Учебное - aco.ifmo.ruaco.ifmo.ru/upload/publications/book_tmpos_2011.pdf · Учебное...
If you can't read please download the document
TRANSCRIPT
-
-
,
.. , .. , ..
I
. ..
-
2011
-
.. , .. , .. . . .. : , 2011. 104 .
, , . , . 200400 , 200203 - 200401 - .
, 200400 , 200203 - 200401 - .
2009 , 12 , . 20092018 . 2011 - ,
- , , 2011
.. , .. , .. 2011
-
1. 4
1.1. 4
1.2.
7
1.3.
11
1.4. .
14
2. 24
2.1. , 24
2.2. 32
2.3. 39
2.4. , 46
2.5. 47
2.6. 51
2.7. . 65
2.8.
67
2.9. 97
99
3
-
1. 1.1.
( . projectus, ) , , , .
, , [1].
() , , , , , . , , , . , , , .
, , [2].
. , ( , - .). , , , , , . , , .
, , , , .
, , .
() , , , , .
4
-
: -, , , . , (. 1.1).
. 1.1.
- , (), . , , .
, , , .. .
, .. .
5
-
, . , , , , , , .
, . , .. .
, , , , , .
, , , , .
. , . , .
, , , . , , , ( ) . . , , , . , , , ..
, .. , .
6
-
. . , ( ), , , , , . ( ), .
. ,
. ,
, .
. , , - [3]. 1.2.
() [4]. , , , , , .
, :
, ;
;
, ;
7
-
. [5] ,
, . , , , . , , , , . , , .
, , , - .
, .
, , , , , .
, , , , , , [6]. (.1.2).
, . . , . , . , , , , ; , ,
8
-
, . , , .
. 1.2.
( . , , ) ( ) () [1]. ( ), .. .
, , . , .. , , .
9
-
, , .
, , , .
( . , ) ( ) [1].
. , . , . , . , , , . , , , , , . , . , ( ), . . - , .
, . , , , .
( . optimum - ) , () [1]. , .. .
10
-
, ; , , .. , . , , . , , .
, , , , . . , . , , , . , . 1.3.
, (). , , , , , . .
2.103-68 , (), , , .
, , ().
, , , - , .
11
-
- - . .
. . . , . : 1. ( , ). 2. , . 3. () :
(, , ), , , .
4. , , (, , , ).
5. . 6. , ,
, . 7. , . 8. , . 9. . 10. , .
, , . , , [7]: : ( ) ....... ( ) ....... f ....... ( ) ....... /D f ( A) ....... D ....... 2y (2) ....... ( )2 2y ....... ....... ....... ( ) .......
12
-
....... : ....... ( )D ( )D ....... ( )'Fs ....... ....... ....... ....... : ....... (, , , ...) ....... / ....... ....... ....... ....... : ....... () ....... ....... ....... ....... ....... : ....... / ....... ....... ....... , ....... ....... : ....... () ....... ( / ) ....... ( / ) ....... ....... ....... : ....... (e, ) ....... ....... ....... .......
13
-
....... ....... : ....... ....... .......
, . , , . , .
, , , , - , , , .
, - , .. 1.4. .
, , , ().
, , : , , .
, - . ( 2.106-96) :
( , );
;
14
-
; ; ,
; ; - ; , ,
..
. , .
2.10595.
, . . .
: (); (, ); . , : , ; , , , ..
[8] .
, . , . .
, , .
, (, , ..).
, .
15
-
, , .
, . , , , .
, , . , , , . , , , .
. , , , .
, . . 1.3.
2.41281 (. 1.4). , ( ), , , . .
; , f , Fs 'Fs (, , ..); , ; ; , ; .
16
-
. 1.3.
17
-
.1.4.
18
-
, , ..; , , , ..; , .
, , , .
, , , , . . . 1.5 1.7.
(. 1.5), , .
, . : , , , , , , , . , , .
, .
, , , , , ( ) ( ), .
, , , . .
19
-
, .
. (. 1.6) , , , .
: , , . .
. , , .
, , () .
, - .
. .
, , . , .
. , , , . - , .
, .
20
-
.1.5. . 1
21
-
.1.6. . 2
22
-
.1.7. . 3
23
-
24
2.
. , . , .
, , . . 2.1[9].
, - . . 2.1. ,
. , :
, , .. , , ( , ), ,
(, , , , ..). .
: 1. ( ,
) , , , ;
2. ( , ) , , , ;
-
25
. 2.1.
-
26
3. ( , ) , , ;
4. ( ) , , . (
) (.2.2) : ( , ); D , D ; 2 , 2' ; :
tg Dtg D
= =
, (2.1)
pS , 'pS .
. 2.2.
D . , D .
-
27
[10] , . :
Dd
=22,1 . (2.2)
= 0,55 D ( ) d ( ) :
Dd813
= .
:
Dd012
= ,
:
Dd014
= .
, , D'. D' 6 1 .
, D' = 6 :
=
32 , Dd014
= , 6D
= .
D' = 1 :
=
014 , Dd014
= , D = .
: DD T 75,02,0 .
( ) (. 2.3) : , , = sinn ,
-
28
2y . :
Dytg
=
=500250 . (2.3)
.2.3.
, , :
=2d
(2.4)
- . [10]:
( )A1000500 = . ,
0,5 1 , :
=
AD 500 . (2.5)
:
250ytg = . (2.6)
( ) (. 2.4) : f , 2
-
29
, 1D f k = , k . :
'2''
=
=
Dtg
yf . (2.7)
. 2.4.
: 2 2 y f tg = . (2.8)
f , / 'D f 2 . , 0,48 0,6438 , . .. [11]:
tg 0,22 0,26100
D fCf
= =
. (2.9)
. , , , , . . , .
( ) (. 2.5) : ; L
-
30
( ); sinA n= , sinA n = : 2y , 2 'y . :
AA
yy
=
= . (2.10)
. 2.5.
, . , . , .
( ), , , , .. . , . 2.1 [12]. . , .
-
31
2.1.
-
I. : II. :
< 2' < 1'
> 0,25 > 0,1
< 1' < 30" < 0,25 < 0,1
< 20" < 10" < 0,1 < 0,05
, . < 8' < 6' < 3'
, 8 2 1,5
,
6> 2<
3> 1>
2> 0,1>
, % < 50 > 50
6 9
3 5
2 4
,
< 8'
< 5'
< 3'
( ), , , . - ( )0,5 1,0D = 2'- 4', 0,25. , . 0,1. , 0,5.
( ) ,
-
32
. : / , - () , .
, . ..[11], T :
2 2,5(1 )
= . (2.11)
( 5,0T ).
( ), , , .
, . 1' 2', . 2.2.
: , , , , . ( L D), . , . .
: (
, , , , .): f , 2 2y 2 2y , /D f () ( )A A ,
, .
-
33
. , , .
. , .
, - (, ) . .
. , .
, , : , , , , , .
, , : , , . .
. , .. . 1. ,
, . , (. 2.4). L : L f . , , :
2y Df
tg A
= =.
-
34
2. ,
. 2.6.
. 2.6.
,
, :
faa =
111 , (2.12)
a f fa z z
= = =
. (2.13)
, :
tg tg y ya a
= = =
.
:
sin2Da
= ,sin2Da
=.
:
-
35
'L a a= + + . (2.14) (2.14)
, :
2
11 0
dL fd
= + =
. (2.15)
, L = , 1= 4L f = + 1= .
3. ( ) ,
, (.2.2). . :
1
2
tgtgT
D fD f
= = =
. (2.16)
:
21 ffL += (2.17)
:
1 2d f f = + . (2.18)
:
1 22 tg 2 tgD f f = = . (2.19)
:
2p
p
zz =
, (2.20)
pz .
pa :
2p pa f z = + . (2.21)
1p pa z f = (2.22)
:
-
36
1f ,
1
Df
,
2, 1pa .
: 2f ,
2f
D,
2 , 2 1p pa a= .
4. ,
(. 2.7). : f , k .
2 : , .
1) .
f , k, :
1 2f f = , (2.23)
+= dL 1f , 2 , d , L
2 2 1
1 1 1
D h f dkD h f
= = =
, (2.24)
D1 , D2 , h1, h2 ,.
2 : 2
22 1
a da f d
+= =
. (2.25)
-
37
)
) 2.7.
) ) :
11
1
1
df ff d
f dKf
+ = =
.
:
1
1
f kf
k
=
,
-
38
d f k= .
11 2 fr =
:
2 2 2
1 1 1a a f
+ =
. (2.26)
2a 2a (2.26):
1 2
1 1 1d f d f
+ = +
:
( )( )2 1 2
f k f kf
f k
=+
. (2.27)
22 2 fr =
2) :
1
1 1
tg tgtg
S S S S
S S S S
hh h d
+
+ +
= + = +
, (2.28)
, h , , d .
, : 1,0f = 1 1,0h = 3tg 1,0=
. 2.7 :
2
h k d
d k
= = +
=
(2.28) :
2 21 tgh d= 2tg :
22
1tg hd
=
-
39
:
1
1 1tg tgS S
SS S S S
n nr hsn n
+
+ +
=
(2.29)
1r 1f :
12
2tg
r = 11 2rf =
r2 2f :
22
2
21
hr =+
22 2
rf =
2.3.
, . , .
H, . E', B :
BEH '= .
, . y0, . , , . y0, :
2sin
=H ,
2'sin'
=
nnH ,
-
40
, , n, n' , , ' .
. , .
, , , , :
22
''
41
=
fD
nnH
y0, y0, . :
=2sinH ,
2'sin'
=
nnH .
. .
, y0 . :
= 2sinH , 2'sin'
=
nnH .
.
, . :
'cos40 = HH
-
41
, , .
, S [2] []. ' []:
E S = . (2.30) ,
)10020(0 .
0 dS. L [/2] :
2LdS = . (2.31)
:
2 p
ED pL
= , (2.32)
p ; E ; ; L .
, /D f :
sin2Dp
= =
:
sinsin
AA
= =
, :
sin2DAp
= =
-
42
. . 2.8.
, :
min i k i= ,
k , , i , .
L , :
2 sin L Q= , (2.33)
, Q . , :
2 sin L Q = , (2.34)
. imin :
mini S= , (2.35)
S . :
minsin
iS L Q
= . (2.36)
: 2 tgD p= .
-
43
.2.8.
.
. 2.9. ,
. m, , , .
2,5 lg 13,89m E= . (2.37)
, (2.37), . , . , . ( ) (/ 2) :
==
EE
k
e (2.38)
-
44
.2.9.
m, (2.37) . , (2.38) .
, , :
2
4
D = , (2.39)
, D .
: = , (2.40)
. imin :
Si =min , (2.41)
S . ,
:
min2
iD S
= . (2.42)
. , , . . 2.10.
-
45
. 2.10.
2 , .
, : 2 = . (2.43)
. :
2e
eI
= , (2.44)
. ,
:
2e
Ip
= , (2.45)
. ,
, :
-
46
ee
EL = . (2.46)
, : pD = 20 . (2.47)
:
fp
= . (2.48)
:
0 0D D = . (2.49)
, :
min
0
2 () e
D if L Q S
=
(2.50)
, , , , , 0Q , S() . 2.4. ,
, , , , .
, , , , . , , .
( , ) .
, , , .
-
47
, , , , , .
, , . 2.5.
f , /D f , 2, 2y, , , , .
, , . , . .
. . , .
, , . , , .
, , - , , . - , , , , , .
(), , , , .
, . :
-
48
1) . -
2) . . ..
3) .
. , . . .
(. 2.2).
2.2
()
,
t 1013,9 s 852,1 r 706,5 656,3 ' 643,8 D - 589,3 e 546,1 F 486,1 F' 480,0 g 435,8 h 404,7 i 365,0
: 1) n ,
en ( Dn ) . en 1,3 2,1en< < , , , 1,45 1,93en< < .
-
49
2) F cn n ( cF nn ).
3) 1eeF c
nn n
=
1 DDF c
nn n
= . 10 120e< < ,
, , 20 90e< < .
4) ''
,21
21CF nn
nnp
= .
, .
:
, , , (, , , );
, , , (, , , ). . 2.11[9].
. 2.11.
1,6028en > , 49,7e < ; 1,6028en < , 54,7e > .
: 8, 19, 10. . 2.12 e en .
-
50
. 2.12. en -
e
. . , , , , , , .
, , . , , [10].
.
21,p e. , . (1, 3, 4 .)
-
51
, , :
21
21021
= ppfSS ,
p1, p2, 1, 2 .
, p1 p2 , . 2.6.
, - . - , , .
. , . , , , . .
, , , . , , .
.
(. 2.13), , h , , , y , . ,
-
52
, .
( ) ( , , ) ( ). . , , ( ). .
. 2.13.
, : 1) , :
11
1 1,0S P
S SS
h h
=
=
= = , (2.51)
1,0 = 1,0f = . , , , h .
: , , :
1 1,0h = 1 1,0pa + = 1 1,0= 1 /py S f = ,
.
-
53
2) :
01
==
=
PS
S S
S
n
, (2.52)
n . 3) :
01
2
=
=
=
PS
S S
SSIXP
hS , (2.53)
. 4) :
01
=
=
= S
SS
PS
SSIIXP
yhS , (2.54)
h , y . 5) .
: , , .
, ( ) .
2 . , . .. [13].
, , ( ) , .
: 1) :
S
PS
SSI QhS
=
==
1; (2.55)
2) :
SSS
PS
SII QhS
=
=
=1
; (2.56)
-
54
3) : 2
1 SS
PS
SSIII QhS
= =
=; (2.57)
4) :
1
1 1 1
1 1 1
S SS P S P
S S S Ss S SIV
S SS S S S
n n n nSh n n h
+= =
+ + +
= = +
= = , (2.58)
:
=
=
=PS
S S
SIV r
nS
1
1
; (2.59)
5) : 3
1 1
1 1 1
S P S PS Ss S S
V S SS SS SS S S
n nS h Qn n h
= =+ +
= = +
= . (2.60)
: S S S SQ P T= +
, 2S e= , 2e ;
2
1 1
1
1
1 1S S S S
SS S
S S
Pn n
n n
+ +
+
+
=
; ( )( )
31 1
21
S S S SS
S S
n nT
n n+ +
+
=
.
:
. . ,
. 1) :
01 1 1
S P S P S P
I S S S S S S SS S S
S h Q h P h T= = =
= = =
= = + (2.61)
2) :
-
55
01 1
1 1 1
S P S P
II S S S SS S
S P S P S P
S S S S S S S SS S S
S h S Q W
h S P W h S T
= =
= =
= = =
= = =
= + =
= +
(2.62)
3)
2 10
1 1 1 1
2 21
1 1 1 11
1 2
1 2
S P S P S PS S
III S S S S SS S S S S S
S P S P S P S PS S
S S S S S S S S SS S S SS S S
S h S Q S Wh n n
h S P S W h S T Qh n n
= = =+
= = = +
= = = =+
= = = =+
= + =
= + +
(2.63)
4)
1 1 10
1 11 1
1 1 S P S PS S S S S SIV
S SS S S S S S
n nSh n n h n n
= =+ + +
= =+ +
= =
(2.64)
5) :
3 20 1
1 1 1 1
22 2 2
1 1 11 1
1 33
3 1 1 1 1
S P S P S PS
V S S S S S SS S S S S S
S P S P S PS
S S S S SS S SS S S S S S
SS h S P S Wh n n
S h S Th n n h n n
= = =
+= = = +
= = =
= = =+ +
= + + +
+ + +
(2.65)
=
= ++
=1
1 11
SK
K KKK
KS hhn
dS ;
( )1 1 11
S SS S S S SS S
W
++ +
+
=
.
, . :
( )
0
0 0
20 0 0
20 0 0
2 20 0 0 0 0
2
2
2 3
I I
II II I
III III II I
IV IV II I
V V III IV II I
S SS S kS
S S kS k S
S S kS k S
S S k S S k S k S
=
= + = + + = + + = + + + +
(2.66)
-
56
2
1 11 1
11 1
kn h
S t
=
.
1 , t1 .
, , . , ..
, .
. , , , , .
, , . , , . .
( , ): 1) :
3
2
12 I
my Sf
=
, (2.67)
m . 2) :
23 tg2 II
my Sf
=
, (2.68)
2 . 3) :
-
57
2
2
1 tg (3 )21 tg ( )2
m III IV
S III IV
z f S S
z f S S
= + = +
, (2.69)
2tg S m IIIz z f S = , (2.70)
21tg tg (3 )2m III IV
y z m S S = = + , (2.71)
21tg tg ( )2S III IV
x z m S S = = + , (2.72)
mz , sz , y , x , . 4) :
:
31 tg 2 V
y f S = . (2.73)
:
2100% 50tg Vy S
y
= =
(2.74)
y x :
( ) ( )
( )
2 2 2 2
2
2 3
3 tg2 2
tg tg 32 2
I II
III IV V
m m M m My S S
f fm S S f S
+ + =
+
(2.75)
( ) ( )2 2 2
2
tg tg 2 2I II III IV
M m M m M Mx S S S Sf f+
= +
(2.76)
m, M .
.
-
58
, . . , , , . , , .
.
. . :
2 202y r x Bx= ,
21B e= . 2 e= .
:
( )2 202 1 y r x x= + . (2.77) 2.3,
.
.
. 2.14.
-
59
2.3
= 2 < < a b< 1 < <
2 1 < < a b> 1= 1=
1 0 < <
a b>
0=
1 < < +
0 < < +
. 2.14. : 1 = , 1,0 = , 1 1,0h = . :
1 1 1 0S h Q= = ,
: 0P T+ = , : PT
= .
P T, 1n = , ' 1n = :
( ) ( )
2
21 1 1 1 4a aP
n nn n
= =
,
( )( )
( )3 32
' ' 1 4'
n nT
n n
= =
.
: 2
1 1
= +
, 0<
-
60
. 2.15.
: ) 0= , 0,1= , 2 02y r x= ;
) 0,1= , 0= , 2
02 2 xxry = (. 2.15);
) 0,1= , 0 , (. 2.15); ) , 0
-
61
2.4
.
2.4
-1,0 -0,5 -0,2 -0,1 0 +0,1 +0,2 +0,5 +1,0
0 19
49
81121
-1 12181
94
-9,0 -
1
-1,0 -2,0 -5,0 -10 - +10 +5 +2 +1
(. 2.17).
. 2.17.
: =1 , 1,0 = , 0,11 =h . :
PT
= , 0P T+ = .
P T:
-
62
( )( ) ( )22 1
nnP n nn n
=
,
( )( )
3
2
n nT
n n
=
,
:
( ) ( )( )
2
3
1
nn n n
n n
=
: ) 1= .
) nn
= .
) , ( )2 n n= n n > , 1 0 < < , . n n < , 1 < < - .
, , .
.
(. 2.7) .
( (2.51)): 1,0f = 1 1,0h = 1tg 0= 3tg 1,0=
:
1 1,0n = 2 1,0n = 3 1,0n =
, . :
1
1
1
0
S SS P
S SIV
S S
n nSh
+=
+
=
= = .
-
63
:
22
2
1 0IVS h+
= =
0= ( ):
22 1
1
== dh
h2 :
22 2 1 0+ =
1,2 1,618034=
2 0> - (.2.7)
2 0,381966h =
:
1 2 2
1 2 2 2
00
I
II II
S Q h QS W W h S Q
= + = = + =
1W , 2W , 3W 22
12
W = 22
21
2W = 1 2
12
W W+ =
12
1
1,0dSh
= =
:
22
2
1 1 2 2
Qh
= =
2 2 2 2Q P T= +
2T 2P
( )322
1 4
T+
= ( ) ( )2
22 2
1 1
4P
= +
2
-
64
( )( )( )
222
2 3 22 2
1 1 21 1
=
+ +
2 = 1,618034, 2 40,1246= .
22
1 2
Q =
112
Q =
1T 1P 32
14
T = 32
14
P =
1
1 32
2 1
=
2 = 1,618034 1 1,47214=
.
(2.29) f ' = 1,0:
236068,1618034,1
22
21 =
=
=r ,
236068,11618034,1
381966,021
2
2
21 =+
=
+=
hr
:
381966,01618034,1
11
1
2=
=
=d
: r1 = 1,236068 e2 = 1,47214 d = 0,381966 r2 = 1,236068 e2 = 40,1246 f = 1,0, SF = 0,381966 e2 = (e2 )
-
65
2.7. . , ,
, . .
. . - .
:
, , , , .
. (.2.18) dmin. , . , .
. 2.18.
dmin (. 2.5, 2.6) (. 2.7, 2.8).
-
66
2.5 D mind D mind
. 1 6 >> 6 >> 10 >> 10 >>18 >>18 >> 30 >> 30 >> 50 >> 50 >> 80
>> 80 >> 120
0,8 1,0 1,2 1,6 2,0 1,4 3,0
. 120 180 >> 180 >> 260 >> 260 >> 360 >> 360 >> 500 >> 500 >> 650 >> 650 >> 800
4,0 5,0 6,0 8,0 12,0 20,0
2.6
mind [] N [] D, 0,3 . 0,3 0,5 . 0,5 2,0 . 2,0
50 0,07 D . 50 120 >> 120 >> 260
0,07 D
. 260 500 >> 500 >> 650
0,05 D
-
. 650 800 0,06 D
0,06 D
0,06 D 50 0,09 D 0,08 D 0,08 D
-
. 50 120 >> 120 >> 260 >> 260 >> 500 >> 500 >> 650 >> 650 >> 800
0,10 D
0,08 D 0,06 D 0,06 D
2.7 D mind D mind
. 6 10 0,7 >> 50 >> 80 1,5 >> 10 >> 18 0,8 >> 80 >> 100 1,8 >>18 >> 30 1,0 >>100 >>120 2,0 >> 30 >> 50 1,2
2.8
mind , , N , D, 0,3 . 0,3 2,0
-
. 6 30 >> 30 >> 60
>> 60 >> 120
0,06 D 0,05 D 0,06 D
0,030 D 0,035 D 0,040 D
-
30 . 30 120
0,06 D 0,07 D
0,040 D 0,050 D
-
67
2.8.
. , , . .. [10]. , , .
, , , . .. , , , -. , , , . , , , ..
, . , , . .
( ). .
. , (. 2.19).
. 2.19. , .
-
68
, , , :
1
1
i m
i ii
n l const= +
=
= , (2.78)
l . 1 2 , 'F . 1 - . 2 - 1 . , y . 1 - ' 'n l , 2 - ' 'nz n MF+ .
: ' ' ' 'nz n MF n l+ = . (2.79)
. 2.19:
( )22 '' zlyMF += . (2.80) (2.80) (2.79) :
22
2
'1'
'12 z
nnzl
nny
= . (2.81)
(2.81) .
, (2.81) . (2.81) , , 2y 2z , ..:
2
1 1nn
= ,
. (2.81) ,
2z : 2
1 0nn
= .
, n n= , .. , :
-
69
2 2y l z= .
, , .
) )
)
)
. 2.20. :
2 2
2 2 1z ya b
+ = ,
a , b - .
(. 2.20 ). : 2
2 2 22
by b za
= .
(. 2.20 ) :
-
70
2 2
2 2 1z ya b
= ,
: 2
2 2 22
by b za
= + .
, (. 2.20 ):
222 22 b by z z
a a =
, (2.82)
(. 2.20 ): 22
2 22 b by z za a
= +
. (2.83)
: 1.
, .. n n< ; 2.
, .. n n> .
1) n n< . 2
1 nn
. (2.80) (2.81),
: 2
2 1 2n bln a
= ,
2 2
1 n bn a
= .
1=n , nn =' , :
1l na
n
=+
, 11
nb ln
=+
, 1
lcn
=
+,
: 1 1ce
a n= = < .
-
71
: 2
01b nr l
a n = = .
.
. 2.21. , :
maxsin cosA = .
. 2.21. ,
, : sin sin n = , 90= o , :
1sin n
= ,
:
max1cosA en
= = .
, (. 2.21).
, F . , ,
-
72
.
2) n n> . 2
1 nn
(2.81) .
1n = , n n= . x
(2.81) (2.83), , :
1la
n
=+
, 11
nb ln
=+
, 1nlc
n
=+
,
l n = , ( )0 1r n l= . 1.
. . 2.22, :
maxlim tgAxba
= ,
max1limcosAx
ac n
= = .
, (. 2.22).
. 2.22. -
-
73
, . , - , .
. . 2.23.
. 2.23.
,
(. 2.23). : AP PA const+ = 2 : , '
ASA' .
( )AS SA S S AP PA + = + = + (2.84)
( )22AP y s z= +
( )22 'PA y s z = + (2.84)
( ) ( ) ( )2 22 2y s z y s z s s + + + = +
-
74
. ,
( )
3 2
2 04z z y
s s sss s + =
++
. . 0y = , .
1 0z = ; 2z s s= +
( )12c
z s s= +
, .
2 2
2 1
2
z ysss s
+ =+
(2.85)
S S' , .
2s sa
+= ; b ss= (2.86)
S S' , (2) ,
2s sa
+= ; b ss=
. 2.24 2.25 . , . , , , , , .
-
75
. 2.24.
. 2.25.
, , . A 'A (. 2.26).
, , .
-
76
. 2.26. .
. (. 2.27) ,
.
. 2.27. .
. - .
(. 2.28) , .
. 2.28. .
-
77
, .
, , - . , .
. 2.29 , .
. 2.29. .
.
. ,
. . , .
. 2.30.
-
78
. 2.30. AMO : + = ,
sin sin
S rr
+= ,
= . (2.87)
'OMA : ' ' + = ,
' sin 'sin '
S rr
= , (2.88)
' ' = . (2.89)
'S . (2.88) :
sin '' 1sin '
S r =
. (2.90)
: 'S const= ,
sin sin
m const
= =
.
, nmn
=
sin sin = , sin sin
nn
=
.
sin sin
nn
=
, (2.91)
= . (2.92) (2.30) (2.29), :
sin 'sin
n n nS r r r r rn n
+= + = + =
,
' n nS rn
+=
(2.93)
(2.33):
-
79
1 1 1 1n nS r S r
= , (2.94)
S : 'n nS rn+
= . (2.95)
(2.87) (2.89) = , :
'= . (2.96)
. , : S r= , S r = .
: 0S = , 0S = .
. 2.31. 50r = , 1n = 1,5182n = . (2.32) (2.34),
125,91S = , 89,93S = . 1A , 1A - .
2A 2A , 50S S= = .
. 2.31.
3A 3A 0S S= = .
. -. . 2.32 .
-
80
. 2.32.
- : n y n y = . (2.97)
:
y ny n
= =
.
: 2
n n nn n n
= = = ,
n n = . :
1
nn
= =
.
'= :
n nn n
= =
.
, . , , , (2.98), 0 - , , .
0 0 = = .
sinsin
nn
=
. (2.98)
:
-
81
2
'
nn
=
, = , = ,
sin sin' sin sin
nn
= =
,
sinsin
nn
=
- ;
:
nn
=, =
sinsin
nn
=
- .
: 1= , = , = ,
sin sin' sin sin
n nn n
= =
- ;
, , .
, . , , .
,
(. 2.33 ). 11n
= ,
22 n= , 2 1 n= = . . n , .
, . 2.33 , , . :
1 2
1n
= , 2 n= , 2 11 n
= = .
.
-
82
. 2.33 .
11n
= , 2 n= , 2 1 1= = .
. 2.33 .
: 1 21n
= , 22 n= , 2 1 1= = .
) )
) )
. 2.33. , .
, . , .
: 1) ,
(.2.34). ,
-
83
. . . , , .
.2.34 ,
. R n f = , , /f v .
: 50f = , 2 25r = , 1 13,33pS = , 2 25pS = , 1,5n = , 5d = ,
1,5p = , p .
2) (.2.35).
-
84
. 2.35. ,
: 100f = , 1 22,222r = , 2 33,7r = , 10,5d = , 1 22,22pS = ,
28,84pS = , 0,754p = , 1,5n = .
3) (.2.36). , . .
: 100f = , 1,5n = , 1 2 22,22r r= = , 29,6d = , 1 22,22pS = ,
24, 43pS = , 0,6p = .
-
85
. 2.36. , ,
.
.
. .
, . :
cos cos
S
n n n nS S r
=
, (2.99)
2 2cos cos cos cos
t
n n n nt t r
=
(2.100)
rs, rt - ; S, S'
; t, t' -
. 2.37.
. 2.37. .
-
86
(. 2.38). , .
. 2.38.
:
( )3
2 21t
yr
y
+=
, : dyy
dz =
, 2
2
d yydz
=
.
, .
Sr - , , .
. 2.38 :
=
sinyrS .
, tg y= , .
. 2.38 :
+=
2ctg11sin , 'ctg y= ,
'1
tg1tg
y=
= ,
2'11cossin
y+== .
-
87
21cosS
yr y y= = + .
:
2
1cos1 tg
=+
, 3
3S
trr
y y=
.
. :
2 21 2y a z a z= + .
, 1 02a r= , : 2 2
0 22y r z a z= + .
, : zaryy 20 222 += ,
:
yzary 20 += .
, :
22 ayyy =+ ,
:
yya
y2
2 = ,
22 yayy = , :
2
220
2202 )()2(
yzarzazrayy ++= .
: 2
03 ryy = .
3y y , :
yyr
r St = 3
3
,
:
-
88
20
3
rrr St = . (2.101)
t S= =
' 't S= (2.102) t S (2.98) (2.99), :
cos cosSn rS
n n
=
2cos cos cos
mn rtn n
=
(2.101), 2cos S mr r = (2.103)
.
(2.101) (2.103) :
0 cosSr r = (2.104)
(2.104) .
, . 2.39. pS
, . 2.39 :
( )ctg ' ctg 'pS y z y = + = + + , .. (2.105) '' = , +='
:
zry
20tg
+= ,
=
sinyrS , (2.106)
0cos 'S
rr
= (2.107)
-
89
. 2.39.
2 202y r z Bz= + (2.108)
,
Bzry
+=
0tg (2.109)
(2.106) (2.107) ,
yr
=sin'cos 0
(2.110)
(2.109) (2.110),
BzrBzzr
++
=0
202tg (2.111)
tg sin. Sin (2.110) cos . tg . , tg .
( )( )00
1tg 1 2B r Bz zr
= + + (2.112)
tg tg (2.105) pS . pS .
-
90
( )0 1 1p rS BB = + (2.113) (2.113)
. (2.113) ,
, , . .
(2.113). , , , :
( )01 1 1prS BB
= + +
( )02 1 1prS BB
= +
01 2
2p p
rS SB
+ =
01 2
2 1p prS S BB
= +
, b 20
2 2 Bzzry +=
0raB
= , 0rb BB
= , 0 1rc BB
= +
1 2
1 2
2
2
p p
p p
S S a
S S c
+ = =
(2.114)
. 2.40.
1 2
2 1
22
l l al l c
+ = =
(2.115)
(2.114) (2.115) , .
-
91
. 2.40.
. 2.41 , , .
2 02y r z= , 0
tg yr
= ,
0cosS
rr
= ,
=sin
yrS ,
= cos'cos ,
=' (2.116)
(12) )'(ctg' ++= yzS p ,
01 2p
rS = , 2pS =
, , .
-
92
. 2.41.
,
. : .
-
93
. 200. , 200-160 , , . , .
. , .
() , , .
.
, , , (. 2.42).
. 2.42.
. , S = , :
21
2
2 4(2 1)
r n nr n n
=
+ (2.117)
1,5n = , : 1 2: 1: 6r r = (.2.43).
-
94
. 2.43.
. :
( ); ; ;
. , ,
. .
, S = , :
21
22
1r n nr n
= (2.118)
1,5n = , 1 2: 1:9r r = , .
, , .
, , .
. : R f n= .
, , .
[16]. , . 4 .
-
95
. 0,6 2 . , , 0,1 0,2 .
, , .
( ), 1 , , (. )
. , , . (. 2.33) , , ,
n1
= .
f ' = 4,0 , 19. = 0,6328 , 19 = 0,6328 n = 1,7410.
: 964,67410,14''' ===
= nfff .
S 'F' = 6,2746 . 1,2 ,
: )1('1 = nfr =6,9640,7410=5,160 .
d2 = 0,1 , SM = 6,1746 .
+=
nnrSM
'13
, : SM = 6,1746 = = r3 (1+1,7410), r3 = 2,2526.
S' :
5465,37410,1112526,2
'13 =
+=
+=
nnrSM .
d3 = 1 , r4 = 3,5465 1 = 2,5465.
-
96
d5 = 1,2 , d4 = 0,5 .
: r1 = 5,16049 d1 = 1,2 n2= 1,7410 19 r2 = d2 = 0,1 n3 = 1,0 r3 = 2,2526 d3 = 1,0 n4 = 1,7410 19 r4 = 2,5465 d4 = 0,5 n5 = 1,0 r5 = d5 = 1,2 n6 = 1,7410 19 r6 =
f ' = 3,9998, SF = 1,3575 . 2.44 .
. 2.44. : () ; ()
-
97
1:1 2.9.
2.9 m tg S y , % W, . 2,0 0,5899 0,0469 0,273 0,655 5,498 1,732 0,4887 0,0366 0,0179 0,56 3,1093 1,4142 0,3825 0,0256 0,0098 0,410 1,3873 1 0,2598 0,0135 0,0035 0,22 0,3477
, . .
1:1,5. , 1:0,5.
, . 2.9.
. . , . , , . , , , . , . , . , Zemax, , . , .
,
-
98
. , , , , , . , .
, . , , , . .
-
99
1. 3- . .: , 1993. 2. - : . . 2-,
. ./ .. , .. , .. , .. ; . .. . .: , 2000.
3. : . .., .., .. - : - , 2006.
4. : / .. , .. , .. , .. ; . .. . .: , 1986. 363 .
5. . 9 ./ .. . . 1. . .: . , 1986. 127 .
6. .. . .: , 1989.
7. Optical system design. Robert E. Fisher, Beljana Tagic-Galeb, Paul R. Yoder. 2nd ed. NY SPIE Press. 2008. 809p.
8. : . .. , .. , .. , .. . .: , 2004. 266 .
9. Haferkorn, Heinz: Optik, 3., bearb. und erw. Aufl.- Leipzig; Berlin; Heildelberg: Barth,1994 -690s.
10. .. . .: , 1966. 564 .
11. .. . (, , ). . 2- . - .: ,1978. - 543
12. .., .. . .: . 2000.-581 .
13. .. . .: . 1968.
14. .. . .: . . ., 1989 383.: .
15. .., .. . , , 1996.-84.
16. .. . . : (), 2002. -98.
17. - . / .., .., .. .; . . ... 3- ., . .-.: , . ., 1980. 742., .
18. .. . .: , 1989.- 221 .: .
-
100
19. .., .., .., .., .., .., .., .. . . .2. 2008. 424 ..
20. .., .., .. : . 4- ., . .: , 2008. 446.: .
21. .., .. . - ..-: , 2008. 79.:.
22. / .., .. , .. . .: , 1982.
23. . . ..- .: , 2009.- 162.
24. .. , .. , .. . : . / . .. , .. . .: . .., 2001. 440.
-
2009 , 12 , -. - 20092018 . 2011 - -,
(1898-1983) - -. 25 1898 . 1915 - . -. -, - . 1918 . : - , ,
. . 1923 , - . 1925 - 1979 -, . . ( . ..) , 1930 - - . - . 1926 - , . 1930 . .. , 39 . -
101
-
12 . - . .. 1935 - . 1947 , : " ". 1966 - " ". .. , -. 200 , 50 . - - , , , - . .. , " ", "", " ", " ", " ". .. .. , .. , .. , .. , .. , .. , .. . - - .. , .. , .. -, .. , .. . -, . - , . , . , . 2000 - " ". , . .. . 10 1953 -. : " 20- - . - , ". , 16 . 1969 .. , - . - 1979 . 11 1983 . - , , -. -. , - -, - - .
102
-
: - ! , . . , , . - ! - ! ! ? - . , : - , - , !
103
-
, ,
. I
. ..
- . .. 00408 05.11.1999 19.12.2011 2432 100 .
-
- - , 197101, -, ., 49
0_.pdf1__4.pdf . ..
2_ .pdf3_1_271211.pdf4_2_271211.pdf , .
5_ _3.pdf6_ .pdf7_Back+log_new.pdf