7.

7.

147

1: A , B . E F, a D M. I, . C E.

: 3 . C , , X, . 3

0= iX 0A =+ XX , 0= iY 0BA =+ FFY ,

0A =M 022 =++ MXaFaFa B

. :

XX A = ,

aFXFB 22

M+= ,

a

FXYA 22M++= .

. z1, z2, z3 z4 .

148

+++=a

s

a

s

a

s

a

s dzMIEdzM

IEdzM

IEdzM

IEU

04

24

2

03

23

02

22

01

21 2

12

12

12

1

s1, s2, s3 s4 ,

111 22z

aFXzYM As

++== M ,

22222 )(22)( zFza

aFXzFzaYM As +

++=+= M ,

33 zXM s =M , M=4sM . e C

+

+

+=

=

==

===a a

sXs

sXs

as

Xs

as

XsX

C

dzX

MM

IEdz

XM

MIE

dzX

MM

IEdz

XM

MIEX

Ux

2

0 04

4043

303

02

202

01

101

0

11

11

11 z

XM s =

)( 22 za

XM s +=

33 z

XM s =

04 =

XM s

Cx

+= FaEI

axC 21

3103 M

F . , F,

+

+

+=

=a a

ss

ss

as

s

as

sE

dzX

MM

IEdz

XM

MIE

dzF

MM

IEdz

FM

MIEF

Uy

2

0 04

443

33

02

22

01

11

11

11

.

11

21 z

FM s =

, )(21

22 za

FM s =

, 03 =

FM s , 04 =

F

M s

+=a

FEIayE

M

41

613 .

7.

149

2 je A D M, F. AB 2I, I. . .

:

. F, Ka

FUyE = ,

U . X 0,

0==

XE X

Ux .

4 . zi, i = 1..4 .

+++=a

s

a

s

a

s

a

s dzMIEdzM

IEdzM

IEdzM

IEU

2

04

24

03

23

02

22

01

21 4

12

12

12

1 ,

si , i = 1...4 , M=1sM , M=2sM , 33 zFM s = , M+= aFzXM s 44 .

150

+

+

+=

=a

ss

as

s

as

s

as

sE

dzF

MM

IE

dzF

MM

IEdz

FM

MIE

dzF

MM

IEFUy

2

04

44

03

33

02

22

01

11

21

111

+

++

==

==

==a

sXs

as

Xs

as

Xs

as

XsE

dzF

MMIE

dzF

MMIE

dzF

MMIE

dzX

MMIEX

Ux

2

04

404

03

303

02

202

01

101

211

11

01 =

FM s , 02 =

F

M s , 33 zFM s = , a

FM s = 4 ,

01 =

XM s , 02 =

X

M s , 03 =

XM s , 44 zX

M s = .

yE xE

+=+= aFEIadzaMaF

IEdzzF

IEy

aa

EM

34)(

211 32

04

03

23

== FaEIadzzaFM

IEx

a

EM32

044)(2

1

3 3 , , B . q C F. D 2 I, I. C.

7.

151

: ,

0=+= FXX Ai ,

0=+= QFYY BAi , 0

232 == QaFaFaM BA ,

Q , qaQ = . , .

FX A = , aqFYA 4

121 += ,

aqFFB 43

21 += .

C F, C Ka ,

FUxC = ,

U .

3 . zi, i = 1..3 .

++=a

s

a

s

a

s dzMIEdzM

IEdzM

IEU

2

03

23

2

02

22

01

21 2

1221

21 ,

si , i = 1...3 , 2111 2

121 zqFzM qs == ,

152

aqzaFzM s )22

2(

22

222 += ,

333 ]43

21[ zaqFzFM Bs +== .

Fq Fq = q z1. C

+

+=

=a

ss

as

s

as

sC dzFM

MIE

dzF

MM

IEdz

FM

MIEF

Ux2

03

33

2

02

22

01

11

1211

01 =

FM s , 22 2

2 zF

M s = , 33 2

1 zF

M s = ,

xC

+=

++

+= aqFIE

aaqFIE

aaqFIE

axC 1219

32

127

31 333

4: A, B . C F. AD 2I, I. C.

: 3

7.

153

X i = 0 X A = 0 , Yi = 0 Y F FA B+ = 0 , MA = 0 02 =+ ABA FaYa M 4 ,

. FB. . z1, z2 z3 .

++=a

s

a

s

a

s dzMIEdzM

IEdzM

IEU

2

03

23

02

22

2

01

21 4

12

12

1

s1, s2 s3 , 11 zFM s = 22 zFM Bs = aFaFM Bs 23 +=

je

=+

+=

aB

ss

a

B

ss

a

B

ss

Bdz

FM

MIE

dzF

MM

IEdz

FM

MIEF

U 2

03

33

02

22

2

01

11 02

111

01 =

B

s

FM 22 zF

M

B

s = a

FM

B

s = 3

F z dz F a F a a dzBa

B

a

22

20

30

212

2 0 + + =( ) FB = -3F/2 .

Y F F FA B= + = 52 MA A Ba Y a F F a= + = 2 12 . C F . , , F,

+

+=

=a

ss

as

s

as

sC dzFM

MIE

dzF

MM

IEdz

FM

MIEF

Uy2

03

33

02

22

2

01

11 2

111

154

11 z

FM s = 02 =

F

M s aF

M s 23 =

C

IEaFFF

IEa

dzaaFaFIE

dzzFIEF

Uy

B

a

B

a

BC

3112

320

2)2(2

11

33

2

03

2

01

21

=

+=

++==

5: ACDB A , B . C F. AC CD I, DB 2 I. C.

: 4 . 3

0= iX 0A =X ,

0= iY 0BA =+ FFY , 0A =M 02 =++ ABFaFa M

,

FB. . z1, z2 z3 .

++=a

s

a

s

a

s dzMIEdzM

IEdzM

IEU

03

23

02

22

2

01

21 2

12

122

1

s1, s2 s3 , o45cos11 zFM Bs = aFM Bs =2 333 )( zFzaFM Bs +=

je

7.

155

=+

+=

aB

ss

a

B

ss

a

B

ss

Bdz

FM

MIE

dzF

MM

IEdz

FM

MIEF

U

03

33

02

22

2

01

11 0

1121

11

22 z

FM

B

s = a

FM

B

s = 2 33 zaF

M

B

s +=

[ ] =++++ a Ba Ba B dzzazFzaFdzaFdzzF 20

33330

22

2

01

21 0)()(22

1

FB = 5F/22 .

FFFY2217

BA =+= aFFaFa BA 1162 ==M .

C F . , F,

+

+=

=a

ss

as

s

as

sC dzFM

MIE

dzF

MM

IEdz

FM

MIEF

Uy0

33

30

22

2

2

01

11

1121 .

01 =

FM s , 02 =

F

M s , 33 zFM s = ,

C

[ ]

IEaF

FFIE

a

FFIE

adzzzFzaFIEF

Uy Ba

BC

13219

31

225

65

)31

65()()(1

33

3

03333

=

+=

+=+==

6: A , B . C F. I, AD 2I. C.

156

: 4 . 3

0= iX 0A =X , 0= iY 0BA =+ FFY ,

0A =M 02 =++ ABFaFa M

, FB. . z1, z2, z3 z4 .

+++=a

s

a

s

a

s

a

s dzMIEdzM

IEdzM

IEdzM

IEU

2

04

24

03

23

02

22

01

21 4

12

12

12

1

s1, s2, s3 s4 , 11 zFM s = , aFM s =2 , )( 333 zaFzFM Bs += , aFaFM Bs 24 = .

je

=

++

+

=

a a

B

ss

B

ss

a

B

ss

a

B

ss

B

dzF

MM

IEdz

FM

MIE

dzF

MM

IEdz

FM

MIEF

U

0

2

04

443

33

02

22

01

11

02

11

11

01 =

B

s

FM 02 =

B

s

FM 33 zF

M

B

s = a

FM

B

s = 4

[ ] [ ] 0221)(

2

04

03333 =++

a

B

a

B dzaaFaFdzzzaFzF ,

02)2(21)

32(

33

323

=++ aFFaaaFaF BB FB = 17F/8 .

7.

157

FFFY89

BA =+= aFFaFa BA 812 ==M .

C F . , F,

+

++

==

as

s

as

s

as

s

as

sC dzFM

MIE

dzF

MM

IEdz

FM

MIE

dzF

MM

IEFUy

2

04

44

03

33

02

22

01

11 2

1111

.

11 z

FM s = , a

FM s = 2 , )( 33 zaF

M s += , a

FM s 24 =

C

[ ][ ]

+++==

a

B

a

B

aa

C

dzaaFaFIE

dzzazaFzFIE

dzaFIE

dzzFIEF

Uy

2

04

03333

02

2

01

21

222

1

)()(111

=

=

++++++= FFEIaFF

EIaFFFFFF

EIay BBBC 8

176

17323

617

32342)

31

2121()

31

21(

31 333

EIFayC

3

4879=

.

7 ACDB A B . D F. I. D.

: 3 0= iX 0A =++ FXX B ,

158

0= iY 0BA =+YY , 0A =M 02 =+ FaXaYa BB ,

4 , . XA ,

AB XFX = , ABB XFFXY 2

1)(21 == ,

AA XFY 21+= .

. z1, z2 z3 .

++=a

s

a

s

a

s dzMIEdzM

IEdzM

IEU

2

03

23

2

02

22

01

21 2

12

12

1

s1, s2 s3 , 11 zXM As = , aXzYM AAs += 22 , 33 zXM Bs = .

F XA ,

11 zXM As = , aXzXFM AAs ++= 22 )21( , 33 )( zXFM As += .

je

=+

+=

aA

ss

a

A

ss

a

A

ss

Adz

XM

MIE

dzXM

MIE

dzXM

MIEX

U 2

03

33

2

02

22

01

11 0

111 .

11 z

XM

A

s = , az

XM

A

s +=

22 , 33 zX

M

A

s = .

7.

159

=++

+++ a Aa

AA

a

A dzzXFdzzaaXzXFdzzX2

03

23

2

0222

01

21 0)()()2

1(

FX A 2318= .

FX B 235= , FYA 23

14= , FYB 2314= .

D

+

+=

=a

ss

as

s

as

sD dzFM

MIE

dzF

MM

IEdz

FM

MIEF

Ux2

03

33

2

02

22

01

11

111 .

01 =

FM s , 22 zX

M

A

s = , 33 zF

M s = .

++

++=a

A

a

AAD dzzXFIEdzzaXzXF

IEx

2

03

23

2

0222 )(

1)()21(1 .

IEaXFx AD

3

)23

16( += IE

aFIE

aFxD33

768,369260 == .

8: A , B C o. M C. I a. CD C.

: 4 . 3

0= iX 0A =+ CFX , (1) 0= iY 0BA =+ FY , (2)

0A =M 0=+ MCB FaFa (3)

160

, FC. ,

CA FX = ,

aFF CB

M= ,

aFFY CBA

M+== .

. z1, z2 z3 .

++=a

s

a

s

a

s dzMIEdzM

IEdzM

IEU

03

23

02

22

01

21 2

12

12

1

s1, s2 s3 ,

M=1sM 22 zFM Cs =M 333 zaFzYM CAs

+== M je

=+

+=

aC

ss

a

C

ss

a

C

ss

Cdz

FM

MIE

dzF

MM

IEdz

FM

MIEF

U

03

33

02

22

01

11 0

111

01 =

C

s

FM 22 zF

M

C

s = 33 zF

M

C

s =

[ ] 0)()(0

330

222 =

++ a

C

a

C dzzaFdzzzF MM

a

FCM

45= .

aX M

45

A = , aFBM

41= ,

aY M

41

A = .

7.

161

C M. , M,

+

+=

=a

ss

as

s

as

sC dzM

MIE

dzM

MIE

dzM

MIE

U

03

33

02

22

01

11

111MMMM

.

11 =M

sM , 12 =M

sM , azM s 33 =

M

,

[ ]=

++=

+++= MMM

MMM

31

32

)(111

03

23

022

01

CC

a

C

a

C

a

C

FaFaEIa

dzaz

aF

EIdzzF

EIdz

EI

IEa

EIaaF

EIa

CM

MMM2431

45

65

37

65

37 =

=

=