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Волгоградский государственный технический университет

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fgJ Hor or # k % 3 h # #5 >?()%, !? + b &, A \ jb ! o-\ &," op %- -%, !-

F =	2J"	;	A = G	2J"

	D			MD

nM ! l ! l fi&-B %

b !-!"# !!@Bh 6&A = "R =o"D=24 (

\ &, , ! o

2J"

MDG

MD2

;

J =

0 % %, !-

! !%B fi&op--%, : "= T5 0$% 'k%, !&, , ! o- ,

MDGT

MD2

" =

;

J =

;

J =

2 0; 6 9; 8 3

2 (0; 6)2

= 1; 78

V2:

2 9

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPORS

;

= 60

TB ! M1

= 50

D = 4 ZV;

" = 1; 5 W$X!Y= Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # 'J

^`_ab_c,d_

?T2

?M1G

, * o

?M2G

, "#jb 0k#"1 # 4 5- oM h %, !-%,2& '- f

[ !

T2 H & (m

jb #"

" =

fg" Hfg&- &$M%Hor or

# k &\% & jb& # +U()41

M = RT2 RT

1 = R(T2 T1) = D2 (T2 T1)

[ ! , * & 4 o %A 5,0 b-f %#! % oM h !'$ -, #U$ #

M1A = T1 M1G;

M2A = M2G T2;

T1 = M1(G + A);

T2 = M2(G A):

>?()%, js ! o&

4 $%

6 % fi&-!U

A = "R = "

0 &, , ! o

D(T2 T1)

D HM2 G " D2 M1 G + " D2 I

J =

0; 04 [0; 06 (9; 8 1; 5 0; 02) 0; 05 (9; 8 + 1; 5 0; 02)]

= 1; 58

10 3

V2:

2 1; 5

IKJ LMJ$N=JPOS

TB ! UYdZ V = 8 V=Z; S = 18 V:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # 'K

^`_ab_c,d_

[ ! , * ooK !M f s%, * #R5

0 %- , * , & ' , "% f #"A !" # b%, !- ,

		MV2		J!2
	T =		+		;
	T =	2	+	2	;
	1	2 5				-
fg or or # k % 3 A # b%, !J = MR						-
	2

>?()%, js ! o fi&-!$% 'k3! & % 6%,V \$ ! % '\ & ' f b-#j

&, , ! o

V = !R;

! = V=R:

MV2

T =

MR2

MV2:

% % or j 2 , # "% f # h %#"",\% &-: ! %s "

%o%, ! ! & ( %

#"1%, !A = F -S fi,F

= KMG: 0

&, , ! o)U

KMGS =

MV2;

K =

3MV

;

4MGS

4GS

K =

3 82

= 0; 272:

4 9; 8 18

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

M = 6

;

TB ! UD = 30 ZV;

T = 8 Z; N = 12

Z 1

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6G[]\% 2 2& # 'J

^`_ab_c,d_'N $

&%M

0 h 4 \ *"-o f sor& ! kor# -' g" %, ! & %,- ! !or 2 &rf fi& -: "A$% '! k # or \ b !#"# ' g"$ #

M ! = !0 J T

fgJ Hor or	# B & #% 3H , , *& ' , "b fg&B-: "s#" & #5:nM$%
fgJ Hor or	!0 = 2 N					# k % 3
# ! AoK ! b%, ! \% 2 2& , k%, \ s-,or s f sor or %						# k % 3

				MD2
	J = MR	2	=	MD2
					:
				4	:
				4

K& !$fi + b f b fi&-# g"

-: "%, !- 4A$% 'k !6U # &

T = 0;

0 &, , ! o)U

J!0

MD22 N

MD2N

M =

;

4 T

2 T

M =

3; 14 6 (0; 3)2 12

= 1; 27

2 8

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! UM = 0; 4 ;

M1 = 0; 3 ; M2 = 0; 7

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # 'T ; T

^`_ab_c,d_'$

T1 &%? T2

?M1G

?M2G

[ !

, * & 4 o %A 5,0 b-f %#! % oM h !'$ -, #U$ #

A =

T1 M1G

;

A =

M2G T2

(1)

H& (, "#j

#"& 4# 4 5or or-! : # k &

-( ()-: *.

T1; T2

M = R(T2

T1)

B 4 fi&-

:$ %

" =

M =

R(T2 T1)

fgJ = 21 MR2 H or or

% 3 # #5`nM ! # ! fi& #-%-!"# ! A& 4 (

:$%

op !A = "R \ !@B &, , ! oo

R2(T2 T1)

" =

R(T2 T1)

;

A =

2(T2 T1)

0 !\ &,-&," o -()%, jbA -%, !-C2U#" &,"

2(T2 T1)

= G

(2)

[+ \ &, , ! o)U

= G

;

= 2G

; T2

= 2GM2

&," o

%, !2U-

T2 -\ %-

2(2GM2

T1) =

T1 MG

4GM2 2

T1 2T1

T1 MG

(4M2 + M)G = (2

+ 2 +

)T1

T1 =

M1(4M2 + M)G

2M1 + 2M2 + M

T2 = 2GM2

M1(4M2 + M)G

M2(4M2 + M)G

M2(4M1 + M)G

= 2GM2

2M1 + 2M2 + M

>?() 2&," o)U

0; 3 (4 0; 7 + 0; 4) 9; 8

= 3; 92

2 0; 3 + 2 0; 7 + 0; 4

0; 7 (4 0; 3 + 0; 4) 9; 8

= 4; 57

2 0; 3 + 2 0; 7 + 0; 4

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

Vd,c1

;

N2 = 10

Vd,c1

;

TB !

N1 = 8

M1 = 70

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # 'M

^`_ab_c,d_

'$'$

&%&%

0 %-

, * , & ' sor or(?&%, !# s- % 3 1 or(

J = J0 + J ;

fgH or or

# l \&+% 3% or(or or % 3 2& #-# 2

H %, * #

= M1R

\&+% or(

0 2& f ! 2& % @\ - -h3 2&\&+ # %% or( f A-&+ *-A B 4;or or #

! *&B%, !-! # ! 2 &

-6%, oK %-: ! : g"B ! % 3

or(m ! *&%, !-J = J0 5

0 !#%, !# h #"1or or & '# s o

) = !2J0

!1(J0 + M1R

, , *& ' , "A$ &+% or(%, !, "A fg&- (-() %

!1 = 2 N1;

!2 = 2 N2:

0 &, , ! o %, !-

N1(J0

+ M1R2) = N2J0

nM ! A ! \&+% oK \% 2 !-4h &," soK !oK # k % 3 1%, !-

J0 =

M2R2:

0 !-%, !-&," o-

N1( 2 M2

+ M1) =

M2;

2N1M1

(N2 N1)

= N1M1;

;

2 8 70

M2 =

= 560

10 8

IKJ LMJ$QSN=JPO

TB ! UD = 0; 8 V;	M1 = 6 ;	;
M2 = 60 ; M = 0; 5		;
R = 0; 4 V;	V = 5 V=Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6G[]\% 2 2& # '!

- '$

V M2

^`_ab_c,d_

0 ! #%, !# Por or#" o\# & ' or or o\& ' or(#J! \ 2& l f ! 2& \ 4 oK *&1oM"- %, !- or or \ & ' & "# ! A oB f oM" , ! # 2& 'O U k

J! = MVR

fg or or J# k-4% 3 or(m !O %, !# 2&+'-

J = J

+ J

+ J0

= MR2 Hor or # s % 3 1oM" ,

= M2R2 Hor or

# k

% 3 1 2&

= 21

M1R2 Hor or # k % 3 A

&, , ! o)U

(M + M2 + 21 M1)R2! = MVR

! =

;

= 0; 098 W$X!Y= Z:

(M + M2 +

2 M1)R

(0; 5 + 60 +

2 6)0; 4

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$t SN=JPO

TB !

W$X!YZ

J = 5

;

!1 = 4

= ;

L = 1; 8 V; M = 6 :

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG[]\% 2 2& # '!

^`_ab_c,d_

e]fg&-: "A$% 'k # / # or # . or# g"# b #" % 3 1 or 0 %-%# *& ' %, ! \ & jbo k %:jk$fi + 6 \ * + ! '#"k !-q-%,B #" f Bor or o % 3 1or *jk\%% ' 5 or # k % 3 1 or(m%, !J 5 - 0 2& \-% ! ! or or # k % 3 1 %:jkB #" %, !#" !- #

J = 121 ML2

b oroK !% ()41or orJ # s+ J 5,0% 3 1 !#%, !# hor(#"1or or \ & '#

!1J = (J + J )!2

J!1

5 4

;

!2 =

= 3 W$X!Y=Z:

J + J

J +

5 +

6 (1; 8)

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

;

TB ! UD = 3 V;

M1 = 180

M2 = 70 ; V = 1; 8 V=Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6H[]\% 2 2& # '!1

^`_ab_c,d_

					g" B fi&- -%,-$4% '
0 2& , , *&+ s-\ #jb &+% oK h#"l 2&,						\	!1 , *.
-% # 2&-# 5,e]fi&-: "A$% &+% or(%, ! 'b-#j- ,

	! =	V	=	2V
	! =	R	=	D
		R		D
e]fg&-: "A$% 'k 2&\--#jk b ! & U4h o# 2& '
	!2 = ! !1
nM ! ! \ %- , , *& ' oK\(?&+ k-#jk6or or, \ & ' %, !# h o - #" & g"# &65 0

							, * , *&+ 6-
!#%, !# h #"1or or & ' s\ # s o"1%, !A !- # &()o2&\							, * , *&+ 6-

!1J1 !2J2 = 0

fg or or% 3# (\&+% or( A 2&-# b ! # 2& 'B #" %, !k- ( U

J1 =

M1R2;

J2 = M2R2:

0 &, , ! o)U

M1R

!2 M2R

= 0;

(! !1) M2 = 0

+ M2

= ! M2;

! =

21 M1 + M2

!1 =

2 1; 8

= 0; 62 W$X!Y=Z:

21 130 + 70

IKJ LMJ$N=JPORS

; M2 = 80

TB !

M1 = 280

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBH

[]\% 2 2& # '

^`_ab_c,d_

U M1

, * o

[ ! !2 fg&- p$% ! '] 2 & '\% B f- #-#jb\\&+% or

!1 Hfg&-: "A \&+ \!%or( '5

0 %-

, * , & ' o & 'or or(?&9%, !# or(# &- oM A !$ #%, !#

or or \# ! b o & '

J1!1 = J2!2;

!2 =

!1:

M1R

2 Hor or

# \&+% 3% or(H%, * # \&+% or(

2 Hor or

J2 = M2R

% 3 1 2& -#5+0

&, , ! o

!2 =

21 M1R2

!1 =

!1:

M2R2

2M2

[ # & ' \&+% or( 2&

-A-#j g"1 fi&-4$%

! = !1 + !2;

B-!-%, # g":# % )- T \-%-% oM"#-!@B '2 -%, * , ! %# f?5!>?%

%, !-

4 M2

T =

!1 + !2

!1 +

!1(2M2 + M1)

2M2

sj -\ % oM"&+% oK \-% g"1 , f &

' = T !1 =

4 M2

;

(2M2 + M1)

' =

4 3; 14 80

= 2; 28 W$X!Y= 130

(2 80 + 280)

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! UM = 60 ;

L1 = 1; 2 V;

N1 = 2

Z 1

L2 = 0; 6 V:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBH[]\% 2 2& # 'N ; A

^`_ab_c,d_ XYUXN

0 % A$% \ b !1$ #%, !# # h #"1or or \ & '# s o

J1!1 = J2!2

fgJ ; J

1 2 H , , *& ' ()4$ % 3 @ !% b !()41or or # ( B##"

= ML2

;

J2 = ML22:

e]fg& - () B$ % #" @ 1-!%%, #U

!1 = 2 N1;

!2 = 2 N2; :

0 &, , ! oML12 2 N1 = ML22 2 N2;

L12N1 = L22N2;

L12

(1; 2)2

2 = 8 =Z:

N2 =

N1 =

v - %#@

L22

(0; 6)2

4 % ,f #", *&or

, "6%,%, !!! )%,Bor!- jb, ,

@ !% # #U

J2!2

J1!1

2 2

A =

[ML2

(2 N1)

ML1

(2 N1)

] = 2

M[L2 N1

L1 N1

];

A = 2 (3; 14)2 0; 06 [(0; 6)2 82 (1; 2)2 22] = 20; 4

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! D =U 75 ZV;

M = 40

F = 1

; R = 12 ZV; T = 10 Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&"; N # '

^`_ ab_ c,d _

&%D

0 A -%, !- oM , !or ;-2&%,' f Afi& - -#j #": - % #

%, !-

" =

fg M = F R Hor or\% # & j J &Hor( or

# k : -% 3 1oK

MD2

J =

MR2 =

e]fg& - ]\: $ %*" s %, !-

8F R

103

0; 12

" =

= 42; 7

W$X!Y= 2:

MD2

40 (0; 75)2

e]fg& -: "A\% $ %,% !- '! B$ % 1%,= "opT!5- -8 %,! B! b-#"%,U

N =

0 %T = 10 CU

42; 7 10

N =

= 67; 9 :

2 3; 14

IKJ LMJ$N=JPOS

TB ! UV ; H = 1000 V:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6G

[]\% 2 2& # ' ^`_ab_c,d_ U ?

'6 $H

R * 6

2&,: ,"B g"6 , )%, ! ",R = R+H ! 3 # %, ] o&R H%, * # o&4-!
	#"
&+ % # *"#j\		MM
	F =		;

		R2

fgH f %, !-# ! !3 \ "M, "H oK ! o& , "R H %, ! " 3l !# %, o& 5
7%, !-# ! !3 \ & !U !		F
	G =		=	M
				R2
	M

\-%# o& \%R = R fiR H%, * # 6 o& f %, !-# !3 \ &%, !G =-G

G H:$% 6\ f *- #" \-%#,l o& 5[? +

G =

;

M = GR2;

GR2

G =

;

(R + H)2

1 +

G =

9; 81

= 7; 33 V :

1 + 63701000

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! UM = 2 ;

1) H = 1000 V; 2) H = 1

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBH[]\% 2 2& # 'A

^`_ab_c,d_	U		?
^`_ab_c,d_


'*		$
	6		H
R			6
			6


	R
&%

2&,: ,"B g"6 , )%, ! ",R = R+H ! 3 # %, ] o&R H%, * # o&4-!

&+ % # *"#j\

F = G

;

fgG H f %, !-# !3 \ *"M, "HoK ! k o& 5, "

! b & (q *"#j % *\ \ A 2&+ s o%, !-, s

1 1

F DR = GMM R R2

= GMM R

R= GMM

R R = GMM

R R + H

fg R H%, * # o& B5M ! b &\%(q\ **"#j or % # !,ss#o& %, !- ,

C )0]%\* 2&+H =b1000-V()= 10

! (

A = 6; 67 10 11 2 5; 98 1024 6; 371 106

+ 106 !

= 1; 7 107 :

6; 37 106

)0]%\ * 2&+ b # H = 1 2U! :

A =

GMM

6; 67 10 11 2 5; 98 1024

= 12; 5

107

6; 37 106

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! M =U 30 ; Z2

; R = 6; 37 10

G = 9; 8 V=

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBH[]\%2 2&A # '

^`_ ab_ c,d _ U

'6 $

R *

v &+\% # "#j 4 #" -! 2&oK ! M, ,4\ - # % o& P%, !-F =, MG 5


nM ! l !&+%\ # "#j #"l%,\()% \-: %! 3 , & ' h -: ! A3%, ! .l
%, o& R , ; 2&: B,""w %, ! R "! 3 # %,oM& 4 -!&+:
\% # *"#j #"	F = MG R 2	;

R	R	DR		1		R	1
A = F DR = MGR2		DR	= MGR2	1		R	1	= MGR;
A = F DR = MGR2	Z	R2	= MGR2	R	1= MGR2		R	= MGR;
Z	Z


A = 30 9; 8 6; 37 106						:
1	1

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$,QSN=JPO

TB ! V =U5 V=Z= 5000 V= Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBH []\% 2 2& # '

^`_ ab_ c,d _ U ?

'6 $H

R * 6

0 1 ! #%,!#!9 %#"f 2 , % f # ! " \ 4( l , 1 - 2&\ .

3 , *& '% f 4	MV2

		= 2 1;
	2	= 2 1;
		F

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