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, 76@ )1,6D0*; =#6/4.> <(#56=,',-.. /5)1716@:'#@ 5/ G/)+=6,+:
=M[
] KH [ ]
] + KH [ ]
S = M[
&71
(17)
(18)
[ ] /5)1716@1'#@ 5/ G/)+=61 (1), ,
[ ]=
D[
]=
n
i =1
D[
i
]
(19)
0,A10.1 (/<GG.-.10', 0 ?,4.#.' /' 4.7, ?,(/0, ),#5)171610.@ 5/&)190/#'. . 4*2),00/&/
?0,A10.@ 7/41).'16D0/> 41)/@'0/#'. . 6@ '1;0.A1#(.; .?+1)10.> /2*A0/ 5).0.+,:'
?0,A10.1 7/41).'16D0/> 41)/@'0/#'. , ),40*+ 0,95.
). /5)171610.. #=++,)0/> 5/&)190/#'.
, 1#6. 5)/.?4/7.'#@ #=++.)/4,0.1 2/6D9/&/
(/6.A1#'4, 01?,4.#.+*; #/#',46@:3.; 5/&)190/#'. (n > 4), ),#5)1716100*; 5/ ),?6.A0*+
?,(/0,+ 5). /'#='#'4.. @40/&/ 7/+.0.)/4,0.@ /70/> .6. 01#(/6D(.; 5/&)190/#'1> 0,7
7)=&.+., 4 #//'41'#'4.. # -10'),6D0/> 5)1716D0/> '1/)1+/> '1/).. 41)/@'0/#'. 7/5=#(,1'#@,
A'/ ),#5)171610.1 #=++,)0/> 5/&)190/#'. 5).26.J,1'#@ ( 0/)+,6D0/+=.
<'/+ #6=A,1 0 = 1,96 5). = 0,95.
3.2.
3.2.1. #6. 76@
, 4;/7@3.; 4 #/#',4
, 0/)+.)/4,0* +1')/6/&.A1#(.1 ;,),('1).#'.(.
21? ),?71610.@ .; 0, #.#'1+,'.A1#(=: . #6=A,>0=: #/#',46@:3.1, '/ 5).0.+,1'#@ 7/5=310.1,
A'/ 5/&)190/#'.
@46@:'#@ #6=A,>0*+. 416.A.0,+., ),#5)1716100*+. 5/ ?,(/0=
),40/+1)0/> 56/'0/#'., '.1. 40='). .0'1)4,6,, /&),0.A100/&/ 5)1716D0*+. ?0,A10.@+.
5/&)190/#'1>, 4#1 ?0,A10.@ 5/&)190/#'1> ),40/41)/@'0*: ',(.+ /2),?/+, +,'1+,'.A1#(/1
/J.7,0.1 5/&)190/#'.
M[
i
]=0,
, #617/4,'16D0/, . +,'1+,'.A1#(/1 /J.7,0.1
#=++,)0/> 5/&)190/#'.
M[
]=0
3.2.2. )17011 (4,7),'.A1#(/1 /'(6/010.1 #6=A,>0/> 5/&)190/#'.
<(#56=,',-.. /5)1716@1'#@ 5/ G/)+=61:
n
[ ]=
&71 n — (/6.A1#'4/
2
i =1
, 4;/7@3.; 4 #/#',4
76@ )1,6D0*; =#6/4.>
[ i]
(20)
;
[ i ] — #)17011 (4,7),'.A1#(/1 /'(6/010.1 #6=A,>0/> 5/&)190/#'. i-&/
3.2.3. )17011 (4,7),'.A1#(/1 /'(6/010.1 #6=A,>0/> 5/&)190/#'. i-&/
G/)+=61:
[ i]=
&71
m
[ iO ] +
2
, %.
/5)1716@1'#@ 5/
2
(21)
Cij
i =1
[ iO ] — #)17011 (4,7),'.A1#(/1 /'(6/010.1 /#0/40/> 5/&)190/#'. i-&/
, %;
m — (/6.A1#'4/ 46.@:3.; 416.A.0, 76@ (/'/)*; 0/)+.)/4,0* .?+1010.@ +1')/6/&.A1#(.;
;,),('1).#'.( i-&/
;
Cij
— #)17011 (4,7),'.A1#(/1 /'(6/010.1 7/5/60.'16D0/> 5/&)190/#'. i-&/
> 46.@:31> 416.A.0*, %.
3.2.4. )17011 (4,7),'.A1#(/1 /'(6/010.1 /#0/40/> 5/&)190/#'. i-&/
5/ ?,(/0= ),40/+1)0/> 56/'0/#'., /5)1716@1'#@ 5/ G/)+=61:
[ iO ] =
&71
iO
/' j-
, ),#5)1716100/>
iO
(22)
KP
—5)1716 7/5=#(,1+/&/ ?0,A10.@ /#0/40/> 5/&)190/#'. i-&/
(5/
0,
(/0()1'0/1
), %;
—
(/<GG.-.10',
/5)1716@1+*> ?,(/0/+ ),40/+1)0/&/ ),#5)171610.@ #6=A,>0/>
)
5/&)190/#'. 5). 7/41).'16D0/> 41)/@'0/#'. = 1;
K p = 3 = 1, 7
3.2.5.
)17011 (4,7),'.A1#(/1 /'(6/010.1 7/5/60.'16D0/> 5/&)190/#'. i-&/
4*?4,00/1 j-> 46.@:31> 416.A.0/>, /5)1716@1'#@ 5/ G/)+=61:
&71
Cij
Cij
=
Cij
,
(23)
KP
— 0,.2/6D911 5/ ,2#/6:'0/> 416.A.01 4/?+/J0/1 ?0,A10.1 7/5/60.'16D0/>
5/&)190/#'. i-&/
/' j-> 46.@:31> 416.A.0*, %.
3.2.6. ,.2/6D911 4/?+/J0/1 ?0,A10.1 7/5/60.'16D0/> 5/&)190/#'. /5)1716@1'#@ .?
0,
.6. 5). ?,7,0.. .?+1010.@ /'0/#.'16D0/> 5/&)190/#'. /' 46.@:31> 416.A.0*
4*A.#6@1'#@ 5/ G/)+=61:
Cij
=
iO
( )K ( )
j
i
(24)
j
&71
K
1#6. 7.,5,?/0 .?+1010.@
+1')/6/&.A1#(.; ;,),('1).#'.(
j
iO
i
( )=
j
0, /
1, /
j
=
j
Oj
(25)
Oj
46.@:31> 416.A.0*, 76@ (/'/)/&/ 0/)+.)/4,0* .?+1010.@
( ) . ),410 7.,5,?/0= ),2/A.; =#6/4.> 5).+1010.@
j
,
.6.
K
i
( )=
j
Oj
j
j
(26)
1#6. 7.,5,?/0 .?+1010.@
+1')/6/&.A1#(.; ;,),('1).#'.(
46.@:31> 416.A.0*, 76@ (/'/)/&/ 0/)+.)/4,0* .?+1010.@
j
iO
( )
j
),410 A,#'. 7.,5,?/0, ),2/A.; =#6/4.> 5).+1010.@
, 5).A1+ 76@ 6:2/> A,#'. ),2/A.; =#6/4.> 0/)+.)=1'#@ /70/ . '/ J1 ?0,A10.1
( )
j
iO
— 0,.2/6D911 7/5=#(,1+/1 .?+1010.1 5/&)190/#'. i-&/
iO
( );
j
, 4*?4,00/1
/'(6/010.1+ j-> 46.@:31> 416.A.0* /' 0/)+,6D0/&/ ?0,A10.@, %;
K
i
( ) — (/<GG.-.10', .#5/6D?=1+*> 76@ 4*A.#610.@
j
Cij
;
—j-@ 46.@:3,@ 416.A.0,;
j
Oj
— 0/)+,6D0/1 ?0,A10.1 j-> 46.@:31> 416.A.0*;
j
— 5).),310.1 j-> 46.@:31> 416.A.0*, 76@ (/'/)/> 0/)+.)/4,0, +1')/6/&.A1#(,@
;,),('1).#'.(,
iO
( ).
j
3.2.7.
). 5)/41710.. /-10(. /2/23100*; +1')/6/&.A1#(.; ;,),('1).#'.(
<(#56=,'.)=1+*;
.
76@ /5)171610.@ 0,.2/6D91&/ 5/ ,2#/6:'0/> 416.A.01
4/?+/J0/&/ ?0,A10.@ 7/5/60.'16D0/> 5/&)190/#'. i-&/
/' j-> 46.@:31> 416.A.0* 4
G/)+=6,; (25) . (26) #617=1' .#5/6D?/4,'D 4 (,A1#'41 j . +,'1+,'.A1#(/1 /J.7,0.1 j->
46.@:31> 416.A.0*, /5)1716100/1 5/ G/)+=61 (6).
3.2.8. ). 5)/1('.)/4,0..
.
, (/&7, .?41#'0* '/6D(/ 0,.2/6D911
0,.+10D911
Hj
Hj
. .
?0,A10.@ j-> 46.@:31> 416.A.0*, #//'41'#'4=:3.1 )1,6D0*+ =#6/4.@+
<(#56=,',-.., 76@ /5)171610.@
'/ ?0,A10.1
Bj
.6.
Bj
Cij
4 G/)+=6,; (25) . (26) 4 (,A1#'41
j
#617=1' .#5/6D?/4,'D
, (/'/)/1 4*?*4,1' 5/@4610.1 0,.2/6D91> 5/ ,2#/6:'0/> 416.A.01
7/5/60.'16D0/> 5/&)190/#'..
3.2.9. ,),('1).#'.(. 5/&)190/#'.
.
76@ )1,6D0*; =#6/4.> <(#56=,',-..:
0.J0@@ . 41);0@@ &),0.-* .0'1)4,6,, 4 (/'/)/+ # 41)/@'0/#'D: , ),40/> 0,95, 0,;/7.'#@
#=++,)0,@ 5/&)190/#'D
76@ )1,6D0*; =#6/4.> <(#56=,',-.., /5)1716@1'#@ 5/ G/)+=61
( )
=±
(27)
6@ A.#6, .?+1)10.> 2/6D91 4 ),#5)171610.1 #=++,)0/> 5/&)190/#'. #')1+.'#@ (
0/)+,6D0/+= ( 0 = 1,96).
3.3.
3.3.1.
). #=31#'4100/> #6=A,>0/> #/#',46@:31> 5/&)190/#'.
4 #/#',4
+1')/6/&.A1#(.; ;,),('1).#'.( (MX), 0/)+.)=1+*; 5/
8.009-84, 5/+.+/ 5)1716/4
7/5=#(,1+/> #.#'1+,'.A1#(/> #/#',46@:31> /#0/40/> 5/&)190/#'.
+
, 4;/7.'
iOS
5)1716 7/5=#(,1+/&/ #)1701&/ (4,7),'.A1#(/&/ /'(6/010.@ #6=A,>0/> #/#',46@:31> /#0/40/>
5/&)190/#'.
[
iO
].
(/'/)/+ # 41)/@'0/#'D:
G/)+=61:
&71
M[
]
/ <'.+ 74=+ MX /5)1716@:' 0.J0:: . 41);0:: &),0.-* .0'1)4,6,, 4
0,;/7.'#@ 5/&)190/#'D
I ( h)
= ±(M [
76@ )1,6D0*; =#6/4.> <(#56=,',-.., 5/
] + K H [ ])
— +,'1+,'.A1#(/1 /J.7,0.1 #=++,)0/> 5/&)190/#'.
(28)
76@ )1,6D0*;
=#6/4.> <(#56=,',-.., (/'/)/1 /5)1716@1'#@ 4 #//'41'#'4.. # G/)+=6,+. (1÷9);
0 — (/<GG.-.10' 'D:710',;
[ ]
— #)17011 (4,7),'.A1#(/1 /'(6/010.1 #=++,)0/> 5/&)190/#'. 76@ )1,6D0*;
=#6/4.> <(#56=,',-.., (/'/)/1 /5)1716@1'#@ 4 #//'41'#'4.. # G/)+=6,+. (10÷16).
4.
'0:1' '%-91*%
(,A1#'41 5).+1), 4*5/6010 ),#A1' 5/&)190/#'.
'1+51),'=)* .0G/)+,-./00/.?+1).'16D0/> #.#'1+* 0, 2,?1 '1)+.0,6, 4*A.#6.'16D0/&/ #4@?. # /2]1('/+ (
) 5/ MX
(/+5/010'/4.
4.1.
,
4.1.1. ,##A.'*4,1'#@ 7/41).'16D0*> .0'1)4,6 # 5)1716D0/ 7/5=#'.+*+. 0.J01>
41);01>
&),0.-,+., 4 (/'/)/+ # ?,7,00/> 41)/@'0/#'D:
.
= 0,95 0,;/7.'#@ 5/&)190/#'D
.?+1).'16D0/&/ (,0,6, '1+51),'=)*.
4.1.2. 1?=6D',',+. ),#A1', @46@:'#@ A.#6100*1 ?0,A10.@ &),0.- 7/41).'16D0/&/ .0'1)4,6,
( )
4.2. !
"
""
#
4.2.1. .,5,?/0 .?+1)10.> '1+51),'=)* — /' 0 7/ 600° .
4.2.2. 1)4.A0*> .?+1).'16D0*> 5)1/2),?/4,'16D — '1)+/<61(').A1#(.> 5)1/2),?/4,'16D
'.5,
( ), (6,##, 7/5=#(, 2.
4.2.3. /6.A1#'4/ (/+5/010'/4 (
), .+1:3.; 0/)+.)/4,00*1 MX, 4
'1+51),'=)*
),40/ 7. ')=('=)0,@ #;1+,
'1+51),'=)* 5).41710, 0, ).#=0(1. /+5/010' 8 (#)17#'4/
5)17#',4610.@ .0G/)+,-..) @46@1'#@ '1;0.A1#(.+ =#')/>#'4/+ 4*A.#6.'16D0/> '1;0.(., 01
40/#@3.+ 5/&)190/#'D 4 )1?=6D',' .?+1)10.@.
4.2.4. /+5/010'*
, 4;/7@3.1 4 #/#',4
'1+51),'=)*, ;,),('1).?=:'#@ 5)1716D0*+.
7/5=#(,1+*+. ?0,A10.@+. 5/&)190/#'. io , =(,?,00*+. 4 ),?7. 3.
*'><*>'+%6 -71:%
*1:.1'%*>'8:
- 51)4.A0*> .?+1).'16D0*> 5)1/2),?/4,'16D
;
- 6.0.@ #4@?.;
- 0/)+.)=:3.> 5)1/2),?/4,'16D; )
- &)=55/4/>
;
- +/7=6D 0/)+,6.?,-..;
- +/7=6D (/++=',-.> 21#(/0',('0*>;
- ,0,6/&/4/--.G)/4/> 5)1/2),?/4,'16D;
- #)17#'4/ 5)17#',4610.@ .0G/)+,-..
,00*1 / ?0,A10.@; #.#'1+,'.A1#(/> . #6=A,>0/> #/#',46@:31> 5/&)190/#'. . ?,(/01
),#5)171610.@ #6=A,>0/> #/#',46@:31> 5/&)190/#'. /'#='#'4=:'.
4.2.5. ).0.+,1'#@ 7/5=310.1, A'/ 5/&)190/#'.
@46@:'#@ #6=A,>0*+. 416.A.0,+.,
),#5)1716100*+. 5/ ?,(/0= ),40/+1)0/> 56/'0/#'..
)17011 (4,7),'.A1#(/1 /'(6/010.1 #6=A,>0/> 5/&)190/#'. 1-&/
/5)1716@1'#@ 5/
G/)+=61 (21); #)17011 (4,7),'.A1#(/1 /'(6/010.1 /#0/40/> 5/&)190/#'. 1-&/
/5)1716@1'#@ 5/ G/)+=61 (22).
)17011 (4,7),'.A1#(/1 /'(6/010.1 7/5/60.'16D0/> 5/&)190/#'. 1-&/
/' j->
46.@:31> 416.A.0* /5)1716@1'#@ 5/ G/)+=61 (23).
?,4.#.+/#'. /' 4.7, G=0(-.. 46.@0.@
(6.01>0,@ .6. #'=510A,',@) 0,.2/6D911 4/?+/J0/1 ?0,A10.1 7/5/60.'16D0/> 5/&)190/#'.
/5)1716@1'#@ 5/ G/)+=6,+ (24) . (25) .6. (24) . (26) . 5/ 7,00*+ ),?7.3.
4.2.6. )17011 (4,7),'.A1#(/1 /'(6/010.1 #6=A,>0/> 5/&)190/#'.
[ ] /5)1716@1'#@
&1/+1').A1#(.+ #=++.)/4,0.1+ #)170.; (4,7),'.A1#(.; /'(6/010.> #6=A,>0*; 5/&)190/#'1>
(,J7/&/
5/ G/)+=61 (20).
4.2.7. =++,)0,@ 5/&)190/#'D
, /5)1716@1+,@ &1/+1').A1#(.+ #=++.)/4,0.1+ 2/6D9/&/
A.#6, 01?,4.#.+*; . #/.?+1).+*; #6=A,>0*; 5/&)190/#'1> (n > 4), 5/7A.0@1'#@ 0/)+,6D0/+=
?,(/0= ),#5)171610.@.
,(.+ /2),?/+, 0.J0@@ . 41);0@@ &),0.-* .0'1)4,6,, 4 (/'/)/+ # 7/41).'16D0/>
41)/@'0/#'D: , ),40/> 0,95, 0,;/7.'#@ 5/&)190/#'D
, /5)1716@1'#@ 5/ G/)+=61 (27).
4.2.8. /+5/010'*, 4;/7@3.1 4 #/#',4
'1+51),'=)*, 0,A.0,@ # n = 2 ),#5/6,&,:'#@ 4
(/07.-./0.)=1+*; 5/+1310.@;, '.1. 0,;/7@'#@ 4 0/)+,6D0*; =#6/4.@;:
1+51),'=), /()=J,:31&/ 4/?7=;, .............. 20±5°
'0/#.'16D0,@ 46,J0/#'D 4/?7=;, ................. 60±20%
'+/#G1)0/1 7,4610.1...................................... 101±10 ( ,
4.3. $
%"
&
'"
"
4.3.1. )17011 (4,7),'.A1#(/1 /'(6/010.1 #6=A,>0/> #/#',46@:31> 5/&)190/#'.
'1+51),'=)* /5)1716@1'#@ 4 #//'41'#'4.. # 5. 3.2.2 5/ G/)+=61 (20):
2
2
[ ]=±
&71
+
+
2
2
+
+
2
)
2
3
+
+
2
3
2
4
3
— /#0/40,@ 5/&)190/#'D '1)+/<61(').A1#(/&/ 5)1/2),?/4,'16@, /5)1716@1+,@ 5/
2
50431 -92;
= 0,0075 ; 600° = 4,5° ;
m
=±
2
4,5o
100% = 0, 75%
600o
— 7/5/60.'16D0,@ 5/&)190/#'D /' /'(6/010.@ '1)+//' 0/+.0,6D0/> 5/
= 0,15
=±
6
t
t
'1)+/<61(')/70*; 5)/4/7/4
24335-80;
4 A'/ #//'41'#'4=1'
100% = ±
= ±3,8o ,
t
3,8o
100% = ±0, 6%
600o
= ±0, 4% ;
— /#0/40,@ 5/&)190/#'D .?+1).'16D0/&/ 5)1/2),?/4,'16@ '.5, `-79,
—
)
/#0/40,@
5/&)190/#'D
&)=55/4/&/
0/)+.)=:31&/
5)1/2),?/4,'16@,
= ±0,1% ;
)
3
3
4
— /#0/40,@ 5/&)190/#'D +/7=6@ 0/)+,6.?,-..,
= ±0, 2% ;
3
— /#0/40,@ 5/&)190/#'D +/7=6@ (/++=',-.. 21#(/0',('0/&/,
3
— /#0/40,@ 5/&)190/#'D ,0,6/&/4/--.G)/4/&/ 5)1/2),?/4,'16@,
,(.+ /2),?/+, #)17011
'1+51),'=)* #/#',4.':
/'(6/010.1
2
[ ] = ±0, 74%
2
2
2
2
5/&)190/#'.
+ ( 0,5 )
2
4
3
4.3.2. )1716D0/ 7/5=#(,1+/1 ?0,A10.1 5/&)190/#'.
G/)+=61 (27)
( )
#=++,)0/>
( 0, 75 ) + ( 0, 6 ) + ( 0, 4 ) + ( 0,1) + ( 0, 2 ) + ( 0,5 )3
2
[ ]=±
(4,7),'.A1#(/1
= ±0,5% ;
.
4 = ±0,5%
'1+51),'=)* 4*A.#6@1'#@ 5/
= ± ( 0,96 × 0, 74 ) = ±1, 45%
4.3.3. ).0.+,1'#@ ?0,A10.1 0.J01> (41);01>) &),0.-* 7/41).'16D0/&/ .0'1)4,6,, 4
(/'/)/+ # 41)/@'0/#'D: , ),40/> 0,95, 0,;/7.'#@ 5/&)190/#'D
'1+51),'=)*:
( )
1.
2.
= ±1, 5%
23.1 5/6/J10.@
#;/70*1 7,00*1 76@ ),#A1', /2/23100*; +1')/6/&.A1#(.; ;,),('1).#'.(
3. ,#A1' /2/23100*; +1')/6/&.A1#(.; ;,),('1).#'.(
=#6/4.> <(#56=,',-..
3.1. 1)4*> +1'/7 ),#A1',
3.2. '/)/> +1'/7 ),#A1',
3.3. )1'.> +1'/6 ),#A1',
4. ).+1) ),#A1',
.
.
76@ )1,6D0*;
4.1. 1')/6/&.A1#(.1 ;,),('1).#'.(., 5/761J,3.1 ),#A1'=
4.2. #;/70*1 7,00*1 76@ ),#A1',
4.3. ,#A1' 5/&)190/#'. .?+1).'16D0/&/ (,0,6, '1+51),'=)*
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