 4380,124 6463,782 4718,048 7173,596

 

14.9

α 71º 08' 14,3" α BA 251º 08' 14,3"
α CD 118º 19' 14,7" α DC 298º 19' 14,7"
α EF 324º 21' 18,0" α FE 144º 21' 18,0"
α GH 159º 58' 14,2" α HG 339º 58' 14,2"

 

14.10

,
β 1 226º 15' 25" s 1 475,885
β 2 201º 36' 36" s 2 693,027
β 3 85º 02' 31" s 3 857,338
β 4 170º 15' 07" s 4 401,239
β 5 172º 53' 18" s 5 841,215
β 6 271º 07' 58" s 6 625,329
β 7 280º 34' 07" s 7 573,421
β 8 84º 46' 52" s 8 989,716
β 9 337º 03' 44"    
β 10 178º 54 26"    
β 11 78º 21 28"    

 

(1), (2) (3), .. , (. 14.11).

1. n = 19 (11 8 ), k = 10, r = 9.

 

 

14.11

. β . α - s, , ,  
Δ Δ Y  
A       (1)          
7108'14,3"        
B 22615'25"   7183,652 4380,124 B  
11723'39,3" 475,885 -218,960 +422,520  
  20136'36"   6964,692 4802,644    
13900'15,3" 693,027 -523,068 +454,628  
M 28034'07"   6441,624 5257,272 M  
23934'22,3" 625,329 -316,693 -539,205  
F 8446'52" 6124,931 6124,924 +0,7 4718,067 4718,048 +1,9 Fo F  
14421'14,3" 14421'18,0" -3,7"        
E          
    (2)    
A        
7108'14,3"        
B 22615'25"   7183,652 4380,124 B  
11723'39,3" 475,885 -218,960 +422,520  
  20136'36"   6964,692 4802,644 1  
13900'15,3" 693,027 -523,068 +454,628  
M 8502'31"   6441,624 5257,272 M  
4402'46,3" 857,338 +616,237 +596,054  
N 17015'07" 7057,861 5853,326 N  
3417'53,3" 401,239 +331,470 +226,098  
  17253'18"   7389,331 6079,424    
2711'11,3"   841,215 +748,281 +384,341  
C 27107'58"   8137,612 8137,565 6463,765 6463,782 Co  
11819'09,3" 11819'14,7" -5,4"          
D   +4,7 -1,7    
    (3)    
H          
33958'14,2"          
G 7821'28"   7894,521 7173,596 G  
23819'42,2"   573,421 -301,075 -488,022  
  17854'26"   7593,446 6685,574    
23714'08,2"   989,716 -535,620 -832,255  
N 33703'44"   7057,826 5853,320 N  
3417'52,2"   401,239 +331,471 +226,096  
  17253'18"   7389,297 6079,415    
2711'10,2"   841,215 +748,283 +384,337  
C 27107'58"   8137,580 8137,565 6463,752 6463,782 Co  
11819'08,2" 11819'14,7" -6,5"          
D   +1,5 -3,0    

 

2. .

, ( , ).

1.

2.

3.

4.

5. (14.100)

6.

7.

8.

9.

(14.100) (1), (2) (3) (. . 14.11), , n(1) = 4, n(2) = 6, n(3) = 5.

, . .

1.

2.

3.

4.

5. (14.101)

6.

7.

8.

9.

(14.101) , ρ = 206265″ 100000.

(14.101) :

Wi = Tio Ti(), (14.102)

Tio Ti().

W1 = 144º 21' 14,3" 144º 21' 18,0" = - 3,7";

W2 = 118º 19' 09,3" 118º 19' 14,7" = - 5,4";

W3 = 118º 19' 08,2" 118º 19' 14,7" = - 6,5";

W4 = 6124,931 6124,924 = +0,007 = + 0,7 ;

W5 = 4718,067 4718,048 = + 0,019 = + 1,9 ;

W6 = 8137,612 8137,565 = + 0,047 = + 4,7 ;

W7 = 6463,765 6463,782 = - 0,017 = - 1,7 ;

W8 = 8137,580 8137,565 = + 0,015 = + 1,5 ;

W9 = 6463,752 6463,782 = - 0,030 = - 3.0 .

. 14.11 . 14.12 . :

14.12

,

Sin αi Cos αi (n0-xi0), (yn0-yi0),
1        
(-1) 0,8879 -0,4601 -1,0587 0,3379
  (1-) 0,6560 -0,7548 -0,8398 -0,0846
(M-F) -0,8623 -0,5064 -0,3167 -0,5392
F        
2        
(-1) 0,8879 -0,4601 0,9540 2,0836
  (1-) 0,6560 -0,7548 1,1729 1,6611
(M-N) 0,6952 0,7188 1,6960 1,2065
N (N-2) 0,5635 0,8261 1,0798 0,6104
  (2-C) 0,4569 0,8895 0,7483 0,3843
C        
3        
G (G-3)-0,8511 -0,5250 0,2431 -0,7098
  (3-N)-0,8409 -0,5412 0,5441 -0,2218
N (N-2)0,5635 0,8261 1,0798 0,6104
  (2-C)0,4569 0,8895 0,7483 0,3843
C        

 

(14.103)

aij qi, (. 14.13).

14.13

i→ j↓ β1 β2 β3 β4 β5 β6 β7 β8 β9
                   
                   
                   
  -0,1638 0,0410         0,2614    
  -0,5133 -0,4071         -0,1535    
  -1,0102 -0,8053 -0,5849 -0,2959 -0,1863        
  0,4625 0,5686 0,8222 0,5235 0,3628        
          -0,1863       -0,2959
          0,3628       0,5235
qi                  

( . 14.13)

β10 β11 s1 s2 s3 s4 s5 s6 s7 s8
                   
                   
                   
    -0,4601 -0,7548       -0,5064    
    0,8879 0,6560       -0,8623    
    -0,4601 -0,7548 0,7188 0,8261 0,8895      
    0,8879 0,6560 0,6952 0,5635 0,4569      
0,1076 0,3441       0,8261 0,8895   -0,5250 -0,5412
0,2638 0,1178       0,5635 0,4569   -0,8511 -0,8409
    0,810 0,810 0,810 0,810 0,810 0,810 0,810 0,810

 

4. .

1. 4 k1 + 2 k2 + 0,1386 k4 1,0739 k5 1,8155 k6 + 1,0311 k7 3,7= 0;

2. 2 k1 + 6 k2 + 2 k3 0,1228 k4 0,9204 k5 2,8827 k6 + 2,7396 k7 - 0,1863 k8 +

+0,3628 k9 5,4 = 0;

3. 2 k2 + 5 k3 0,1863 k6 +0,3628 k7 -0,0306 k8 + 1,2679 k9 6,5 = 0;

4. 0,1386 k1 0,1228 k2 + 0,9375 k4 -0,3510 k5 +0,7654 k6 0,7844 k7 + 0,7 = 0;

5. -1,0739 k1 0,9204 k2 0,3510 k4 + 2,3327 k5 + 0,1144 k6 + 0,5182 k7 + 1,9 = 0;

6. -1,8155 k1 2,8827 k2 0,1863 k3 + 0,7654 k4 + 0,1144 k5 + 4,3786 k6 -1,2495 k7 +

+ 1,2284 k8 + 0,6387 k9 + 4,7 = 0;

7. 1,0311 k1 + 2,7396 k2 + 0,3628 k3 0,7844 k4 +0,5182 k5 -1,2495 k6 + 3,4238 k7 + +0,6387 k8 + 0,5579 k9 1,7 = 0;

8. -0,1863 k2 0,0306 k3 + 1,2284 k6 + 0,6387 k7 + 1,9065 k8 + 1,2832 k9 + 1,5 = 0;

9. 0,3628 k2 + 1,2679 k3 + 0,6387 k6 + 0,5579 k7 + 1,2832 k8 + 2,0749 k9 3,0 = 0.

(14.104)

(14.104) :

k1 = + 0,474; k2 = - 0,375; k3 = + 0,740; k4 = - 0,379; k5 = - 0,983; k6 = - 0,614; k7 = + 0,422; k8 = - 2,263; k9 = + 2,534.

(14.104) .

5. .

14.13:

14.14

. β . α - s, , ,  
Δ Δ Y  
A       (1)          
7108'14,3"        
B 22615'26,48"   7183,6520 4380,1240 B  
11723'40,78" 475,8847 -218,9627 +422,5182  
  20136'37,22"   6964,6893 4802,6422    
13900'18,00" 693,0301 -523,0761 +454,6230  
M 28034'07,53"   6441,6132 5257,2652 M  
23934'25,53" 625,3374 -316,6888 -539,2171  
F 8446'52,47" 6124,9244 +0,4 4718,0481 +0,1 F  
14421'18,00" 0,00"        
E          
    (2)    
A        
7108'14,3"        
B 22615'26,48"   7183,6520 4380,1240 B  
11723'40,78" 475,8847 -218,9627 +422,5182  
  20136'37,22"   6964,6993 4802,6422 1  
13900'18,00" 693,0301 -523,0761 +454,6230  
M 8502'31,33"   6441,6132 5257,2652 M  
4402'49,33" 857,3368 +616,2274 +596,0623  
N 17015'07,03" 7057,8406 5853,3276 N  
3417'56,36" 401,2332 +331,4621 +226,0995  
  17253'19,97"   7389,3027 6079,4271    
2711'16,33"   841,2052 +748,2631 +384,3547  
C 27107'58,37"   8137,5658 +0,8 6463,7818 -0,2 C  
11819'14,70" 0,00"          
D          
         
    (3)    
H          
33958'14,2"          
G 7821'28,26"   7894,5210 7173,5960 G  
23819'42,46"   573,4133 -301,0701 -488,0160  
  17854'27,16"   7593,4509 6685,5800    
23714'09,62"   989,7087 -535,6104 -832,2528  
N 33703'46,74"   7057,8405 5853,3272 N  
3417'56,36"   401,2332 +331,4621 +226,0995  
  17253'19,97"   7389,3026 6079,4267    
2711'16,33"   841,2052 +748,2631 +384,3547  
C 27107'58,37"   8137,5657 +0,7 6463,7814 -0,6 C  
11819'14,70" 0,00"          
D          

 

6. .

(. 14.14), . 14.12.

( ) 3- , .

.

.

1 , 0,1".

 





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