: 1.

: .. ,

.. , ..

-

2009

Copyright & A K-C

- 22 2009 ., 1 . / /, - .-. , . .. . 1 / 2 - /. : 010701 , 010803 - , 010801

Copyright & A K-C

3

-1/1

, -

.

, -

. . , , - , , , , - . , kx, :

xrkxxm &&& --= , (1) r .

mk

=20w , mr

2=d , (2)

(1) 02 20 =++ xxx wd &&& . (3)

(3) - ( < 0) ( )

0 cos( ),tx a e td w a-= + (4)

a0 , ,

2 20 .w w d= - (5)

, (3), - (5)

220

2dw

p

-=T , (6)

. . -

0 .ta a e d-= (7)

a0 - t = 0. - (4), , .

Copyright & A K-C

4

, 1, . (7) , , e 2,73 . . , :

td

1= . (8)

. , -

. , -, D :

0( )

1 0

.t

Tit T

i

a a eD ea a e

dd

d

-

- ++

= = = (9)

-, :

TD d==Q ln . (10) , (8), ,

eNT 1

==Qt , (11)

Ne , e .

Q=

pQ (12)

. , , -

, (1) - -. , (3) (4), (2) 0 .

: , ,

. (. 1) 1,

2 3, 4. - , . 5, 6, 4.

Copyright & A K-C

5

7. 8, - 4 .

. 1.

1. .

. 2. 3 .

, 5 1 10 , .

3. , 78 , .

4. ( (9)), D, - . , . , D ( - , ).

5. D T - . . , ET

6

2, 1. 7. D, , -

. , .

1 t, c , c a,

D

a,

D

, -1

1. .. / .. . ., 1989. . 2.

. 264267. 2. .. / .. . ., 1975. . 432437.

1. .

. (t) (t). 2. . 3.

, . 4. , . -

. 5. , .

D, , .

Copyright & A K-C

7

-1/2

, - .

-

, , , , , , , , , , . . . - , , - .

, . 10 20 000 . , , - .

, , , , , - . - , , , -. .

-

( ) cos( )t a tx w= , (t) .

(,t) , , = /, , - :

)2cos()cos()(cos)(cos),( xtakxtacxtatatx

lpwwwtwx -=-=-=-= . (1)

, k = /c = 2/ . (1) .

, - . , - . -

Copyright & A K-C

8

, - : , . .

, -

)2cos()2cos(),( 2211 xtaxtatx lp

wlp

wx -+-= , (2)

a1 a2 , x1 x2 .

, - a1 a2

)2cos(2 2122

21 D++= l

paaaaa . (3)

= 1 2 . (3) , -

,

22 ln=D , n = 0, 1, 2, 3... , (4)

. . . , ,

, :

2)12( l+=D n , n = 0, 1, 2, 3... . (5)

(4) (5) : , , . a1 = a2 , (3), ( ).

-, . . - , , :

0mg

RTc = . (6)

T , 0 , R

, V

P

CC

=g

.

Copyright & A K-C

9

- , , , . - \\

rEc =// , r

Gc =^ , (7)

, , G . G =

= 2G(1+ ), 0 < < 1/2, , > G \\ > , .

: , ,

. (. 1)

, , . () , . () . , , - . , , . . . , l .

. 1.

Copyright & A K-C

10

(5) (n = 0) :

2l

=D .

, , , l

l2=D . , -

, -

nl4=c . (8)

1. , - 1, ( ). - .

2. , (- ), . - l, .

3. 10 , - .

4. -. , -, E

11

1. , . 2. ? ? 3. . -

. 4. . .

. 5. : , , . 6. . -

, . 7. 0 ?

-1/3

-,

V

P

CC

=g -

.

- (). - S - . , c

llD

=e (. 1). - , :

Slm

=r , (1)

l .

Copyright & A K-C

12

. 1.

, , -

( )llSm

D-=D+ rr . (2)

, S . (2) - (l + l):

( )( )22 llS

llmD-D+

=D+ rr .

, l2

13

, SdtEdtSc ere =2 ,

rEc =2

rEc = . (5)

, , , , , , , , (5).

. F - - , (4)

VVEp D=D .

dp dV -,

VdV

dpE -= , (6)

, - .

, , , 16 20 000 . - , , , . - constpVg = . ,

01 =+ - dVpVdpV gg g .

pV

dVdp

g-= . (7)

(6) (7) pE g= . (8)

Copyright & A K-C

14

,

Vm

=r ,

mrRTp = .

(8),

mgr

RTE = . (9)

(9) (5), - :

mgRTc = , (10)

RTc

CC

V

P mg2

== . (11)

, .

- . , - . L

2lnL = (n ,

), , , , . , . , , . , /2 . ().

- = ,

ncL =02 n , (12) 0 .

(12) n . - , 0 = f(n),

LcKa 2

= .

Copyright & A K-C

15

1-7, . 2.

. 2. 1-7: 1 ; 2 ; 3 ; 4 -

L, . , - . , 1. . - , , - . , , - . , - . , , . L .

1. . 2. .

( ).

3. , , 1- -

Copyright & A K-C

16

. 1.

1 t1 = C t2 = C t3 = C -

0 , , / 0 , , / 0 , , /

4. , 2, 3, , 7 . , -. 1. , t1.

5. t2 = 4045 C. . 24.

6. , t3 = = 5560 C. . 24.

7. -, , , , .

1.

0 = f(n) - aK .

2. , aK , aLKc 2= (11), -, = 2910-3 /.

3. .

1. .. / .. . . : , 2002. . 2.

2. .. / .. . . : , 2003. . 2.

Copyright & A K-C

17

1. ? - .

2. . 3. . -

, , -.

4. . 5. . 6. ?

? 7. ?

. 8. -

? 9. -

? ? 10. -

?

-1/4

.

m l , , - h (. 1). - , - . - - , , 1 2 - . , .

Copyright & A K-C

18

. 1. (), -

. - -, .

, -. - , . 1- :

111 MJ =e , J1 = ml , 11 je &&= , M1 .

M1. , , mglsin1 mgl1. , - , . h1h2 = = h(1 2). , , -, ch(1 2), ch2(1 2). - :

)( 212

112 jjjj ---= chmglml && . (1)

, :

)( 122

222 jjjj ---= chmglml && . (2)

(1) (2) , - , . :

21 2 1 2

2 21 2 1 2 1 2

( ) ( ),

( ) ( ) 2 ( );

ml mglml mgl ch

f f f f

f f f f f f

+ = - + - = - - - -

&& &&&& &&

Copyright & A K-C

19

1 2 1 2

2

1 2 1 22

( ),

2( )( ).

glg chl ml

f f f f

f f f f

+ = - + - = - + -

&& &&

&& &&. (3)

: 211 jj +=Q , 212 jj -=Q , (4)

lg

=21w , 22

22

2mlch

lg

+=w . (5)

(3)

21 1 1

22 2 2

0,

0.

w

w

Q + Q =

Q + Q =

&&&& (6)

, (4) (3) - , :

1 1 1 1

2 2 2 2

cos( ),cos( ).

A tA t

w dw d

Q = +Q = +

(7)

(7) (4) 1 2

)cos(2

)cos(2 22

211

11 dwdwj +++= t

AtA ,

)cos(2

)cos(2 22

211

12 dwdwj +-+= t

AtA . (8)

A1, A2, 1, 2 , , -, . , - . t = 0 , , - , . .

aj =)0(1 , 0)0(2 =j , 0)0()0( 21 == jj && . (9) , (9) -

: A1 = A2 = , 1 = 2 = 0

( !). (8) :

)cos(cos2 211

tt wwaj += ,

)cos(cos2 212

tt wwaj -= . (10)

Copyright & A K-C

20

1 2, (5), - (m, l, c, h) -. - . - .

(8) , , . .

1. . , , - 1, . .

2. , - . , , -. -, 2. - .

, ( ) . . - . - . , - .

(10). , : 1 2 ( , , h/l). - (10) :

tt2

cos2

cos 12121wwww

aj+

-

= ,

tt2

sin2

sin 12122wwww

aj+

-

= .

= (1 2)/2 , (1 + 2)/2 . ,

tt weaj coscos1 = , tt weaj sinsin2 = , (11)

, cos t sin t -, cos t sin t. , 1 2

Copyright & A K-C

21

, - . .

(8) 1(t), 2(t), (11), , . 2. - , , - , , . . .

(. 2). -, -. , , :

= 2 = 2 1. (12)

. 2.

(5) , , . , .

, -

(. 3). , - , . - .

Copyright & A K-C

22

. 3.

1. 1. , -

( ). 2. -

. 3050 . 5 . .

3. 1. , , 3050 . 5 .

4. 2. - .

2.

1. , , , , . .

2. - (. 2). - 5 .

3. (12), .

3.

1. ,

(. ) , - , . 5 - .

Copyright & A K-C

23

2. , 2 3.

4.

1. . 2. 5 . 3. 2-, 3-, , 7- ,

. 4. -

. 5. ,

. .

1. .. / .. . ., 1975. . 459466. 2. .. / .. -

. ., 1966. . 307311.

1. . - . ?

2. , . ?

3. ? ?

4. ? 5. ,

, ( > ), - .

Copyright & A K-C

: 1.

: ,

,

..

. 6084/16. . . . 1,4. 150 . 396.

-

. 394000, . , . . , 10. . 208-298, 598-026 ()

http://www.ppc.vsu.ru; e-mail: pp_center@ppc.vsu.ru

- .

394000, . , . , 3. . 204-133

Copyright & A K-C