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, 2014 .
2
.
" "-
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. -
CIP - ". ", 528(075.8) , [ ] / . - , . , . - : " ", , 2014 (URL): http://e-lib.ugd.edu.mk/naslovna.php. - . - 02.10.2014. - : . 260-261 ISBN 978-608-244-101-6 ) - COBISS.MK-ID 97141514
_____________________________________________________________________________3
. 2202-61/5 07.02.2014 .
,
" "- .
2011, .
.
" "-
-
. -
-
4
, () , . , , , , , . II , 2003 . . , , . II , , .
, , . , . , , , . -. . -. , . , , ..., , . .- () , . -. , . -. - . , .
_____________________________________________________________________________5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . 6 ................. ........................................................... 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . . 14
. . . . . . . . . . . . . . 15 () ............................................ 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 ....................... 19 .................................................................... 20 ............. 22
- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 .... 22
, . . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 ................................................................. 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 ........................................................... 33 .............................................................................................................. 38 . . . . . . . . . . . . 39
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 . . . . . . . . . . . . . . . . . . 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
............................ 52 . . . . . . . . . . . . . 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 . . . . . . . . . . . . . . . . . . 62 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 , , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 . . . . . . . . . . . . . . . 66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 . . . . . . . . . . . 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
. . . . . . . . . . . . . . . . . . . . . . . . . . . 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 . . . . . . . . . . . . . . . . . . . . 76
. . . . . . . . . . . . . . . . . . . . 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 ..................................................................... 88 .......................................................................................................... 90 , ............................... 92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
. . . . . . . . . 94 . . . . . . . . 95 . . . . . . . . . 96 , . . . . . . . . . . . . . . . . . . . . . 97
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
. . . . . . . . . . . . . . . . . . 106 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 . . . 106 ................................................................................................... 109
_____________________________________________________________________________7
.................................................................................................... 116 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
, GNSS GPS . 129 . . 130 ... 13 0 TOPCON........................... 13 4 WILD TC-1000 , GNSS I GPS............ 1 40 GPS LEICA VIVA GS08. . . . . . . . . . . . . . . . . 145 . . . . . . . . . . . . . . 149 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
() . . . . . 150 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 . . . . . . . . . . . . . . . . . . . . . . . . . . 152 . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
. . . . . . . . . . . . . . . . . 155 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 . . . . . . . . . . . . . . . . . . . 158 . . . . . . . . . . . . . 160 . . . . 276
. . . . . . . . . . . . . . . . . 163 . . . . . . . . . . . . 163 . . . 165 . . . . . . . 167
GPS - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 . . . . . . . . . . . . . . . . . . . . . . 175 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 (), . . . . . . . . . . 179
8
(). . . . . . . . . . . . . . . . . . . . . . . 180 . . . . . . . . . . . . . . . . . . . . . . . . 182 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
. . . . . . . . . . . . 189 . 192
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 .. . . . . . . . . . 194 .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 .. . . . . . . . . . . . . . . . . . . . . . . . . . . 196 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 , . ................................................................................................ 204
......................... 206 ................................................................................. 206
. . . . . . . . . . . . . . . . . . . 208 ...... 209 ......... 210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
. . . . . . . . . . . . . . . . 212 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
. . . . . . . . . . . . . . . . 213 . . . . . . . . . . . . . . . . . . . . . . . . . . 216 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 . . . . . . . . . . . . . . . . 219
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 . . . . . . . . . . . . 227
...................................................................................... 227 ........................................................................................ 230 ............ 231
_____________________________________________________________________________9
. . . . . . . . . . . . . . . . . . . . . . 234 ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 ............................ . . 234 .................................................................. 234 ........................................................ 235 ........................................................... 236 ...................................................................... 237 ................................................................... 237 .............................................. . . . . . . . . . 239 .............................. 240 ......................................... 241 ............................................... 244 - ................................................ 247 ............... 248 .................................... 249 ............................................................................... 250 ............................................ 251 ........................... 251 ..................................................................... 252 .................................................. 253 ................................. 253
. .................................. 257 ....................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
..................... . . . . . . . . 258 .......................................... 258
. . . . . . . . . . . . . . . . . 259
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
10
-
-
,
_____________________________________________________________________________11
() (), . , . , 1300 II , , , . , , .
, , . harpedonaptes (). , .
, . , , . , .
(), .
, . . , , , . , , . , .
: , , -, ,
12
. , , , , , .
, , , :
(.. ) (.. ) . ,
. , () , . , , , () . , () , , , .
, , . () , ( ). : , , , , .
, , , , .
, , , , . , , - .
_____________________________________________________________________________13
. ( 900 - 800 . ...). , . , (384 -322 ....) , () 400 000 (1 = 192 m), .
(276-196 ....). . .. , . , ( ) . , , ( ). , , , .
1528 . . , (Q=10.011km) 1% . .
, , . 1615 1617 ., , . , .
1669 . . (Q) 10 008,9 km, ().
. 1672 .,
14
. , . , (1643-1727 .) . , . , , .
, . 1718 . , . , 1735 . . , ( ) 1744 . , . ( ), 1736 1737 ., , , . , , , (. 1.1).
(.1.1)
, 18- , , , . 40 000 000- . .
_____________________________________________________________________________15
(. 2.1)
, , , 1872 . . , , . , , , (. 2.1 ).
, . 50 m, 150 m. . , , , . .(. 3.1)
(. 3.1)
16
, , . 1 . 1:
ElipsoidGolema poluoska
a (m)Mala poluoska
b (m)Spleskanost
Dalamber (1800) 6 375 653 6 356 564 1 : 334.0
Besel (1841) 6 377 397 6 356 079 1 : 299.2
Hajford (1909) 6 378 388 6 356 911 1 : 297.0
Krasovski (1942) 6 378 245 6 356 863 1 : 298.3
WGS (1984) 6 378 137 6 356 752 1 : 298.3
, . , . . , 1984 ., WGS 84, , , .
, , , .
. ( ) , () .
(,) , . () ( ) . 0 90 , 0 - 90 , , (. 4.1).
_____________________________________________________________________________17
(. 4.1)
() () ( ) . . 0 180, .
, (. 5.1).
(.5.1)
(V) . . (N) . .
() (.5.1). .
18
T1 ( S ) (.6.1). , , T T T1 , S , . 00 360 0 .
, T1 S .
(.6.1)
. A. 0 360 .
, - .. , . () P1P2 = 2b (.7.1).
_____________________________________________________________________________19
(.7.1)
, : P1- , P2- . (), , , ( E 1E E2). , , , (U1U U2 ). , , (P1E1P2E2).
(.8.1), , :
() - , 2a = 12 - , 2b = P1P2 - ,
OFOF 21 == -
(.8.1)
20
( a b ) . , , . , :
a
e = ...(1.1)
, :
b
e = ...(1.2)
. (.8.1) :
222 ba =
( 1.1) (1. 2) :
222
2
abae = ...(1.3)
2
222
bbae = ...(1.4)
:
aba
= ...(1.5)
, , . , :
bba
= ...(1.6)
. :
b
ac2
= ...(1.7)
.
_____________________________________________________________________________21
, ( a b), ( a ).
M, , . , . , (.9.1).
(.9.1)
(P1MP2)
M, . , M. (A1MA2). (B1MB2). . M . , (= 0), 90 (= 90 ).
(M) :
22
32
2
1
1
)sine(
)e(aM2
= ....(1.8)
(N) :
221 sine
aN
= ...(1.9)
( ) , ( ) .
()
, , (.10.1).
(.10.1)
, , , . , . , (M N) :
_____________________________________________________________________________23
MNR = ...(1.10) 100km
R= 6377 km.
(), (.11.1).
(.11.1)
, , , . , , . . , ABCD A 1 B1 C1 D1 (.12.1).
(.12.1)
24
, (.13.1).
(.13.1)
, , , . , , , . , , (.13.1).
, . , , , , , .
, . , .
_____________________________________________________________________________25
( - ), , , . , , .
( .14.1)
, ( ) (.14.1). ( -) , , (.15.1).
(.15.1)
26
. , , : 1. ; 2. ; 3. .
, , : - ( ); - ( ); - ( ) . , .
, .. , .
. ( ) , . .
, : - ( ) ; - ( ); - .
() , - (.16.1)
_____________________________________________________________________________27
(.16.1)
(.17.1)
( ) , (.17.1).
, 0 90 ( .18.1).
28
(.18.1)
. -, , , .
. . , :
- ; - ; - ; - ; - ; - ;
- .
_____________________________________________________________________________29
-
-
. , - - 3 (.19.1).
(.19.1)
,
7- , 21 . . , 21- x-, , y-, . x y O (.20.1).
(.20.1)
, x , y .
30
y-, , x- 500 000 m. , y- 500 000 m, 500 000 m. y 7, 7- .
,
, . , , . , 18- , .
- , - . , , , 90% 10% . , (Mtre de archives), . 30 , , , 1872 . , . 6, , . (Bireau international des poids et mesures ) , . 30 , , , , .
(90% 10% ) . , ( a - b ) 1 m. (.21.1)
_____________________________________________________________________________31
(.21.1)
SI , 1
650 763,73 ( Kr 86 ) , 2P10 5d5.
, , : 1/299 792 458 .
: 1 dkm () = 10 m = 101 m. 1 hm () = 100 m = 102 m. 1 km () = 1000 m = 103 m. 1 Mm () = 106 m. 1 Gm () = 109m. 1 Tm () = 1012m. ,
, .
: 1 dm () = 0,1 m = 10-1 m. 1 cm () = 0,01 m = 10-2 m. 1 mm () = 0,001 m = 10-3 m 1 () = 0,001mm = 10-6 m 1 m () = 0,001 = 10-9 m
, , . .
32
, . , , , , , , . :
1 (, ) = 2,634 cm
:
1 in (inch , - ) = 2,54 cm 1 ft (foot , - ) = 12 in = 30,48 cm 1 yd (yard , ) = 3 ft =91,439 cm 1 mile ( - ) = 1639,34 m 1
0,6858 m.
:
1 m2 ( ) = (1 1) m2
1 a () = (10 10) m2 = 100 m2 1 dka () = (10 100) 2 =1000 m2 =10 a 1 ha () = (100 100) m2 = 10 000 m2 = 100 1 km2 ( )= (100 x 1000)2 =1000 000 m2 = 100 ha : 1 = 1600 . = 918,67 m2
() , () , . () . . 10 ( ) . :
10 = 60' ( ) 1' = 60" ( )
_____________________________________________________________________________33
1g( ), . , , , .. 1g = 100 c = 100` ( ) 1 c = 100 cc = 100`` ( )
:
gogo :: 400360= ...(1.11)
( 1.11 ) :
== ggo . 900109
oog . 111
910
== ... (1.12)
, .
, , , . . , ( ) , (d) ( ) (.22.1).
(.22.1)
(.22.1), :
34
=d ...(1.13)
:
go 4003602 == ...(1.14)
:
go 200180==
... (1.15)
() :
3572957795157180 .. ooo
o ==
''.)'(' 3438746771343760180 ==
...(1.16)
''206265806'.'206264')'6060180('' ==
:
7636619772463200 .. ggg
g ==
ccc
c .)( 63661977246366100200 ==
...(1.17)
cccccc
cc .)( 6366207724636619100100200 ==
()
:
=
== o
or
... (1.18)
() :
=== rrro ...(1.19)
1. :
498662 .g=
_____________________________________________________________________________35
ggo . == 90109
49866290 ..o =
2487456 .oo =
'''oo 551456 =
2. :
'''o 3749136 =
oog . == 1119
10
82694136 .oo =
82694136111 ..g =
0299152 .gg =
cccgg 9902152 =
3. () , : r = 1, 3564:
35641.r =
roo =
35641357 ..oo =
7217277 .oo =
'''o 184377 = 4. 0 :
'o 35225 =
''
r =
36
''
r 343813535
=
936883.r =
5. , :
rgg =
936883763 ..gg =
779256250 .g= cccg 9377250 =
(),
, . (1 :M) (1/M), M . 1 : M .
D , d , :
MDd 1
= ... (1.20)
O (1.20) :
MDd = ...(1.21)
: MdD = ...(1.22)
(1.21) 1 : M, M. (1.22) (D), 1 :, d ( ) M.
: 1: 250, 1: 500, 1: 1 000, 1: 2 000, 1: 5 000 1: 10 000.
_____________________________________________________________________________37
, , . , 1: 500 1:1000. , .
, : 1 : 25 000, 1 : 50 000, 1: 100 000 1: 200 000. 1: 200 000 .
, , . , , , , , .
6. d = 13, 7 mm 1: 2 500 :
d= 13, 7 mm = 0, 00137 m M = 2 500
D=d . M= 0, 0137. 2 500 = 34, 25 m
D= 34, 25 m
7. d 1 : 5 000 137, 53 m ?
m.D 53137=
5000=M
027505000
53137 ..MDd ===
mm..d 527100002750 ==
mm.d 527=
38
:
- ? - ? - ? - ? - ? - ? - ? - ? - , ? - ? - - ? - ? - ? - 1 Mm ( ) ? - : 10 y () 100 m ? - m2 ? - m2 ? - ? - ? - : = 370 = 42g ? - 600 ? - 1 m ? - ? - 1 : 2500
320 m ?
_____________________________________________________________________________39
-
40
. , , . , (.1.2).
(.1.2)
, . , , . , , . , :
1. , 20 km; 2. , 15 - 25 km; 2. , 9 - 18 km; 3. , 5 - 13 km; 3. , 3 - 7 km; 4. , 1 - 4 km.
1. 27 8 , 35 (.2.2).
_____________________________________________________________________________41
(.2.2)
1. . , . , : .. , , , (.3.2).
(.3.2)
, , .. (.3.2). , , (.4.2).
42
(.4.2)
, ( 1b ) ( 111 ,, ), (.5.2).
(.5.2)
, . 1 :
msin
asin
csin
b===
1
1
1
1
1
1
...(2.1)
(2.1) 1a 1c ,..
111
11
sinmsinsin
ba == ...(2.2)
:
111
11
sinmsinsin
bc == ...(2.3)
, . 2b , , 1b , (.5.2).
_____________________________________________________________________________43
, S (.6.2).
(.6.2)
(, , , , , ) , , 100 400 km (.7.2).
(.7.2)
2. 1. . 2. , 2. (.8.2).
(.8.2)
44
3. 2. , , . 4. , .
1, 2. 3. . . 3. 4. . , , .
, , GPS , EUREF 1996, GPS (Global Positioning System) , , GPS .
2004 . GPS , 1 : 25 000. GPS , ..
(. 9.2)
2010 ., GPS- , GNSS ( Global Navigation Satellite Sustem ) , (MAKPOS) (. 9.2). GPS - .
_____________________________________________________________________________45
, 1. 1,20 1,40 m. (.10.2).
(.10.2) (.11.2)
0,25 x 0,25 x 0,75 m, , 3 - 5 cm . () (.11.2).
, (.12.2), .
(.12.2)
46
, . : , , , . (.13.2).
(.13.2)
1 .. . , 1 , , , , . , . , 1.
, : , .
(.14.2)
_____________________________________________________________________________47
, .. . (.14.2)
, , 900.
. , (.15.2)
(.15.2)
.
(.16.2)
, (.16.2).
48
(.16.2) B :
+= AB ...(2.4)
, , : () , , .
() BA , A
B, , x- ( x- ) . (.17.2).
(.17.2)
BA A B
AB (.17.2).
BA AB :
180= BAAB ...(2.5)
, (.17.2) :
( )( ) x
yxxyy
tgAB
ABBA
=
= ...(2.6)
_____________________________________________________________________________49
, BA :
( )( )AB
ABBA xx
yyarctg
xyarctg
=
= ...(2.7)
(.16.2), B, :
( ) ( )2222 ABABAB xxyyxyD +=+= ...(2.8) :
BA
BA
ABcos
xsin
yD
=
= ...(2.9)
:
( ) ( )BA
ABBA
ABAB
cos
xx
sin
yyD
=
= . ..(2.10)
BA 45, :
( )
yxyxtg BA
+=+ 45 ...(2.11)
(.18.2)
50
(.18.2) , 0 360. y x. .
I
(0o-90o) II
(90o-180o) III
(180o-270o) IV
(180o-360o) AB yyy = + +
AB xxx = + +
xy
.
:
I ++
= x)(y)(tg =BA
II +
= x)(y)(ctg 90+= BA
III
= x)(y)(tg 180+= BA
IV +
= x)(y)(ctg 270+= BA
( ) .
xy
,
(90, 180
270
) ,
y x .
_____________________________________________________________________________51
1. : 8976
54
23 i ,,
:
y x 2 21 660,32 14 515,78 3 21 536,46 14 483,16 4 21 100,71 15 218,51 5 22 801,43 14 819,16 6 21 790,78 13 635,21 7 20 944,14 13 424,70 8 21 269,97 14 467,91 9 22 142,96 14 444,01
. y x 32+450=1200 14' 44'' : 2 21 660,32 14 515,78
: 3 21 536,46 32 = 750 14' 44'' 14 483,16
y = +123,86 x = +32,62 x+y=+156,48 x-y = -91,24 D = 128,08 . y x
45+450=148012'52'' : 5 22 801,43 14 819,16 : 4 21 100,71 45 = 1030 12' 52''
15 218,51 y = +1 700,72 x = - 399,35 x+y = +1 301,37 x-y = - 2 100,07 D = 1 746,98 . y x
67+450=301002'13'' : 7 20 944,14 13 424,70 : 6 21 790,78 67 = 2560 02' 13''
13 635,21 y = - 846,64 x = - 210,51 x+y = - 1 057,15 x-y = + 636,13 D = 872,42 . y x
98+450=316034'06'' : 8 21 269,97 14 467,91 : 9 22 142,96 98 = 2710 34' 06''
14 444,01 y = - 872,99 x = + 23,90 x+y = - 849,09 x-y = + 896,89 D = 873,32
52
. , BA ABD , (.19.2), y x :
BAAB
BAAB
cosDx
sinDy
=
= ...(2.12)
(.19.2).
(.19.2)
( AA x,y ) A y x, B( BB x,y ). (.19.2) :
xxx
yyy
AB
AB
+=
+=
...(2.13)
2. 120
12080 =169
o1733 D=769,45m 80
_____________________________________________________________________________53
( 80y = 21100,71; 80x = 15218,51).
( )
m,x
m,y
m,,,xxx
m,,,yyy
,cos,cosDx
,)'''sin(sinDy
,xm,D
,y
769,45
9114467
9721269
9114467607505115218
9721269261697121100
60750337116745769
261693317167
511521845769
71211003371167
120
120
80120
80120
12080
12080
80
8012080
=
=
==+=
=+=+=
===
+===
==
==
( 00 x,y ) , ( BBAA x,y,x,y ) (AB), .. ( BA , ) (.20.2).
54
(.20.2)
AB. (.21.2).
(.21.2)
A B, CD ( yx ) 1 2 ( ), PB , PC, P1, P2 PD. (B) , :
BC pp =0 ...(2.14)
_____________________________________________________________________________55
B, C D, , :
AB
ABBA x
yarctg
=
AC
ACCA x
yarctg
= ...(2.15)
AD
ADDA x
yarctg
=
(1) o . o ..
BAo =1
02 =CAo ...(2.16)
33 =DAo
, :
3321 oooo ++= ...(2.17)
o , :
oB =
0 += oC
11 += o ...(2.18)
22 += o
3 += oD , ( ), . ( DCB ,, ) B, C D
.,, DACA
BA .
v o , . , iv :
56
BBAv =1
CCAv =2 ...(2.19)
DDAv =3
,. . ][v =[( )]= 0 ...(2.20)
o , . , , . v :
6 2. 15 3. 25 4.
, . , ( io ) :
BBA po =1
CCA po =2 ...(2.21)
DDA po =3
, i , :
BB po +=
CC po +=
11 po += ...(2.22)
22 po +=
DD po += , , . 5. : - , - , , - ( iiio = ),
_____________________________________________________________________________57
- ( o ),
(noo i ][= ),
- , : ii o +=
- , (2.18), :
on += ][][ -
iiiv = , :
0][ =v . 3. :
Y [ ]m X [ ]m 10 13 952,73 19 486,84 13 17 779,66 18 903,69 15 15 289,86 16 752,50 32 13 776,62 17 487,66 52 15 050,18 19 361,79 87 17 386,05 16 758,22
' " ' "
15 52 0 00 00 32 13 0 00 00 87 73 35 43 6 23 30 21 32 279 40 02 15 45 23 40 6 306 12 58 10 294 31 04 10 317 41 45 52 339 58 58
58
=5215 16 14' 44" =8715 89 50' 37"
=3215 295 54' 41" =1015 333 56' 27" ???
. . . iiio = ii o += f ' " ' " ' " ' " "
15 52 16 14 44 0 00 00 16 14 44 16 14 45 -1
87 89 50 37 73 35 43 14 54 89 50 28 +9
32 295 54 41 279 40 02 14 39 295 54 47 -6
6 306 12 58 322 27 43
10 333 56 27 317 41 45 14 42 333 56 30 -3
10 28 70 31 04 59 23
13 45
24 13
=1332 70 31' 10" =1032 5 02' 03"
=1532 115 54' 41" =5232 50 30' 03"
. .. iiio = ii o += f ' " ' " ' " ' " "
32 13 70 31 10 0 00 00 70 31 10 70 31 04 +6
6 23 30 21 94 01 25
15 115 54 41 45 23 40 31 01 115 54 44 -3
10 5 02 03 294 31 04 30 59 5 02 08 -5
52 50 30 03 339 58 58 31 05 50 30 02 +1
24 03 70 31 04 59 23
35 20
59 23
_____________________________________________________________________________59
. .
(.22.2)
T( 00 x,y ), , , , Ta Tb T (.22.2).
, T, Ta, Tb.
Ta Tb ba d.
:
ab
abba xx
yytg
= ...(2.23)
:
60
ba
abba
ab
cos
xx
sin
yyd
=
= ...(2.24)
ba , a b , (T,Ta,Tb) , :
ab
babb
baaa
=
=
=
...(2.25)
,
180 , ..: 180=++ ba ...(2.26)
, :
msin
dsin
dsin
da
b
b
a ===
...(2.27)
(2.27) :
ab
ba
sinmd
sinmd
=
= ...(2.28)
ad bd
a b , :
bbbaaa sindysindy == ;
bbbaaa oscdxoscdx == ; ...(2.29)
, 0y 0x , . , :
bbaa yyyyy +=+=0
bbaa xxxxx +=+=0 ...(2.30)
:
- (2.23) (2.24) ba d.
_____________________________________________________________________________61
- (2.25) a , b (2.26) ,
- sin
d (m)
(T,Ta,Tb),
- (2.28) ad bd ,
- (2.29) ,
- (2.30) T.
4. o61 o51 o23. .
Y X
=a 84 41' 52" bT 32 16 045. 69 71 284. 96
=b 159 42' 05" aT 15 15 398. 05 69 571. 16
+ 647. 64 +1 713. 80
=ba 20 42' 05" =d 1 832. 09 =m 1 896. 69
== baaa 63 59' 47" =ad 1244. 34
== babb 41 00' 00" =bd 1704. 68
== ab 75 00' 13"
180 00' 00"
== aaa sindy +1 239. 02 == bbb sindy + 591. 38
== aaa cosdx + 114. 99 == bbb cosdx -1 598. 81
=+= aa yyy0 16 637. 07 =+= bb yyy0 16 637. 07
=+= aa xxx0 69 686. 15 =+= bb xxx0 69 686. 15
62
, , , .
(.23.2)
a b , (.23.2), :
a
a
a
aa x
yxxyytg
=
= ...(2.31)
b
b
b
bb x
yxxyytg
=
= ...(2.32)
(2.31) (2.32) :
aaa tg)xx(yy = ...(2.33)
bbb tg)xx(yy = ...(2.34) (2.33) (2.34) :
bbaaab tg)xx(tg)xx(yy = ...(2.35) :
bbaabaab tgxtgx)tgtg(xyy += ...(2.36) :
ba
bbaaabtgtg
tgxtgx)yy(x
+= ...(2.37)
_____________________________________________________________________________63
(2.37) x , ax , bx , :
ba
bababa tgtg
tg)xx()yy(xx
= ...(2.38)
ba
aababb tgtg
tg)xx()yy(xx
= ...(2.39)
: Atg)xx()yy( babab =
Btg)xx()yy( aabab = ...(2.40)
Ctgtg ba = :
CAxa = C
Bxb = ...(2.41)
(2.31) (2.32) :
aaa tgxy =
bbb tgxy = ...(2.42) , ,
, ..
bbaa yyyyy +=+=
bbaa xxxxx +=+= ...(2.43)
, , , :
- ( ab xx ) ( ab yy ),
- A, B C, (2.40),
- ax bx , (2.41),
- ay by , (2.42), ,
- ( 0y , 0x ) (2.43).
64
5. o6 o15 o32. .
T : 6 aT : 15 bT : 32
=by 13 776. 62 =bx 17 487. 66 =a ' "
322 27 43
=ay 15 289. 86 =ax 16 752. 50 =b 94 01 25
ab yy - 1 513. 24 = ab xx + 735. 16
== babab tg)xx()yy(A + 8938. 14
=atg
=btg
- 0.7683828
- 14.2164739
== aabab tg)xx()yy(B - 948. 36 == ba tgtgC + 13.4480911
== aaa tgxy - 510. 70 ==
CAxa + 664.64
== bbb tgxy + 1 002.54 ==
CBxb - 70.52
=+=+= bbaa yyyyy0 14 779.16 =+=+= bbaa xxxxx0 17 417.14
_____________________________________________________________________________65
:
- ? - ? - ? ? - ? ? - , ? - ?
? - ? - ? -
? - ? - () ( )
, ? -
? -
?
66
_____________________________________________________________________________67
. , (.1.3).
(.1.3)
, ',
, (.1.3) , , , .
. ( - 00) , 1 2(.2.3), ..
= 2 - 1 ...(3.1)
(.2.3)
68
, , (.3.3).
(.3.3)
1 2 (.4.3), :
= ( 2 + 3600 ) - 1 ...(3.2)
(.4.3)
, , , , .
(.5.3)
_____________________________________________________________________________69
, (), (TA), , (TB). - . (1) , (A) , (2) (B) (.5.3).
, .
- , .
(.6.3)
70
: , , , , , , . (.6.3).
,
,
, . . . , , , (.7.3).
(.7.3)
. , (.7.3).
, , .
. , , , , .
:
- () (V- V); - () (H - H); - () (C - C)
_____________________________________________________________________________71
- (L - L).
(.8.3).
(.8.3)
, ,
.. . () , , , . , . . , , . , , , (.9.3).
(.9.3)
72
. ( ) (.10.3) , (.10.3). . .
(.10.3) (.10.3)
, , . () . , (.11.3).
(.11.3)
30, 20, 10, 2, 3 6 (.11.3).
_____________________________________________________________________________73
, . Rp (.10.3) . . . , , . Lv (.10.3) , .
(.20.3)
, , . , , . , , . (.20.3)
, . , .
74
(.21.3). , . , .
(.21.3)
, . , . , , . , , 2/3 .
, .
.
(.22.3).
, , : (CM) (L-L), (.22.3). , , , (.22.3).
_____________________________________________________________________________75
(.22.3)
, , . 2,26mm., 1 , . 2mm, . , , , (.23.3).
(.23.3)
. , .. (.24.3 ).
(.24.3)
76
. , , , , .
.. . ,
, . :
Rb
= ...(3.9)
: b - ;
R - . (3.9) ,
R, ( ), , . , , .
, , R , (L-L) . , 1 () , ( ), ( ), (.25.3).
(.25.3)
_____________________________________________________________________________77
, - ( ), , .
, . , , , . , : .
, . , , . , :
1. () , . , ,
2. , , .
() (.30.3).
(.30.3)
() , :
- (),
78
- () - , .
, , : , (.31.3).
(.31.3)
, , . , , ( ) , , (.32.3).
(.32.3)
, , . , , (.33.3). , . , . , (.33.3).
_____________________________________________________________________________79
(.33.3)
.
, . , , , (.34.3)
(.34.3)
, , , . , . . .
80
. , , . .. . ( ), . .. , . ( ) , , .
,
. , , (.35.3) (.35.3 ), .
(.35.3) (.35.3)
. , , . : , , (.36.3).
(.36.3)
_____________________________________________________________________________81
, . : , , . , , , , .
. , .. . , , .
, , , . , , , . , . . , , . , , , 2 - 3 mm . , , . .. .
, . , . , , . 2-3 m ,
82
, . , , 2 5 mm.
(.41.3)
, . 4 - 6 . , (.41.3).
() () . , , () . .
. , . , , , . , . , , , , .
, , :
- , , ;
- . , ;
_____________________________________________________________________________83
- .
- () , . , . , . 1-2 mm.
. . , . . , , . .
. , , . , .
, , . , . . , .
84
,
. , , . , (V-V), (H-H), (C-C) (L-L) , :
1 : (L-L) (V-V);
2 : (V-V) ;
3 : (H-H) (C-C) ;
4 : (H-H) (V-V).
. , , (1) (2), , (.42.3).
(.42.3)
, . , , . , , . , .
_____________________________________________________________________________85
. ( ) (1 2), (k) (.43.3). .
(.43.3)
, . , (3). , (.44.3).
(.44.3)
, .
86
, (1 2). , , (.45.3).
(.45.3)
(1 2), , (3) . , . .
( ) (21 ),
, (1 2)
(21 ) (k1).
. ,
(22 )
(3), (22 ) (k2)
. .
, (H-H) (C-C) , :
) )
_____________________________________________________________________________87
. , A . (I) (.46.3) A (L1) . , (I-I) (H-H) (.47.3).
(.46.3) (.47.3)
(II) (.46.3) , (L2), (II-II). , , (H-H).
(.47.3) L1 (I -I) L2 (II-II) (2C), :
( ) ( )CLL 2180 102 = ...(3.23) 2-3
, , . (2C) , . L2 (-C). . A . A (KH-KH). , , A , .
88
, , L1 I 29226 42", L2 II 112 28 30" : L1 L2 180 2Np , . . 108, . , :
''4262292)180''3082112(2 += C
''1082 +=C (-) II :
112 28 30- 54 = 112 2736
, 112 2736. , (KH-KH) , (112 2736), A (.48.3).
(.48.3)
(H-H) (V-V), . , .
() . A (.49.3).
_____________________________________________________________________________89
(.49.3)
, , . , , , I II A, . (II-I) , . , , .
, , .
(.50.3)
90
, , K1 K2 , (.50.3). K2 , K1 , , .
. , : , , , , , , . , , .
(.51.3)
, (.51.3). , , .
321 ,, 4 ,
321 ,, 4 :
_____________________________________________________________________________91
11 =
122 =
233 = ...(3.24)
344 =
. , , , , .
. giro, , . , , , . , , , .
, , , . ( 043210 PPPPPP ). , , , , .. ( 012340 PPPPPP ). , , , (.52.3).
, . , . , . , C (.52.3), :
92
I
II
C P0 0' 0'' P1 1' 1'' P2 2' 2'' P3 3' 3'' P4 4' 4'' P0 5' 5''
(.52.3)
, ..
2ii
i
+
= ...(3.25)
i i . , , . , , .
_____________________________________________________________________________93
I
II
C P0 0'+ 0"+ 12 0+13/2 P1 1'+ 2 1"+ 11 1+13/2 P2 2'+ 3 2"+ 10 2+13/2 P3 3'+ 4 3"+ 9 3+13/2 P4 4'+ 5 3"+ 8 4+13/2 P0 0'+ 6 0"+7 5+13/2
, (
2
13),
. , 1 :
0101011 213
213 =
+
+== PP ...(3.26)
, (2C), :
I)II(c = 1802 ...(3.27) (3.27) II
, I . (2C)
, , . , , .
, , . , . n :
nA
180= ...(3.28)
94
.
, . , 1 12 , 2 - 10 , 2 - 8 , 3 - 6 , 3 - 4 4 - 3 .
, , 2 () , 3 () .
_____________________________________________________________________________95
:
- ? - ? - ? - ? - ? - ? - ? - ? - ? - ? - ? ? - ,
? - ? - ? -
? -
? -
? - "" ? -
? -
? -
? -
? -
, ?
96
,
_____________________________________________________________________________97
, , .
, 4- . , ( ), . :
( p z )
( n,...,, 21 ),
( ns,...,s,s 21 ), . (.1.4)
.
(.1.4)
, , (x,y) (P) (Z) , (p) (z) .
, , .. . , ,
98
. .
, , .. . , , , . (.2.4) .
(.2.4)
, , I . (II , III IV ), , . (.3.4) .
(.3.4)
_____________________________________________________________________________99
, .. (.4.4).
. , , , .
(.4.4)
, ( 100 ) , , .. . , , (.5.4). .
(.5.4)
100
, , .
() . , , , .
, . , , . ( ) , , , .
, . . , , , , , , . , , , .
, , , , , . , , . .. , , , , , , . , 1, .
, , . :
_____________________________________________________________________________101
- 1800 , , ;
- . , 2: 1;
- 2, 5 km , 2,0 km 1,5 km . 4,0 km.
- , .
, :
- ;
-, , . , , , , .
- . , , , , , .
- .
- , , , , .
102
,
, . .
. , : ( , , ) ( ). , , .
, , (.6.4).
(.6.4)
, , (.7.4). .. .
_____________________________________________________________________________103
(.7.4)
, , .
, . , , , .. , . 27.
(.8.4)
104
, , . , , . , . 27 , .
,
, , . , , .
. , , .
( , , ), , . , , , , . , , , .
, . . , : (.9.4).
_____________________________________________________________________________105
(.9.4) ,
. , , , . , . , . .
, , , . . . , .
106
, , .
(.10.4)
(.10.4) D D r, ..
rDD = ...(4.14)
, r . r.
(.11.4)
BBC (.11.4), :
2tghr = ...(4.15)
ABB , :
Dharcsin= ...(4.16)
r :
_____________________________________________________________________________107
21
21
=
DhDD ...(4.17)
:
DhrDD2
2== ...(4.18)
(r) (4.15). , (4.14), D. , 1 cm.
, :
22 hDD = ...(4.18) D, (.21.4)
: cosDD = ...(4.18)
(4.16) .
,
, , . , .
, . , , . 3 , (.12.4).
108
(.12.4)
, , , , : a, b c. :
( ) += 180 ...(4.23) :
msin
csin
bsin
a===
...(4.24)
:
msin
a=
...(4.24')
(b c). (4.24) :
sinmc
sinmb
=
= ...(4.25)
(.13.4) (.14.4)
, (.13.4), :
cosccosba += ...(4.26)
_____________________________________________________________________________109
(, ) a (.14.4). , , . , 180 ..
180++ ...(4.27)
f :
( ) ++= 180f ...(4.28)
, :
3fvvv === ...(4.29)
, , :
3
3
3
fv
fv
fv
+=+=
+=+=
+=+=
...(4.30)
, : 180=++ ...(4.31)
, (4.24) b c, ..
sinsin
asinmb == ...(4.32)
sinsin
asinmc == ...(4.33)
, , (4.26).
.
110
(.15.4)
(.15.4) b c . (4.24). m :
msin
c=
...(4.34)
:
msin
b=
...(4.35)
, :
mbarcsin= ...(4.36)
, 180, ..
( ) += 180 ...(4.37) a, :
sinma = ...(4.38) (4.26).
(.16.4)
, (.16.4), ..
_____________________________________________________________________________111
cosbccba += 2222 ...(4.39)
:
cosbccba += 222 ...(4.39')
, :
acbcacos
2
222 += ...(4.40)
abcbacos
2
222 += ...(4.41)
: 180=++
,
. () b c (.16.4), , :
2
2
+
=+
tg
tg
cbcb ...(4.42)
( + )/2, :
290
2
=+ ...(4.43)
( + )/2 (4.43), ( )/2, :
22 ctg
cbcbtg
+
= ...(4.44)
:
( )( )
+
=
2
2 ctg
cbcbarctg ...(4.44)
112
( + )/2 ( )/2, ..
22
22
+=
+
+=
...(4.45)
, :
sinc
sinb
sina
==
a, , ..
sinsin
csinsin
ba == ...(4.46)
( )/2 . b>c , b
_____________________________________________________________________________113
2. b c ABC = 48o3400, = 64o2600 = 67o0100 a = 138,28 m h = 4,12 m.
( ) 0010180 =++ 023001 ===fvf
000067
045264
043348
=
=
=
( ) 0000180 =++
45645184
2813822
,sin
am
,haa
==
==
m,sinmc
m,sinmb
81169
39166
==
==
3. ABC b = 166,39 m c = 169,81 m = 48o3400.
02 001067
02 006264
02 004348
=
=
=
114
004348
81169
39166
=
=
=
m,c
m,b
m,,a
,,,a
cosbccba
3013812419126
972373944642883563227685
222
==
+=
+=
235264
4464696995620275
2
222
=
=
+=
,,cos
acbcacos
230067
4744602329217976
2
222
=
=
+=
,,cos
abcbacos
230067
235264
30138
=
=
=
m,a
4. a1 ( 15) , .
Y X 15 46 332,26 52 338,26 16 46 826,28 52 422,31
.
2 1 0o 00' 00" 15 48 56 20 3 111 42 50 2 60 36 00 15 102 12 40 16 173 44 20 32108
49111
22336108
88254111
21
221
22
222
11
22
,hcc
,haa
,h,c
,h,a
'
'
'
'
==
==
==
==
_____________________________________________________________________________115
2,3,15
1,2,15
2,3,15
056375
0132104
036462
046341
2
2
2
=
=
=
=
m,sinmc
m,sinmb
,sin
am
35102
4376
099115
22
21
2
2
==
==
==
37929802
22
7518432108
89314376
11
1
11
1111
111
111
,tg
ctgcbcbtg
,cb,c
,cb,b
=
=+
=
=+=
==
m,a
,sinsin
csinsin
ba
8481
8481
1
11
11
1
11
=
===
( )
041371
210111
808197
180
21011119371930
12501
3
3
3
333
333
23
3
2
3
3
223
=
=
=
+=
====
=+=
,sinacsin
sinc
sina
m,xya
( )
8454100
360 132
=
++=
116
, . , , , , , .
, , 1:10 000. , , , , . , , , (.17.4).
(.17.4)
, , . , , , , . , , , , , . , , .
_____________________________________________________________________________117
, , : - , , - - .
:
1801 += 'nnn ...(4.47)
(4.47) , , ,
(+180) (-180
).
.
(.18.4)
32 , , 2 2, (.18.4), :
180221
32 += ...(4.48)
32
21 ( ) 2 , (.19.4), :
180221
32 ++= ...(4.49)
118
(.19.4)
(4.47), (4.48) (4.49), (.18.4) (.19.4) , 180. , ( ) 180, 180 , .
180, 360
, 360
. , (.20.4).
(.20.4)
(.32.4), :
1
1
+
+
=
=
iiii
iiii
cosdx
sindy
...(4.50)
_____________________________________________________________________________119
( 21.4).
(.21.4)
, , : ( BBAA x,y,x,y ) ,
( AC ) (DB ) , ,
A, B, C D. (A, 1, 2, 3, B) (d1, d2, d3 d4), .
(4.47), (4.48) (4.49), (.33.4), :
1805180
1804180
1803180
1802180
180
3213
3213323
21221
32
1112
1
1
+++++=+=
++++=+=
+++=+=
++=+=
+=
BAACB
BDB
AAC
B
AAC
AACA
AACA
...(4.51)
(4.51) . , :
1801
+= =
nn
ii
AC
DB ...(4.52)
120
(4.52) . , .
(f) , (4.52), ..
( )
+=
=
n
ii
AC
DB nf
1180
...(4.53)
, :
n,' 01= ...(4.54)
n,' 51=
f>, , f
_____________________________________________________________________________121
BB
A
AA
cosdxsindy
cosdxsindy
cosdxsindy
cosdxsindy
34344
323
3233
22
2122
11
111
==
==
==
==
4
3
2
1
...(4.57)
, . , , , ..
[ ] [ ] ABAB xxxyyy ; ...(4.58) fy fx :
( ) [ ]
( ) [ ]xxxf
yyyf
ABx
ABy
=
= ...(4.59)
, (fd). :
22xyd fff += ...(4.60)
(.22.4)
(.22.4). , , B, B' , , fd. , (4.60), :
122
22 lfd += ...(4.61)
, , l . , l () . , . , .
. , 50 m, :
[ ] [ ]
[ ] [ ]
[ ] [ ] 0500004000600
0500003000450
0500002000350
,d,d,
,d,d,
,d,d,
III
II
I
++=
++=
++=
...(4.62)
:
[ ] [ ] 030000012000100 ,d,d, ++= ...(4.62') fd>,
, . , , .
fd
_____________________________________________________________________________123
444444
333333
222222
111111
x'
y'
x'
y'
x'
y'
x'
y'
vxxvyy
vxxvyy
vxxvyy
vxxvyy
+=+=
+=+=
+=+=
+=+=
...(4.64)
, , .:
''B
''
''''
'''
'A
''A
xxxyyy
xxxyyy
xxxyyy
xxxyyy
43434
323323
212212
1111
+=+=
+=+=
+=+=
+=+=
...(4.65)
5 : 1 2 .
. Agl.vrednost [o] [] []
6 32 210 00 00 1 19 51 40
1 6 300 05 00 2 80 37 40
2 7 71 47 15 1 180 02 00
KOORDINATI T~. Y X o 6 14 779,16 17 417,14 o 7 15 511,46 17 492,00 o 32 13 776,62 17 487,66 o 87 17 386,05 16 758,22
124
- d () h (. .)
(m) (m)
-------------------------------------------
6 - 1 327,26 6,18
1 - 2 226,93 5,64
2 - 7 276,79 6,22
:
.19 1 2
=632 940 01 25 =6 169
0 51 40
=877 1110 22 38 =1 140 32 40
=2 251 45 15
d 1 = 327,20 =7 175 11 23 d 2 = 226,86
d 3 = 276,72
7 87 79 24 23 2 264 13 00
_____________________________________________________________________________125
126
, , , (.23.4).
(.23.4)
, , , . , i , :
( ) =
=n
iinf
11802
...(4.66)
'i , :
( ) 'nfn
ii
=
+=1
1802 ...(4.67)
.
, yf xf ,.:
[ ] [ ] 00 == '' x;y ...(4.68)
:
_____________________________________________________________________________127
[ ]
[ ]xf
yf
x
y
=
= ...(4.69)
, .
,
. (.24.4) , , , . , , , .
(.24.4)
, (4.47), (4.48) (4.49), , (4.64), (4.65).
6 : 3 4 ,
Y X
1 10 005, 84 20 276, 49 2 = 1820 15 00
2 10 210, 00 20 132, 20 3 = 1060 38 40
128
S1 = 132,56
S2 = 110,26
:
21 = 182
0 15 00
''03'5753180
''23'18127180
332
43
221
32
o
o
=+=
=+=
mSxSymSxSy
89.64cos m15.98sin
34.80cos 105.44msin4322
4322
3211
3211
====
====
_____________________________________________________________________________129
75.1162089.6486.05120
404.59 1089.15315.44 10
86.0512034.8020.13220
315.44 10105.44210.00 10
234
234
123
123
=+=+=
=+=+=
==+=
=+=+=
xxxyyyxxxyyy
, , (), , (), (.39.4).
(.25.4) AA x,y , BB x,y -
, i , id , . , , , . , (.25.4), :
130
111 - +=+= OBBA
222 - +=+= OBBA ...(4.71)
................................................
nnBBAn O +=+= -
:
OBBA = - ...(4.72)
.
( i ), (4.71), ( id ) , ( ii x,y ) :
1111 yysindyy AA +=+=
2222 yysindyy AA +=+= ...(4.73) ......................................................
nAnnAn yysindyy +=+=
:
1111 xxcosdxx AA +=+=
2222 xxcosdxx AA +=+= ...(4.74) ......................................................
nAnnAn xxcosdxx +=+=
_____________________________________________________________________________131
. , .
, , . , , .
(.26.4)
. , (.26.4), , .
, 1, a 1 . , 1 c 1 .
1, :
)(180 += - ...(4.101)
132
:
msin
csin
bsin
a===
...(4.102)
b c , : mb = sin ...(4.103)
mc = sin ...(4.104)
1 . , D , . .
22 )xx()yy(D ABAB -- += ...(4.105)
1 c( )D )( , . , :
sinD
sinc
=
:
sinDcsin =
:
)sinDcarcsin( = ...(4.106)
:
)(180 += - ...(4.107)
, 1 ,
360 ..
( ) += -1 360 ...(4.108) , (4.107), (4.108) (1), .
(.42.4), 1, a , 1 .
_____________________________________________________________________________133
(.27.4)
. 1, . .
)(180 += - ...(4.109)
:
msin
csin
bsin
a===
...(4.110)
b c :
mb = sin ...(4.111)
mc = sin ...(4.112)
1, D A , ..
22 )xx()yy(D ABAB -- += ...(4.113)
:
sinD
sinb
=
:
)sinDbarcsin( = ...(4.114)
, , :
)(180 += - ...(4.115)
134
(.28.4), 1, 1P , 2P , , .
(.28.4)
, 1, 1 2 1P , 2 2P , 1a 2a . 1b , , .
, , 21APP , :
)180 22 += 2(- ...(4.116)
:
msin
csin
bsina
===22
22
2
...(4.117)
2b c , :
mb =2 2sin ...(4.118)
mc = 2sin ...(4.119)
1AP1 1(a )c )( 1 . , 1 1 :
2- 1
90=+2
11 ...(4.120)
_____________________________________________________________________________135
1 1 ,
: 221
1
111 gcotcacatg
+=
-- ...(4.121)
1 1 , ..:
221111
1 -+= ...(4.122)
221111
1 -+= ...(4.123)
1b , :
11
11
11
sinsin
csinsin
ab == ...(4.124)
, 2ABP , , D , . .
22 )xx()yy(D ABAB -- += ...(4.125)
:
sinD
sinb
=2 ...(4.126)
:
)sinDbarcsin( 2= ...(4.127)
3 2ABP 180 ,
: )180 += (-2 ...(4.128) (.43.4), 1
360 , :
)(- 1 +=360 ...(4.129)
, 21 3 360 , . .
)(360 321 ++= - . ...(4.130)
136
:
- ? - ? - ? - ? - ? - ? - ? - ? -
? - ?
! - ? -
? - ? - ? - ? -
? -
? -
? -
? -
? -
? -
?
_____________________________________________________________________________137
, GNSS GPS
- TOPCON WILD TC 1100 , GNSS GPS GPS Leica VIVA GS08
138
, , . .
, :
- , ,
- , ..
- , . , ,
, , .
. (v) (t) ..
tvS = ...(5. 1)
, : seckm/c 300 , , , , (.1.5).
(.1.5)
_____________________________________________________________________________139
, : tcS =2
2tcS = ...(5.2)
, . , , (.2.5).
(.2.5)
t, , , , t, , .
, , :
- - ()
. ,
: - , , - , , - , . ,
, , .
, , , . , ,
140
() , , , , . , .
. , , .
, . - , . , , .
, , ( .3..5)
(. 3.5)
, .
, , , , (.4.5).
_____________________________________________________________________________141
(. 4.5)
, . , , . , , , , :
( ) ( )[ ] mmS kmSm = 6103232 ...(5.3)
142
TOPCON105N
Topcon 105N
(IPX 6), (.5.5)
(.5.5)
Topcon 105N
: -
, ;
- ;
- ,
- , .
POWER ZEROSET. (PSM) (PPM). , .
_____________________________________________________________________________143
, (.6.5)
(.6.5) , Battery empty .
, (F1) (F2).
F4 (ENTER).
Topcon 105N :
- 5. -
: (2 mm + 2ppm), 2000 m. 45 mm
30X, 1,3 m. 9 (
) , 24 000 . Topcon 105N ( ), 24 (.7.5).
144
(.7.5)
: POWER - (ON/OFF)
; * - ,
, ;
XYZ- ; DIST- ; ANG - ; MENU - ; ESC -
; ENT - ; F1,F2, F3 F4 - . Topcon 105N
.. , . (F1), (F2),(F3) (F4). , Topcon 105N , . , , , .. , , .
, , 8 500 4000 .
_____________________________________________________________________________145
WILD TC- 1100
, , . WILD TC - 1100 (.8.5).
(.8.5)
, WILD TC-1100 , . , , , (, , ) . , .
, . . .
WILD TC - 1100 "1 , "3 .
ppmmm 22 ppmmm 25 .
. , , .
146
3 km, . . ( 30 km ). , (- 200C) (+500C). 30X.
( ) , . , . . , , , , .
WILD TC 1100, LEICA - WILD TC 2002. , , , . , :
- ",10 - ",50 - ppmmm 11 - ppmmm 13 WILD TC 2002
WILD TC 1100. , , , , WILD TC 1100.
_____________________________________________________________________________147
,GNNS GPS
GNSS (Global Navigation Satellite System), GPS (Global Positioning System) . , : NAVSTAR, GLONASS GALILEO. .
NAVSTAR GPS, GPS .
GPS , : , , .
24 , 20 000 km , 6 , 12 . (.9.5).
(.9.5) GPS
, : - L1, , 1575,42 MHz 19 sm - L2, , 1227,60MHz
148
24 sm. L2 , (PPS).
(L1 L2) : C/A ( ), P , (PPS - Precise Pozitioting Service) (.10.5).
(.10.5)
, 3 (.11.5).
(.11.5)
( Colorado Springs) ), (Hawaii, Ascension Island, Diego Garcia Kwajalein ) (.12.5).
_____________________________________________________________________________149
(.12.5)
, , , , .
.
GPS GPS , .
GPS , , , () () (.13.5).
(.13.5)
150
. (.14.5).
(.14.5)
, . , , .
GPS C/A , . GPS , , . : , (WGS 84), GPS .
.
_____________________________________________________________________________151
GPS Leica VIVA GS08
Leica VIVA GS08 GPS , , .
Leica Geosystems GPS . , Net-Roverot , (.15.5).
(.15.5)
SMARTWORX VIVA LT , , .
Leica VIVA GS08 . RTCM 3.1, ( - ) . 3.5 G .
GNNS NAVSTAR . GNNS . VIVA GS08 Netrover, GNNS GS08 SmartAntena (.16.5).
152
(.16.5) (.17.5)
GS08 SmartAntenna- , . (Bluetooth) ( ).
. Leica VIVA GS 08 ( GEB211 7,4 V/2.2Ah Lithiumlon) 7 .
CS 10, LeicaVIVA GS08 . (.17.5).
CS 10 : - ( VGA), - (1 GB NAND), - (512 MB SDRAM CF/SD), - - (Bluetooth) .
Leica VIVA GS08 . , Leica, .
_____________________________________________________________________________153
, GNNS GPS :
- ?
- !
- ?
- () ?
- ? - ? -
WILD TC -1100? -
WILD TC -1100?
- GPS- ? - GPS- ?
154
()
GPS -
_____________________________________________________________________________155
, , ( ), , , .
, : , , GSP , .
()
()
. . , , d(.1.6).
(.1.6)
, (.2.6).
156
(.2.6)
A, B S
. (S) A B, , (.2.6).
, , . , (72) , (73) , . , (.3.6). , , .
(.3.6)
_____________________________________________________________________________157
. , . , . , , .
. , , .
. , , . 1 999, 1. , , , .
150 - 200 , , , .. . , . 4', 3'.
. , , .
158
, . , 130 m, , 150 m, () , 180 m. , (.4.6).
(.4.6)
(.5.6), (.6.6) .
_____________________________________________________________________________159
(.5.6)
(.6.6)
, . , 5 - 10 sm, 1 - 2. , .
160
. , (.7.6)
(.7.6)
(x)
(y) (-), (.8.6).
(.8.6)
, ,
_____________________________________________________________________________161
(x). (y) , .
. , ,
90. ,
. .
, ( 100 300 m) . , ,