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Основы геодезии и топографии

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. 52

,

"

12 = + 1 + 180˚,23 = 12 + 2 + 180˚,

 

( 4.22 )

 

n.(n+1) = n-1,n + n + 180˚

 

 

= n(n+1) + n+1 + 180˚.

 

- 1

n+1 " ("

$ +) CD).

 

(4.22),

 

 

n+1

 

 

= + i + (n+1)180˚,

 

n+1

 

 

1

 

 

i = – – (n+1)180˚.

( 4.23 )

 

1

 

' ,

"

:

 

i+1

= i + i+1

+ 180° ,

 

i+1

= i i+1

+ 180° .

8

(4.23)

 

%

111

. 8 $

(4.20).

") )! * # # * #. 8

 

 

 

 

 

.

',

 

1 2

 

 

 

 

 

 

x12 = x2 – x1, 12 = 2 1.

 

.

 

 

 

 

! " .

1)

(x1, y1), (s12) " ( 12)$ (x2 , y2). 8

% " :

12 =s12 cos 12 , y12 = s12 sin 12;

( 4.24 )

x2 = x1+ x12 = x1+s12 cos 12 , y2 = y1+ y12 = y1+s12 sin 12. ( 4.25 )

2) +

(x1, y1) ( 2,y2) $

% . 8

" :

x12

= x2

x1,

(4.26 )

y12

= y2

y1.

(4.27 )

8 ,

tg 12 = (y2 – y1)/(x2 – x1);

s12 = (x2 – x1)/cos 12 = (y2 – y1)/sin 12;

_________________

s12 = (x2 – x1)2 + (y2 – y1)2 .

: $

112

" (4.24) (4.25) –

$ .

!

". '

"

fx = x – = x – 0 = x ,

f = – = – 0 = .

( 4.28:)

 

+

 

______

_________________

 

fs = fx2 + fy2

= H( x )2 + ( )2 .

( 4.29 )

, ,

, " fx fy

" $ .

- = ; – = .

fx = x – = x - ( - ),

(4.30 )

f = – = - ( - ) .

+

(4.29).

. %

,

$

1/2000 , − 1/1500

− 1/1000.

!

/xi = - (fx/ s)@si , /yi = - (fy/ s)@si.

( 4.31 )

113

$

( ),

:

/ i

= - fx, /i = - fy.

4.3. + # *

+ $

 

. + $

% ,

.

.

/

( (

, " ( ). + % , "

" = (

= ) . + %

– “ ( ” .

& $ " $

 

 

 

. &

 

 

 

"

" ( ,

.) (

$ -

$ , .)

.

. 8 " " :

− (

);

(

);

;

;

.

114

4.3.1. #

B

– . +

,

$ .

8 " :

.

"

$ + ), "

( .53).

$ + ) , +,

, ) – .

"" , ""

b. ) 2 "

 

h = a – b.

( 4.32 )

a›b,

$ ,

a‹b

. + ! :

 

 

 

HB = HA + h.

( 4.33 )

 

 

 

 

 

 

 

 

. 53

. 54

+

H = HA + a = HB + b,

( 4.34 )

115

A A + ).

" +

, +. / ) . ) i +,

b ( . 54). "

h = i – b.

( 4.35 )

+ )

 

$

 

 

( ),

+) "

$ ( ) "

( . 55).

/ +-1

, ,

+ 2,

, " , ""

. . $ + )

:

n+1

n+1

 

hAB

= ai – bi .

( 4.36 )

 

i=1

i=1

 

+ ) :

 

 

 

n+1

 

HB = HA + hi.

( 4.37 )

 

 

i=1

 

+)

.

. 55

116

) )* ( "$!

4 * B <

$(

"! . -

"

,

% , + )

$ . ! , $ + ),

' D,

. - J C F.

) +

E+ FB:

h = EA – FB.

&, . 56 : C+ = +' C' FB = BD – DF . + E' DF $"

, S R.

(2.3) E' DF :

EC = k1 = S12/2R, FD = k2 = S22/2R,

. 56

S1 S2 + ) . + .

2 ,

: , . 8$

$

117

, ( . 57).

. 57

, ,

$

. ,

", N, $

 

,

 

"

.

/ " N " $ 1

%

 

",

. .

$ .

1 * " " * " * # " * * ( " * (

B ! $* * $!" ( B <.. (

B < ". ' ,

, $ CDIDD ( c. 57),

: ='D+ b=DD), . .

$ ,

''D DDD $" . 8 "

" " $ R1. +

R/R1 = % ,

0.16 ( $

0.11− 0.22).

& ''D DDD " $ :

''D= r1 = S12/2R1 DDD = r2 = S22/2R2 ,

118

S1 S2 − ( )

( ) , R1 R2

.

, R1 = R2 = R/K,

r1 = (S12/2R)K, r2 = (S22/2R)K.

:

h = (a + k1K – k1) – (b +k2K – k2) = (a – b) – [k1(1 – K) – k2(1 – K)].

+ f

f1 = k1(1 –

K),

f2 =k2(1 –

K).

'

 

 

 

h = (a –

b) –

(f1 – f2).

( 4.38 )

( ,

f1 = f2. %

" ".

) A " * ! ; " ". !

" ,

.

!$ " "

. &

$ $ % :

" " " .

% $ -

$ .

! $

" (

" ) "

, .

& " .

119

1. + $

(UU1||VV1) $

%

.

. /

" 50 . / " + ,

( . 58, ). +

" i.

), ,

- b1.

" , " i2,

- b2

( . 58, ).

,

b01 b1. +

, ) +:

h = i1 – (b1 + x).

$ ) +

) :

. 58

hD = i2 – (b2 + x).

120