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Волгоградский государственный технический университет

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[НЕСОРТИРОВАННОЕ]

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V; ' = AT + BT3;

Z3 W$X!Y= Z; B = 0; 2 W$X!Y= ;

! #" $ # % & '

&," ! # - ./ ! - 0 1% 2 + ! 3 %# 41 -:

;5=< >?() @ "A@B &+ ,< C D!E F

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB IKJ LMJ$N=JPO$QRO,S

TB ! R =U 1; 2

A = 0; 5

T = 4 Z

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&A ; A# ; A'

^`_ ab_ c,d _

e]fg& -: "1 $ % 'h%\ fi&- #jb- \6k $%# %$jk l%, !-

- U

! =

= (AT + BT3)0 = A + 3BT2;

" =

= (A + 3BT2)0 = 6BT;

nM ! f 3 , *& '

% oK *& ' $ % #"

= "R = 6RBT;

AN = !2R = (A + 3BT2)2R;

0 &

$ %

>?() 2&,"

= Q + N

opA - A 2& (q &," or or # s- % or

T = 4 ZU

= 6 1; 2

0; 2

;

V= Z2

;

4 =2 12

= (0; 5 + 3 0; 2 4 ) 1; 2 = 16; 43 V=

0 &

= 16; 49 V=Z2:

A = Q(1; 44)2

+ (16; 43)2

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO$Q+t S

TB ! R =U 1 V;

= AT

+ BT2;

A = 8 V=Z; B = 1 V= Z2;

T = 2 C:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&V; A # '

^`_ ab_ c,d~A _

KAA

v % ' - \#jb %#"h$jk U

V =

= (AT + BT2)0 = A + 2BT:

>wor or # sT =- 2%ZU or

V = 8 2 1 2 = 4 V=Z:

nM ! f 3 , *& '

:$% U

A =

= (A + 2BT)

= 2B = 2 ( 1) = 2 V=

% oK *& '

$% 2

AN = V

= 4 V=Z2:

0 & $% U

A = QAN2 + A2 = Q42 + ( 2)2 = 4; 47 V= Z2:

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO$Q S

;

TB ! X1 = A1 + B1T + C1T

X2 = A2 + B2T + C2T2;

A1 = 10 V; B1 = 1

; C1 = 2

;

A2 = 3 V; B2 = 2

; C2 = 0; 2

;

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # '

; A1

;

^`_ab_c,d_

v % 1 g" %-\!()%, js % #-\ b-% or() 1 ! s$% ,

V1 =

V2 =

DX1 = (A1 + B1T + C1T2)0 = B1 + 2C1T;

DX2 = (A2 + B2T + C2T2)0 = B2 + 2C2T;

0 % %, !- -: "A % \%T = \ &, , ! o

B1 + 2C1T = B2 + 2C2T; 1 + 2 ( 2) = 2 + 2 0; 2 1 4 = 2 + 0; 4 ; = 0; 23 Z;

>?% oM"\ &, & ' ! % 3, 2& ' !5T = 0r 2& B B, , &+-\ f &
oj !$B, !o	k % %, !-\B (-2& (?& \%, !] k-&,F 6 , * , *&


! ! s-% or 5
eK$% #" U
		DV1		0	= 2C1 = 2( 2) = 4 V2 ;
A1 = DT			= (B1 + 2C1T)		= 2C1 = 2( 2) = 4 V2 ;
A2 =		DV2	= (B2 + 2C2T)0	= 2C2		= 2(0; 2) = 0; 4ZV
A2 =			= (B2 + 2C2T)0	= 2C2		= 2(0; 2) = 0; 4ZV
		DT				Z2

eK$% #" 1 !-g"# k ! s-% or 5 GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO$Q RS 3

TB ! UR = 0; 5 V; ' = AT + BT ;

A = 2 W$X!Y=Z; B = 0; 2 W$X!Y= ;

T = 3 Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # 'A

^`_ab_c,d_ e]fg&-: "A$% 'k h fg& !- - :$%- 6U$&

! = D' = (AT + BT3)0 = A + 3BT2;

" = D! = (A + 3BT2)0 = 6BT;

nM ! f 3 , *& ' % oK *& ' $ & $ b%, !- #"( U

= "R = 6RBT;

= !2R = (A + 3BT2)2R:

0 &

$ %

A = QA2 + AN2

= Q(6RBT)2 + (A + 3BT2)4R2:

>wor or # sT =- 3%Z\ or&

$ %

6%, !-

A = Q

(6 0; 5 2 3)2 + (2 + 3 0; 2 32)4 (0; 5)2

= 32; 8 V=Z2:

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! R =U 8 V;

AN = 4 V=Z2;

= 60 :

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&V; A # '

^`_ ab_ c,d~A _

KAA

% oK *& '

$ % %, !-

= !2R =

[ +

V = Q

= P

= 5; 66

ANR

4 8

V :

0 & $ % U

A =

COS

nM ! f 3 , *& '

: $ %

COS2

AN2

AN2 = S

= ANS

= A2

AN2

= ANTG( );

COS

A = 4 TG(60 ) = 6; 93

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO$Q S

TB ! X =UAT + BT3;

A = 6 V=Z;

B = 0; 125 V= Z3;

T1 = 2 Z; T2 = 6 Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&< V ># ' ^`_ ab_ c,d _

v % 'b 1%, !-

V =

= (AT + BT

)

= A + 3BT

= 6 0; 375T

;

-% or$% 's ! !"1%, !- 4A\% 2 2&," o !# &-#

>w $! or or % ()4# sT0

T0 U

6 0; 375T0 = 0;

T0 = S

0; 375 = 4 Z:

0 2&f or or#$% ' 6 !"6 ! % 3, 2&+'-# -#jb g"646 %,- o

, \%, !-&

0]$'\% 4

()4$ 41 sor or #

T0 %, !-

S1 = (AT0 + BT13) (AT0 + BT13) = (6 4 0; 125 43) (6 2 0; 125 23) = 4; 5 V:

T6-f " 'b%,-, b \ o%, !-&

! sor or # ! b-% or

T2 # \%: # \$ '

S2 = (AT0 + BT03) (AT2 + BT23) = (6 4 0; 125 43) (6 6 0; 125 63) = 7 V:

v% 2 \#"#"$ -: " % ' U

< V >=

S1 + S2

4; 5 + 7

= 2; 88 V=Z:

T2 T1

6 2

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS

TB ! UX = AT + BT3;

A = 3 V=Z; B = 0; 06 V=Z3;

T1 = 0;

T2 = 3 Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # '

VX;

AX; < VX

>; < AX

^`_ab_c,d_

v % 'b 1%, !-

= (AT + BT3)0 = A + 3BT2 = 3 + 0; 18T2:

eK$%

AX = DVX = (A + 3BT2)0 = 6BT = 0; 36T:

>wor or

# s-% orU

T1 = 0

AX1 = 0; 36 0 = 0:

VX1 = 3 + 0; 18 (0)2 = 3 V= Z;

>wor or

# s-% orZU

T2 = 3

AX2 = 0; 36 3 = 1; 08 V=Z2:

VX2 = 3 + 0; 18 (3)2 = 4; 62 V= Z;

0]$'\% 4

()4$ 41 sor or #

S = X2 X1

+ BT23) (AT1

T2 %, !-

= (AT2

+ BT13) = (3 3 + 0; 06 33) 0 = 10; 62 V:

v% 2 #"#"1$% ' U

10; 62

< VX >=

= 3; 54 V=Z:

3 0

T2 T1

v% 2 $% !U

4; 62

< AX >= VX2 VX1

= 0; 54 V=Z2:

T2 T1

3 0

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS	$Q
	' = A + BT + CT3;
TB ! R =U 0; 2;
A = 3 W$X!Y; B = 1		;


T = 10 Z;	C = 0; 1
		3 :
GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2& # '
	A ; AN; A

^`_ ab_ c,d _ e]fg& -: "A $ % 's %, !- ,

! = D' = (A + BT + CT3)0 = B + 3CT2;

e]fg& - ] : $ % !U

" = = (B + 3CT2)0 = 6CT;

% oK *& ' $ % U

= !2R = (B + 3CT2)2R

nM ! f 3 , *& ' : $ % !U

= "R = 6CTR

>wor or # sT =- 10% ZUor

AN = ( 1 + 3 0; 1 102)2 0; 2 = 168; 2 V=C2; A = 6 0; 1 10 0; 2 = 1; 2 V=C2

0 &

$ % U

A = QAN2 + A2 = Q

(162; 2)2 + (1; 2)2

168; 2 V=C2:

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO$Q S

TB ! H =U2 V;

= 0; 5 V;

M = 200

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6HW Y d P

c,d _

^`_ ab_

0 * + "A H-@()!% @! (!% A "1+\&!%:"# ! A s $ % '

V =

2GH;

b ! ! \& -#: P

!(m k !s $ % '

2GH1:

V1 =

\o & ' b@ !% A MV A \+ !%,- -&A%, !#-\ 2& s + !%,\&A@ # !%; f

\o & ' `%,MV1 \%, !- & 5v6- - %\%,ol-,& \ "6' # oor- \ & ' ? o

@ !% # b%, !-

+ V1)

P = MV + MV1 = M(V

P = M(P

+ P

) = MP

+ P

)

2GH

2GH1

P = 0; 2 P2 9; 8 (

2 + P0; 5) = 1; 88

IKJ LMJ$N=JPO

TB ! M =U 8

;

V = 250 V= Z

M1 = 6 ;

U1 = 400 V= Z

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&U # '

^`_ ab_ c,d _

! #%, #! h \ "1' o

MV = M1U1 + M2U2

= M M1

= 8

6 = 2

&, , ! o)U

fg M2

U2 =

MV M1U1

8 250 6 400

200 V=C:

v %

U2 \ &, !&+%! '3, Hor2& ''!@B 4 4\ & -$ %, \%, o - &,

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO O O,S

;

TB !

V1 = 3

= ;

M1 = 210

M2 = 70

; U1 = 4 V=Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2& # '

U21

^`_ ab_ c,d _ U2

JM1 J

JM1

0 % - , *\ , & &' ' s2& o jk 1(?&%, !-2& -U $ o

[

(M1 + M2)V1

, * o

U2 \H % \ 'h 2&2& -jk ;A ! & \! 2 B'!f. A

& - % ()f # &R5+&' % or(op !-

M1U1 \M2U2

0 ! #%, #! h "1' o

[

(M1 + M2)V1

= M1U1 M2U2

+ &, , ! o

U2 =

+ 1 V1

v % 's 2& - # b !

# 2& ' s 2& jk

U21 = U1 + U2 = U1 +

+ 1 V1 =

+ 1 (U1 V1)

U21 =

210

+ 1 (4 3) = 4 V=Z

IKJ LMJ$N=JPO O t S

TB ! M1U= 60

;

= 480 V=Z;

= 30

;

= 18 ;

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&U # '

^`_ ab_ c,d _

W M1; U1

# &

% -

, *\ , & &' ' s#(?&1%,o or(!-65

0 ! $#%, #! b \o "'\ 2&- () % 2&+\% 6 oroK3\o&4 ' -6 \&+, !%:". +

% or(, bf % # \%,# !!-*&&' ! ! ! k%,#j 6U!- , b # &

M1U1 COS M2U2 = 0

[ +\ &, , ! o

U2 =

M1U1 COS

60 480 COS(30 )

= 1; 4 V= Z:

18 103

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPORS O

;

V = 8 V=Z:

TB ! M =U 300

= 60

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&P # '

^`_ ab_ c,d

~V0

T6 ] + !%, ]@ !%

# \b \%f # &!-" &,"%%, ,!- "s#" "s&+ !

= V SIN

\& + #!%,! b !- &," "1 $ % 1 # or #"

VX0

V SIN :

] or

\ & ' 6 b@o !%

PX = M(VX0 VX) = 2MV SIN

! #%, #! h \ "1' \ ob \o&, ()4%,$ !-4

PX = 2MV SIN ;

P = 2 0; 3 8 SIN 60

= 4; 16 V=Z:

IKJ LMJ$N=JPOS

TB ! M1U= 60 ;

M2 = 20 V=Z

V = 2 V=Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&U # '

^`_ ab_ c,dJ _~U1

~U2

[ !

6 ! % # 'B& ' 2& jk h !

, * $ %o ' 2& -\ &+U1

\ &+

U2 5[ # 2& ' , "1 \%, %!- & ~U2 'k~U #"\ ! ,op (% %, !- ,

V = U1

+ U2;

nM ! A\ %! - , , *& ' s \ 2& - & \ A' ! 2%,#jk!h \ "1' o

M1U1 M2U2 = 0

] h-! %, !-\ &, ,4 ! o)U

= V

U2;

(V U2) M2U2 = 0;

U2 =

V=Z

1 = 0; 75

M1 + M2

60 + 20

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS O

TB ! V =U400 V= Z;

M1 = 0; 4M;

U1 = 150 V= Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&U # '

^`_ ab_ c,d _

0 ! #%, #! h \ "1' o

M2U2

M1U1 = MV

fg U1; U2 H $ % 1 $ & - 5

>?()%, jsoK! o ( $

&$ - % , , *&oK' !# , !%:" \+ !-- &,"

%, !-

M1 = 0; 4M; M2 = M 0; 4M = 0; 6M

0; 6MU2 0; 4MU1 = MV; 0; 6U2 0; 4U1 = V;

V + 0; 4U1

400 + 0; 4 150

= 767 V=Z:

0; 6

IKJ LMJ$N=JPOS O

TB ! L =U1; 8 V;

M1 = 8 ;

M2 = 4 ;

= 3

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2&V # '

^`_ ab_ c,d _

C L

M2-

U~V

[ ! ,U * o% '6@ \ !%,& 64h- or-6or$ fi\]+&,"\# \ * - @ k !% ! %:"

-s

o)5 0 #%,! !$ \# h"' o

M2V = (M1 + M2)U;

U =

+ M2

\ &- s%, Bor '!@B oKh-! oror(m@ !%,

nM ! !oK !

M1 + M2 B"-4k , !or 2

- () 4A '

, or2& jk% % 'koK &! 5 04 %op

U =

>p + *& '

\% 4#@B% f2 ! oP # or @ !%, b # opoK./ !B-b !(\ o&%:"5-!@B 4

0 &, - % f@# !%\ "lor , s- ()H 5+0 !%! ow f

% \f %#" 4-\ ! 3 6U, *& '!

M1U2

= M1GH;

U2 = 2GH;

>?()%, -js()! \o! ! #"# #"13 #H %, soK% ! U f@ &!%,

H = L(1 COS );

0 &, , ! o)U

= 2GL(1 COS );

V =

Q2GL(1 COS );

V =

9; 8 1; 8(1 COS 3 ) = 440 V=Z

0; 004

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPOS O

TB ! M1U= 300 ; M2 = 80 ;

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\%2 2& # ' ^`_ ab_ c,d _

nM ! B ! 6 + !\%or & ! ]# f 4 \ 2& ` + !%, or & !

B ,!,$ -$: *& 'or '#"

% 'V 5[ ! ! , * o % 'sor & ! ! 6 b + !%,U 5

r 2& \% % 'koK ! 4 # bj 2& \ b !#%, !# h\& ' #"1 o

+ M2)V

M2U = (M1

, * , & ' , "% f #"1or & ! #U"

T1 =

M2U2

"% f #"1or & ! b-or \ 2& + !%, b%,, !$ -: !*& '- ,4

T2 =

(M1 + M2)V2

;

] \ %-f b %, !-

#" UM2U

V =

;

M1 + M2

(M1 + M2)

(M2U)2

M22U2

T2 =

(M1 + M2)2

2(M1 + M2)

, "1 # # j 2&, 6 %, !- , 5[? + k 0T %, !-

% f #" %, * % oK !3

T1 T2

= 1

M22U2

= 1

2(M1 + M2)

M2U2

M1 + M2

300

= 0; 974:

300 + 8

GBGBGBGBGBGBG6GBG6GBGBG6GBG6GBG6GBG6GBGBG6GBG6GBG6GBGBG6GBG6GB

IKJ LMJ$N=JPO OS

TB !

;

V1 = 4

M1 = 1

= ;

M2 = 2

; V2 = 3 V=Z:

GBGBGBGBGBGBG6GBG6GBG6GBG6GBGBG6GBG6H[]\% 2 2& # '

U1; U

^`_ab_c,d_

!#%, !# h\& ' #"1 o

M1V1 M2V2 = M1U1 + M2U2

(1)

0 !#%, !# h % f#"\% A \%# f o + !%

M1V12

M2V22

M1U12

M2U22

(2)

>?()%, js ! o

U2 # %, !-C ? \ !#" -&," op-%, !-

U2 =

(V1 + U1) V2

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