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.………………………………………………………………………....... 5

1. ………………………………………………………..... 61.1. . ...……………………….… 71.2. ………………….…………………………….... 111.3. . ( )……...……….... 111.4. .……………...…………………………..... 121.5. .………………………………..... 141.6. .…………………....... 171.7. ………………...... 181.8. ……………………………………………………..... 191.9. .……..……..… 201.10. .………………………...……... 211.11. .( )………………………….…... 221.12. ………………………………………..... 251.13. .……………………………………………..….…..... 251.14. .……………………………….……..… 251.15. , .…………………….…... 261.16. .……..………………..…..… 281.17. , .……….... 281.18. .………….………………... 291.19. . .……………………………………..….. 311.20. .…………………………….... 321.21. .………………………………………...... 331.22. .... 331.23.

.……………………………………..… 341.24. ……..….…... 351.25. , …………….... 371.26. ………………..… 371.27. …………………………………….. 401.28. …………………………………………………… 411.29.

…...…………………………………... 411.30. …………………………………………………….. 441.31. ……………………………………………. 46

…………………………............ 50

4

2. ………………………………………………...….. 522.1. ……………………………………………………… 522.2. .……….…………………………….. 552.3. …………………...………………………… 622.4. ……………………………….…….. 642.5. …………..… 662.6. …...……….... 682.7. …………...………………….. 732.8. ……….. 77

………………………………….. 83

3. ………………...……………………...…………..…….. 853.1. ……………………..………………….. 853.2. ……...… 863.3. …..…. 873.4. ………...… 883.5. .…….………………………. 893.6. ………………………….... 923.7. ( )

.…………………………….………………. 943.8. .…………………………… 973.9 …………………………………… 983.10 ……... 993.11

)………………………………………………………… 993.12 ………………………………..…………. 1013.13 …………….. 1023.14

( )……………………………….. 1043.15

………………………………………………………… 1053.16 ……………………………………… 1063.17 .

…………………………………………... 1083.18 . …………………………………………….. 1103.19 …………………………………………… 1203.20 ………………………………………………..... 1253.21 .

…………………………………………………………. 126………………………..……….. 128

…………………………………………. 132

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29

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30

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42

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45

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46

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47

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49

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, ?

51

34. ?35.

?36. ?37. ?38. ?39. ?40. ?41. ?42. ?43. ?44. ?45. ?46. ?47.

?48. ?49. , ?50. ?51. ?

52

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.

53

, xyz,

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it irix , iy , iz .

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54

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55

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56

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-r .

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kzjyixkdtdzj

dtdyi

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,.

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58

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59

dtdS

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60

dtSd

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22

nWWW,

– ( ) W

nW .W , W nW .

( )

2

2

dtSd

dtdW

61

.

dtd

,

Wdt

d

222

zyx

zzyyxxWWW ;

dtdW

, .

, .

0W , .

nW2

n

.

2

nW ,

– .

2222n

2

dtdWWW .

W n

WWW )€,cos( ;

WWnW n),cos( .

W

nWWtg .

.

62

( )

dtzyxSt

0

222,

dtdxx ;

dtdyy ;

dtdzz –

. «+» «-»

S; S, «+», –

«-»..)const( , .

tSS 0 . «+» ,

, – «-«. –

, constW .

tW0 .

2tWtSS

2

00 .

2.3 :

1 – , ;

2 – , ,.

( ) . ( )

– .

Oxyz ).

63

1 – . . 1

2221 zyxO 1111 zyxO , .

2221 zyxO , , Oxyz .

1111 zyxO , ,

2221 zyxO Oxyz .

Oxyz r , 1111 zyxO – . 1

Oxyz1or .

1orr ,

111111o kzjyixrr1

, (2.3)1, 1, z1 – , 111 zyOx

.

11o z,i,r1

– , . (2.3) ,

:

131121111o azayaxxx1

;

231221211o azayaxyy1

; (2.4)

64

331321311o azayaxzz1

111 ooo z,y,x – 1 Oxyz ;

111 z,y,x – 1111 zyxO ;333231232221131211 a,a,a,a,a,a,a,a,a – ( )

2221 zyxO 1111 zyxO .

11211 )€,cos( axxii ; 12211 )€,cos( ayxji ; 132121 )€,cos( azxki ;

21211 )€,cos( axyij ; 22211 )€,cos( ayyjj ; 232121 )€,cos( azyki

31211 )€,cos( axzik ; 23211 )€cos(€ ayzjk ; 332121 )€cos( azzkk (2.4) 111 z,y,x

: 111 ooo z,y,x

mna )3,2,1n,m( .,

:0aaaaaa;1aaa 333123211311

231

221

211 ;

0aaaaaa;1aaa 323122211211232

222

212 ;

0aaaaaa;1aaa 333223221312233

223

213 .

,

– 1 . . 1

. (2.4)

.,

, ,

.,

.

2.4 .

, , ,

.

65

Oxyz . 1 ( ) 1111 zyxO , .

, 1111 zyxO ,

Oxyz , .,

Oxyz.

1o131121111o xxazayaxxx11

;

1o231221211o yyazayaxyy11

;

1o331321311o zzazayaxzz11

;1aaa 332211 ;

0aaaaaa 323123211312 ;1o xxx

1;

1o yyy1

; (2.5)

1o zzz1

; (2.5) 1111 zyxO – ,

111 ooo z,y,x –, )t(fx 1o1

; )t(fy 2o1; )t(fz 3o1

)t(rr11 oo .

.

66

– 1 ( )., .

, .

.,

111

ooo

dtrd

dt)r(d

dtrd

const ;1o

11

oo W

dtd

dtdW

1oWW

, 1 – ., 1 ,

, .

.

2.5

, ., ,

..

xyz Z, . .

1x1y1z1 , z1 z.

xyz

67

12111113112111101M ayaxazayaxxx ;22121123122121101M ayaxazayaxyy ; (2.6)

1333132131101M zazayaxzz ;0zyx 010101 ;

0aaaa 32312313 ; 1a33 ;;sina12 ;sina 21 ;cosaa 2211

(2.6) 11,1 z,yx - ;

221121,12 a,a,aa - , )t( (2.7)

, – .

, .

(2.7) .

- . - z

, («+»), («-»).

.

68

2.6 - ,

. - , ,

:

kdtd

t , t , :

dtd

tlim

0t.

.

, 1 , 1 ;

30n

60n2 ;

30n

n – : [n], .

– , .

– , :

kdtd

t , t , :

dtd

tlim

0t;

, .

2 , 21 , 2 ;

, , ,

, ,, .

69

.

, .

.,

.

z .

xyz - ;x1y1z1 – ,

– r :

11111 kzjyixr (2.8) x1,y1,z1 – x1y1z1 )

111 k,j,i - x1,y1,z1 ).:

dtkdz

dtjdy

dtidx

dtrd 1

11

11

1 ;

1k , 0dtkd .

70

dtjdy

dtidx 1

11

1 (2.9)

dtid 1

dtjd 1

:sinjcosii1 ;

cosjsinij1 ,

i , j - xyz .:

;jjdtdcosjsini

dtd

dtdcosj

dtdsini

dtsinjcosid

dtid

11

1

;iidtdsinjcosi

dtd

dtdsinj

dtdcosi

dtcosjsinid

dtjd

11

1

dtid 1

dtjd 1 (2.9)

iyjx 111

, , ,

111 zyOx :11x yV ; 11y xV ; 0V 1z ;

r111 zyOx .

jxiyzyx

00kji

r 111

111

111

.

r , r -

, , – .

, ,

r , , .

( )

71

rsinr ,. (

)., ,

,00 0 ,

RR ;

, .

,

.dtrdr

dtd

dt)r(d

dtvdw

dtd

dtrd ,

.wwrw.

– w – w .

72

rw, ,

r , . w , v .

w :r,sinrw ,

- . .

vw .w ,

v , v .

( ) w2v

2sinv)v,sin(vw

v . ( ) ,

,

;www 4222222

42w, w w ,

22wwtg ;

.)

const , .:

t0

) , const , .

:t0

2tt

2

00

73

2.7 ,

. – ,

Oz ). –

xOy , ,

.

.,

xOy, , ,

, xOy.,

.

.1 – . O1x2y2

Oxy. O1x1y1,

O1x2y2 , Oxy.

, ,

Oxy :12111101M ayaxxx ;

22121101M ayaxyy , (2.10)cosaa 2211 ; sina12 ; sina21

74

(2.10) 1x , 1y - , 211222110101 a,a,a,a,y,x -.

, );t(fx 101 );t(fy 201 )t( (2.11)

, : 1

1., ,

. (2.11)

.:

, , .

. .

. - Mr , :

01M rr ,01r - 1 Oxy;

- - O1x2y2;

:

dtd

dtrd)r(

dtd

dtrd 01

01M (2.12)

dtrd 01

1

dtrd 01

01 ;

dtd

O1x2y2.

dtd

01M

O1x2y2

1:01M )

MO101M

(2.12) :01M ,

75

01M01M (2.13),

01

01M .

.:

1- – (2.13)

.2- – ,

, coscos 01M

3- – , ,

( ). ( )

, , ,.

– .

.

76

0p ;0p , p ,

, D, . - . . 0 .

, :MpM

pMM ,Mp -

;- ; – .

: pDD ; pCC ; pBB ; pAA .,

, , ( ).

D - ; D

D

p; pB

pDpB D

B .

77

2.8 :

1. , ,

, , ,

.2.

, , ,

A B .

3., ,

, A B .

78

4. , , (

), .

5.,

, , –

.

:sinycosxxx 1101M

cosysinxyy 1101M

, . Oxy:

)cosysinx(xx 1101M

)sinycosx(yy 1101M

. :2

11012

11012M

2MM sinycosx(y)cosysinx(xyx

79

.

;x)x,cos(M

MM ;y)y,cos(

M

MM

.. :

01M

, :

;WWWWWWdtd

dtd

dtd)(

dtd

dtdW

01M010101M0101M01

0101

MM

0101 W

dtd - 1;

dtd - 1

1MOdtd -

1.

MO1W -

1.0101M01 WWW -

1.0101M W -

1;0101M01 W,W,W :

MOW 101M ;;MOW 1

2201

;)()()W()W(W 422222MO

2MO01M 11

80

01MW 01W

;W

Wtg 22

MO

MO

1

1

, ,

.: 0101M01M WWWW

.

( ).,

, .

, –.

81

01W - 1

- ; - ; -

2tg .

1 1Q

;W

QO42

01

1

Q – ; Q:

11111 0Q00Q0Q0Q WWWWWW

01QW

11

1 O42

42

04210Q W

WQOW ;

1QOW 1Q

2tg

1QOW .

11 OQO WW ; 0WQ ; Q,

.,

MQMQMQM WWWW

82

42MQM MQWW

,

.;QAW 42

A

;QBW 42B

;QCW 42C

QAQB

WW

A

B , 2

, . ( )

)cosysinx(xx 1101M

)sinycosx(yy 1101M

.

)sinycosx()cosysinx(xx 112

1101M

)cosysinx()sinycosx(yy 112

1101M

Oxy .

83

211

211O

211

211O

2M

2MM

)cosysinx()sinycosx(y

)sinycosx()cosysinx(x

yxW

1

1

M

M,M W

x)xWcos( ;M

M,M W

y)yWcos(

1. , ?

2. , ?

3. ,?

4. ,?

5. , ?

6.?

7.?

8. ?9.

?10.

?11. ,

?12. , ?13.

?14.

?15.

?16.

?17.

?

84

18. ?19. , 20. ?21.

?22. ?23. ?24. ?25. ?26. ?27.

?28.

?29. ?30. ?31. ?

85

3. – ,

, .:

– – , .

– – .

–, .

3.1. ( ):

, .

, .

. ( )

, .

Fdt

)m(d Fdtdm

, , , ,

mFW :

, . FWm ,

m – ; W – ;F – , .

. ( ),

( ) .

– .

BA FF ;

AAA WmF ; BBB WmF

BBAA WmWm

A

B

B

A

mm

WW ;

86

, ,

, .. ( ):

, , ,

.11 FWm ; 22 FWm ; nn FWm

n21n21 F...FF)W...WW(mFWm ; n21 W...WWW

n21 F...FFF .

n21 F,...F,F , , – F .

3.2 .,

, .

FWm ; Fdt

rdm 2

2

(3.1)

(3.1) – ;

m – ; 2

2

dtrdW – ;

F – , . (3.1)

, n

1kkxFxm ;

n

1kkyFym ;

n

1kkzFzm (3.2)

x , y , z – W;

n

1kkxF ,

n

1kkyF ,

n

1kkzF – .

(3.2) .

(3.1) ,

n

1kkb

n

1kkn

2n

1kk F0;Fm;F

dtdm

87

;FmW;FmWn

1kknn

n

1kk

2

nW,dt

dW –

.n

1kkb

n

1kkn

n

1kk F;F;F – ,

.

3.3 ,

, ,

.

F – , .F W W

;FFF 21

;WmF1

2F R . 2F.

RF;0RF 22 .:

, F

).RFF1 .

,RFWm

88

RFdt

rdm 2

2

.

( )n

kzkz

n

kyky

n

kxkx RFzmRFymRFxm

111;; .

n

knkn

n

kk RFmRF

dtdm

1

2

1;;

n

kbkb RF

1;0

3.4

F . RFF1 . 1F

;WmF1

, ,F

1F 1F .

0FF1 (3.3)F

,

;WmF (3.3)

:;mWF;mWF;mWF zzyyxx

89

(3.3)

.0mWF

;mmWF;mWdt

dmF

bb

2

nn

F – .nF – , .

0FRF (3.4):

F , RF .

(3.4) , .

– ( ).

3.5 . ,

, ( , ). ( ). ,

, .

. : 1) ; 2) , -

; 3) , .),r,t(FF .

.

)t(fz);t(fy);t(fx 321 ,

2

2

x dtxdmxmF ;

2

2

y dtydmymF ; (3.5)

2

2

z dtzdmzmF .

90

,

2z

2y

2x FFFF ;

;€,cos;€,cos;€,cosFFzF

FF

yFFFxF zyx

,

)t(SS ,F , ,

) n

kkbbn FFmF

dtdmF

1

2

;0;;

( ) F : ;FFFF 2b

2n

2

:;€,cos;€,cos;€,cos

FFbF

FFnF

FFF bn

.,

.:

1 – ;2 – , ;3 – , .

,).,r,t(FF

()

;)z(F)z(F)t(FFzm

;)y(F)y(F)t(FFym

;)x(F)x(F)t(FFxm

zzzz

yyyy

xxxx

(3.6)

. .

)c,...,c,t(zz)c,...,c,t(yy)c,...,c,t(xx

61

61

61

(3.7)

(3.6), 61 c,...,c .

91

(3.7).

)0t( .,

:

;z)0(z;y)0(y;x)0(x

;z)0(z;y)0(y;x)0(x;0t

000

000

– .

(3.7) 0t , ,

);c,...c,0(zz);c,...c,0(zz

);c,...c,0(yy);c,...c,0(yy

);c,...c,0(xx);c,...c,0(xx

6161

6161

6161

00

00

00

);z,y,x,z,y,x(fc

);z,y,x,z,y,x(fc

);z,y,x,z,y,x(fc

);z,y,x,z,y,x(fc

);z,y,x,z,y,x(fc

);z,y,x,z,y,x(fc

000000

000000

000000

000000

000000

000000

66

55

44

33

22

11

(3.7)

).z,y,x,z,y,x,t(zz

);z,y,x,z,y,x,t(yy

);z,y,x,z,y,x,t(xx

000000

000000

000000

.

92

3.6 1.

m P .

. :

;gdtzd;0

dtyd;0

dtxd

:gz;0y;0x

;0m;dtzdz;

dtydy;

dtxdx

;mgzm;0ym;0xm

:

;cdtgz;cy;cx321

, :

;cdt)cdtg(z;cdtcy;cdtcx

;cdtgdtdzz;c

dtdyy;c

dtdxx

635241

321

1c ,

2c ,

3c – ;

4c ,

5c ,

6c – .

1, 2,… 6.

2. , .

93

, .

;cdtcdt)t(Fm1x

;cdt)t(Fm1

dtdxx;cdt)t(F

m1x

;dt)t(Fm1xd);t(F

m1

dtxd

)t(Fxm

21

11

x

xx

xx

x

1 2 – , .

3. ,

)r(FF

:

;)(2

;)(2

;)(12

)(1

)(

;

)(

1

1

1

2

cdxxFm

dxdt

cdxxFm

x

cdxxFm

x

dxxFm

xdx

xFdx

xdxm

dxxdx

dxxd

dtdx

dxdx

dtxdx

xFxm

x

x

x

x

x

x

;)(2 2

1

ccdxxF

m

dxt

x

1 2 .

94

4. , )(F .

.)(

;)();(

;)(

;)(

);(

);(

2

1

cdttx

dttdxtdtdxx

cxF

xmdt

xF

xmddt

xFdt

xdm

xFxm

x

x

x

x

1 2 .

3.7 ( )

, .

1.,

.,

, ,.

.eF – ;iF – .

95

, , , 1 2

, 0FF i2

i1 .

i0R

.

0FRn

1k

ik

i0

() .

i2

i1 FF .

;0FMFM i20

i10 – .

.10M .

;0FMFrMn

1k

ik

i0

n

1k

ikk

i0

) .2. .

, , ( ) ,

., ,

.

1 2 .

)111 z,y,x – 1 2;

96

222 ,, zyxl – .

( )0l)zz()yy()xx()z,y,x,z,y,x(f 22

122

122

12222111 (1), (1) ,

, ., ,

F R .,

, , x, y, z.

, , n 3 n .

, n h ,

hn3S,

, .

;n3S;hn3S

3. .) n

.

, i

ke

k FF . k-

97

;;

;

2

2i

ke

kkk

k

ik

ekkk

FFFdt

rdW

FFFWm

in

en

nn

ie

ie

FFdt

rdm

FFdt

rdm

FFdt

rdm

2

2

2222

2

1121

1

.) n

.

, F R k-

kkk

k RFdt

rdm 2

2

, n ,

nnn

n RFdt

rdm

RFdt

rdm

RFdt

rdm

2

2

2222

2

1121

1

.

, 3 n .

3.8 1. –

, , .

2. ( ) –, ( ),

, .

98

3. – , ,

, .

4. ( ) – , ,

, , .

3.9 1..

, ( ),

..

. Oxyz .

111zyxO1

Oxyz.

ar – . ;rr – . 4er – . .

.

.

99

.

3.10 .a

r e

..

rea rrr,

dtrd

dtrd

dtrd rea

rea

3.11 ()

,

krea WWWW

rek 2W ,e – ;

r – .

;€,sin2 rerek WW

100

,FWm (3.8)

aWW – .,

krea WWWW

FWWWm kre .

ker WmWmFWm .

ee WmF – ;

kk WmF – ;

eF kF – .

ee mWF ;

:;WmF kk

(3.8) ker FFFWm (3.9)

, (3.9) ,FFRFWm ker (3.10)

R – . (3.9) (3.10)

,

)

101

;

;

;

111

111

111

1

1

1

ke

n

kkr

ke

n

kkr

ke

n

kkr

zzz

yyy

xxx

FFFzm

FFFym

FFFxm

)

;

;

;

1111

1111

1111

1

1

1

kez

n

kkr

key

n

kkr

kex

n

kkr

zzz

yyy

xxx

FFRFzm

FFRFym

FFRFxm

(3.9) (3.10) .

, ,

, , , ,

.

3.12 .1.

.,

, :) ( ).

;FWm

;dtdW;constm

;Fdtmd

dtdm

dtFmd (3.11)., m

, , dtF –.

:,

.

102

(3.11)

0

t

0

dtF)m(d

Smm 0 , (3.12)t

0

dtFS – , ,

.

, , .

(3.11) (3.12) ,

;;

;;

;;

01

1

0

01

z

n

kk

n

k

yk

x

n

kk

SzmzmdtFzmd

SymymdtFymd

SxmxmdtFxmd

z

y

x

n

k

t

okz

n

k

t

k

n

ky

t

kx dtFSdtFSdtFSzyx

11 01 0;;;

3.13 – ,

, n

1kkkmQ ;

;zmQ;ymQ;xmQn

1kkkz

n

1kkky

n

1kkkx

cMQ , – n

1kkmM – ;

c – .

.

, .

103

e0 SQQ , (3.13)

Q – t;

0Q – ;0tn

1k

t

0

ek

e dtFS – ,

. (3.13)

;SQQ;SQQ;SQQ ez0z

ey0y

ex0x zyx

(3.14)

, , , ,

.:

1. .

2. , ,

,0F1k

ek Q

e0 SQQ .2. .

, ,

n

1k

ek dtFQd

n

k

ekc

n

k

ek

c

c

n

k

ek

FWMFdt

dM

MQFdtQd

11

1;

:n

k

ekc

n

k

ekc

n

k

ekc zyx

FzMFyMFxM111

;;;

: 1. , .

2. , , ,

, .constc

104

3. , , ,

, .constxccx

3.14 )

-.

mrK0 .

0K

– .,

( ) , ( ):

0K, .

0K 0k –2

n

1k00 k

kK

105

3.15 .

FWm,

;FrWmr

FMFr

;dtkd

dtmrd

dtdmr,

dtdW

0

0

FMdtkd

00 (3.15)

( ):

. , .

(3.15)

FMdt

dk;FMdt

dk;FM

dtdk

zz

yy

xx (3.16)

, n .

.

;

......................................

;

;

000

20200

10100

2

1

in

en

n

ie

ie

FMFMdtkd

FMFMdtkd

FMFMdtkd

, n

k

ik

n

k

ek

n

kFMFM

dtkd

k

10

10

1

0 ,

dtKd

dtkd

dtd

dtkd n

k

n

k

kk 0

1

0

1

0

;0FMn

1k

ik0

:n

1k

ek0

0 FMdtKd (3.17)

106

:

( ) ) ,

, ( ).

(3.17)

;FMdt

dK;FMdt

dK;FM

dtdK n

1k

ekz

zn

1k

eky

yn

1k

ekx

x (3.18)

:1.

, (3.17) (3.18) .

2. , , ( )

, , .

constK0FM 0

n

1k

ek0 ( ).

3. , ,

, .

2 3

constIK zz ,

0FMn

1k

ekz (

z).

3.16 .

107

dtd

dtd

,FMI

FMdt

Id

2

2

n

1k

ekzz

n

1k

ekz

zz

zI – ;n

1k

ekz FM – .

2mlI

2

z

2z mRI

108

2mRI

2

z ;

;4

mRII2

yz

3.17 ..

– ,

, , .

,2

T2

m – ; – .

. = .

:222n

1k

kn

1k

2kk

kkk zyx2

m2

mT

x , y , z – k-.

:) .

, ck :

;2

M2

m2

mT2c

n

1k

2ck

n

1k

2kk

109

;2

MT2c

n

1kkmM – .

) .km kk h , –

; kh – . z.

;2

I2

hm2

hm2

mT2

z2n

1k

2kk

n

1k

2kk

n

1k

2kk

,2

IT2

z

zI – :n

1k

2kkz hmI

.) .

:

;2

I2

MT2

c2c

cI – , .

c

110

, , .

) .:

,2

I2

MT22

c

– ; c – ; I –,

; – .,

, .n

1kk ,TT

kT – , .

3.18 . .

F .cosSFA .

FF S

. – ;

2 – ;

2 – ;

2 – F S .

– = .

1 2 n kS .

111

, F

, F1 2.

21

coscos1

00

limMM

kk

n

kk

Sn

dSFSFA

1 2. – ,

dScosFdA ., rddS , rd –

.rdcosFdA ,

rdFdA .F rd

,kdzjdyidxrd

;kFjFiFF zyx

dzFdyFdxFdA zyx .,

21MMzyx dzFdyFdxFA . (3.19)

(3.19)

, F .N ().

112

Fdt

rdFdtdAN

FN , – .

F ,, .

= = .

, .)

e0R

crd .

, )c

e0c

en

e2

e1c

enc

e2c

e1 rdRrdF...FFrdF...rdFrdFdA

;rdRdA ce0

) , ,

ezM

;dMdA ez

)

, .dMrdRdA e

cceO

.

Fdtvdm

rd):

rdFrddtvdm

)2

mv(dvdvmvddtrdmrd

dtvdm

2

113

rdF2

mvd2

:v

v MM

2

0 0

rdF2

mvdMM

T

T 00

dAdT

A2

mv2

mv 20

2

ATT 0

:, ,

:ATT 0

:ik

ek

kk FF

dtvdm

krd :

ki

kke

kkk

k rdFrdFrddtvdm

2

2kk

kkkkk

kvmdvdvmvd

dtrdm

ki

kke

kkk rdFrdFvmd

2

2

n

k

n

kk

ikk

ek

n

k

kk rdFrdFvmd1 11

2

2n

k

n

k

ik

ek dAdAdT

1 1

n

k

n

kk

ikk

ek rdFrdFdT

1 1(3.20)

, .

(3.20) :n

1k

n

1k MoM

ik

MM

ek

T

To

dAdAdT0

n

k

n

k

ik

ek

T

ToAAdT

1 1

114

:

, .. .

– , ( , ).

:- , ;- ;- .

, , , . (

– , ,).

, , .

:cF ,

c - ( ); - .

F , .

( ).

cxxm ,

0xmcx (3.21)

2kmc

(3.21) 0xkx 2 ; (3.22)

(3.22) – .

, 0kr 22 ; ikr12 .

, (3.22) ktcoscktsincx 21 , (3.23)

115

1, 2 – ., ,

cosac1 ; sinac2 ;1c 2c 3.23 :

ktcossinaktsincosax

)ktsin(ax (3.24)- (

).,

, .

(3.24): - - ;

)kt( - ; - ;

k - ( ) – 2 .

mck ;

.

.

(3.24) )ktcos(akx (3.25)

,

x . 2 , 2 .

(3.24) :

116

2)kt()Tt(k ;2ktkTkt

k2T (3.26)

.

., ,

.

T1

:1. ( )

, , .

2.,

3..

4.,

( m ).5.

, .6.

.

cFR .

R R v .

vbR , b – .

:xbcxxm

117

0mcx

mbx

:

m2bh - , ;

mck 2 - ,

., :

0xkxh2x 2 (3.27), (3.27) . (3.27)

.

:0khr2r 22

:22

12 khhr (3.28)

.:

1.kh -

(3.28)22

12 hkihr . (1) :

tkcosctksincex 21ht (3.29)

1 2 - ; 22 hkk ; 2

kh - . (3.28)

2212 khhr

(3.27) :tr

2tr

121 ececx (3.30)

1 2 - ; =2,718; 3.

kh ( ) , ().

:hr12 ;

(3.27) :

118

ht1 ectcx , (3.31)

1 2 - . (3.30) (3.31) , , kh kh ,

, .

. (3.29) .

cosac1 ; sinac2

tkatkaex ht cossinsincos ,

sintkcoscostksinaex ht

tkaex ht sin (3.32)22 hkk (3.32)

. (3.32) , ,

, . hte , .

119

, htae.

.

(3.32) )tkcos(eak)tksin(ahex htht (3.33)

:;0t ;x)0(x 0 0x)0(x

(3.32) (3.33) :

00

0

hxxxktg ; 2

2002

0 )k()hxx(xa ;

:

22 hkk .

T

kh1k

2hk

2k2T

222(3.34)

(3.34) , .

, *

.1, 2, 3….

.:

120

hTht

)Tt(h

ht

)Tt(h

i

1i eae

ae)tksin(ae)Tt(ksinae

aaq

hTeq -

, *;

Thaaln

1i

i

. , ,

.

3.19 – ( )

, , , z ,

t. –

, .,

),z,y,x(uu

:

;dxduFx ;

dyduFy ;

dzduFz (3.35)

)z,y,x(uu - , ),z,y,x(uu

.

121

, ),z,y,x(uu

( , ).

,

iF ,

)z,y,x(uu . 5

, .

)z,y,x(uu :1. ,

, , .

2. , ,

(« ») )z,y,x(uu .

zyx F,F,F.

– , .

122

. rd F . F rd

.:

zyx Fdz

Fdy

Fdx ; (3.36)

.:

) , P , P

:PF,0F,0F zyx

(1) :

0dxdu ; 0

dydu ,

constu , xOy .

Pdzdu .

pdzduPdzdu ; Constdzpdu

constPu z (3.37) (3.37)

, .

123

z;constcz ;constcz 1 ;constcz 2 ;constcz n

.,

z .,

P ., « »,

,.

) ., :

cF , – ( );

- , F , , , 0F .

cFddu

const2

cu2

(3.38)

, 2222 zyx ,

const)zyx(2cconst

2cu 222

2

, , :

124

constcR 12 ; constcR 11 ; constcR 22 , …. constcR nn .,

- z,y,x.

F

zyx FFF ,, ;dxduFx ;

dyduFy ;z dz

duF

kdzjdyidxrd

F rdrdFAd ;

dudzdzdudy

dydudx

dxduAd ;

duAd

.

0M

M

U

UuuduAdA

0 00 ;

0uuA (3.39) (3.39):

, .

125

.-

,

.

3.20 )z,y,x(uu

. .

,,

.

, ,

0.

)z,y,x(

126

)z,y,x(uu )z,y,x( .0 0 0.

;ucuuA 00MM0

0 – .0 ,

)., ;constu

, 0cu 00 , ;u

«-».

:uuA ;

:

;dxd

dxduFx ;

dxdyduFy ;

dzdzduFz

, :

constzPu ;,

:;

2222 constzyxcu

3.21 . .

0. 0 0.

:n

ukAmvmv

1

20

2

22n

1ukA - .

An

uk 0

1;

mvmv0

20

2

22,

const22 0

20

2 mvmv

127

const2

2mvE TE

- – .:

..

. :

n

u

u

u

ik

eko AATT

1 1

-oTT ,

constT .

constTE:

.,

, . – .

, .

, .

:n

uk

n

u

n

u

ik

ek

n

uk AAAA

11 11n

ukA

1- .

,

AAn

u

n

u

ik

ek

1 1,

n

uk

n

uAA

11k .

, :n

1uoTT ,

128

n

1ukA-oTT

n

1ukA)-)(

n

1kA- EE

. -

, ).

1. ?2. ?3. ?4. ?5. ?6. ?7.

?8.

?9.

?10. .

?11. ?12.

?13. ?14.

?15. , ,

?16. ?17. ?18. ?19. ?20.

?21. ,

?22.

129

?23.

?24.

?25.

? ?26. ,

?27.

?28. ?29. ?30.

?31. ,

?32. ?33. ?34. ?35.

?36.

, ?37. ?38. ?39. ?40.

( )?41.

( )?42.

?43. (

) ?44.

?45.

?46.

?47.

?48. ?49. ?

130

50. ?51. ,

?52. ?53.

?54. ?55. ?56. ,

?57.

, ?

58. ?59.

?60.

?61.

?62. .63.

?64.

, ?65.

, , ?

66.?

67. ?68. , ?69.

?70.

?71.

.72. , ?73. , ?74. ?75.

, ?76. ?77. ?

131

78. ?79. ?80. - ?81. ?

? ?82. ?83. .84. II ?85.

?

132

1. ., ., . : : 2 . - .1: . . - .: , 2004. -

599 .2. ., ., .

: : 2 . - .2: . - .: , 2004. - 590 3. . . - .: , 1970. -

579 .4. . . - .:, 1986. -448 .