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Ⱦɜɢɠɟɧɢɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ ɩɪɨɬɢɜɨɬɨɤɨɦ (ɪɢɫ. 70).
M
Ɋɢɫ. 70. Ⱦɜɢɠɟɧɢɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ ɩɪɨɬɢɜɨɬɨɤɨɦ
ɋɚ ɢɡɦɟɧɹɟɬɫɹ ɨɬ
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ:
min
C ɞɨ
a
''
(1)
'
ɫɪ
max1
C , (
a
(1) (1)
ɧ
2
min
a
ɤ
.
max1
CC o
).
a
Ⱦɜɢɠɟɧɢɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ ɩɪɹɦɨɬɨɤɨɦ (ɪɢɫ. 71).
Ɋɢɫ. 71. Ⱦɜɢɠɟɧɢɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ ɩɪɹɦɨɬɨɤɨɦ
ɋ
ɢɡɦɟɧɹɟɬɫɹ ɨɬ
ɚ
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ:
ȼɵɜɨɞɵ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɫɯɟɦ ɩɪɨɬɢɜɨɬɨɤɚ ɢ ɩɪɹɦɨɬɨɤɚ:
min
C ɞɨ
a
(2)
'
ɫɪ
1–
max2
C , (
a
(2) ( 2)
''
ɧ
2
max2 max1
CC ; 2 –
aa
min max2
CCo ).
aa
ɤ
.
21
'!'.
ɫɪ ɫɪ
Ʉɢɧɟɬɢɤɚ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ
ɍɪɚɜɧɟɧɢɹ ɦɚɫɫɨɩɟɪɟɞɚɱɢ ɜ ɩɪɨɰɟɫɫɟ ɚɛɫɨɪɛɰɢɢ:
ɚɝ
MKF ' (237)
ɝɝɫɪ
ɢɥɢ
ɚ a
MKF ', (238)
ɝ a ɫɪ
ɝɞɟ
ɚ
– ɦɚɫɫɚ ɪɚɫɩɪɟɞɟɥɹɟɦɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɩɟɪɟɯɨɞɹɳɚɹ ɢɡ ɝɚɡɚ ɜ ɚɛɫɨɪɛɟɧɬ
ɝ
ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɤɝ/ɱ;
81
F – ɩɨɜɟɪɯɧɨɫɬɶ ɦɚɫɫɨɩɟɪɟɞɚɱɢ, ɦ2;
E
E
ɝɝ
''
ɝ
'
' '
Ʉ
ɝɞɟ
ɤɝ/(ɦ
E
ɬɚ, ɤɝ/(ɦ
ɧɤ
ɫɪ
ɚ a*
ɫɪ
, Ʉɚ – ɤɨɷɮɮɢɰɢɟɧɬɵ ɦɚɫɫɨɩɟɪɟɞɚɱɢ,
ɝ
ɝ
ɚ
2
ɚɚ
''
ɧ
2
1
1Km
E
ɝɚ
E
– ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɨɬɞɚɱɢ ɨɬ ɩɨɬɨɤɚ ɝɚɡɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɬɚɤɬɚ ɮɚɡ,
ɝ
.
2
ɱ);
– ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɨɬɞɚɱɢ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɬɚɤɬɚ ɮɚɡ ɤ ɩɨɬɨɤɭ ɚɛɫɨɪɛɟɧ-
.
2
ɱ).
ɝ *
ɢ
i ɝɝ
x
ɢ
i
;
K
ɚ
i
ɋɋ' ;
i
ɋɋ
11
ɚɝ
;
aa
1
,
E
m
ɤɝ
2
ɦɱ
;
Ɋɚɛɨɬɚ ɫɯɟɦɵ
ɂɫɯɨɞɧɚɹ ɝɚɡɨɜɚɹ ɫɦɟɫɶ G
ɸɬɫɹ ɞɨ ɡɚɞɚɧɧɵɯ ɬɟɦɩɟɪɚɬɭɪ
ɢ ɚɛɫɨɪɛɟɧɬ Gɚ ɜ ɯɨɥɨɞɢɥɶɧɢɤɚɯ 1 ɢ 2 ɨɯɥɚɠɞɚ-
ɝ
T
ɢ
T
ɢ ɩɪɨɬɢɜɨɬɨɤɨɦ ɩɨɞɚɸɬɫɹ ɜ ɤɨɥɨɧɧɭ 3.
ɝ0
ɚ0
ȼ ɤɨɥɨɧɧɟ 3 ɩɪɨɢɫɯɨɞɢɬ ɢɡɜɥɟɱɟɧɢɟ ɰɟɥɟɜɨɝɨ (ɪɚɫɩɪɟɞɟɥɹɟɦɨɝɨ) ɤɨɦɩɨ-
ɧɟɧɬɚ ɢɡ ɢɫɯɨɞɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ ɫ ɩɨɦɨɳɶɸ ɠɢɞɤɨɝɨ ɚɛɫɨɪɛɟɧɬɚ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɦɚɫɫɨɨɛɦɟɧɧɨɝɨ ɩɪɨɰɟɫɫɚ ɦɟɠɞɭ ɝɚɡɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɚɦɢ
ɩɨɥɭɱɚɸɬ:
ɜɧɢɡɭ ɤɨɥɨɧɧɵ – ɧɚɫɵɳɟɧɧɵɣ ɚɛɫɨɪɛɟɧɬ G
ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɰɟɥɟɜɨɝɨ
ɧɚ
(ɪɚɫɩɪɟɞɟɥɹɟɦɨɝɨ) ɤɨɦɩɨɧɟɧɬɚ ɫɧɚ;
ɜɜɟɪɯɭ ɤɨɥɨɧɧɵ – ɨɛɟɞɧɟɧɧɭɸ ɝɚɡɨɜɭɸ ɫɦɟɫɶ G
ɥɟɜɨɝɨ (ɪɚɫɩɪɟɞɟɥɹɟɦɨɝɨ) ɤɨɦɩɨɧɟɧɬɚ ɫ
.
ɨɝ
ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɰɟ-
ɨɝ
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ – ɤɨɧɰɟɧɬɪɚɰɢɹ ɪɚɫɩɪɟɞɟɥɹɟɦɨɝɨ
ɤɨɦɩɨɧɟɧɬɚ ɜ ɨɛɟɞɧɟɧɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ ɫ
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ – ɨɛɟɫɩɟɱɟɧɢɟ ɫ
ɨɝ.
= ɫ
ɨɝ
ɧɚ ɦɢɧɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɨɦ ɞɥɹ
ɨɝɡɞ
ɞɚɧɧɨɣ ɭɫɬɚɧɨɜɤɢ ɡɧɚɱɟɧɢɢ.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ.
82
ɋɯɟɦɚ ɧɚɫɚɞɨɱɧɨɝɨ ɚɛɫɨɪɛɟɪɚ (ɪɢɫ. 72).
Ɋɢɫ. 72. ɋɯɟɦɚ ɧɚɫɚɞɨɱɧɨɝɨ ɚɛɫɨɪɛɟɪɚ
Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ
ɋɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɭɫɬɚɧɨɜɤɢ (ɪɢɫ. 73).
Ɋɢɫ. 73. ɋɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɭɫɬɚɧɨɜɤɢ:
1, 2 – ɯɨɥɨɞɢɥɶɧɢɤɢ, 3 – ɚɛɫɨɪɛɰɢɨɧɧɚɹ ɧɚɫɚɞɨɱɧɚɹ ɤɨɥɨɧɧɚ
83
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
M
ɝɞɟ Ɇ
dc
()
SH h GcGc M
– ɦɚɫɫɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɩɟɪɟɯɨɞɹɳɚɹ ɢɡ ɝɚɡɨɜɨɣ ɮɚɡɵ ɜ ɠɢɞɤɭɸ ɜ
ɝɧɚ
U
ɨɝ ɚɩɩ ɚɩɩ ɧɚ ɝ ɝ ɨɝ ɨɝ ɝ
, (239)
ɨɝ
dt
ɧɚ
ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɤɝ/ɱ.
dc
ɨɝ
0:
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
ɂɡ ɜɵɪɚɠɟɧɢɣ (241) ɢ (242) ɫɥɟɞɭɟɬ, ɱɬɨ
ɧɚ
ɝɞɟ
– ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɦɚɫɫɨɩɟɪɟɞɚɱɢ.
ɝ
dt
Gc G c M
ɝ ɝ ɨɝ ɨɝ ɝ
(,, ),cfGGM
ɨɝ ɨɝ ɝ ɝ
ɧɚ
. (240)
ɧɚ
(241)
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ ɜ ɧɚɫɵɳɟɧɧɨɦ ɚɛɫɨɪɛɟɧɬɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
U
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
ɧɚ ɚɩɩ ɧɚ ɝ ɚ ɚ ɧɚ ɧɚ
dɫ
dt
dt
ɧɚ
0
:
Gc M Gc . (243)
ɧɚ ɧɚ ɝ ɚ ɚ
dc
Sh M Gc Gc
ɧɚ
ɧɚ
. (242)
ɧɚ
ɂɡ ɜɵɪɚɠɟɧɢɣ (242) ɢ (243) ɫɥɟɞɭɟɬ, ɱɬɨ:
ɧɚ
ɝɞɟ M
ɧɚ
– ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɦɚɫɫɨɩɟɪɟɞɚɱɢ.
ɝ
(, , )cfGGM , (244)
ɧɚ ɚ ɧɚ ɝ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɨɛɳɟɦɭ ɤɨɥɢɱɟɫɬɜɭ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɩɪɨ-
ɰɟɫɫɟ ɚɛɫɨɪɛɰɢɢ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dc
U
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
ɇɚ ɨɫɧɨɜɚɧɢɢ (245) ɢ (246):
()
SH h GcGc
ɨɝ ɚɩɩ ɚɩɩ ɧɚ ɝ ɝ ɨɝ ɨɝ
dɫ
ɨɝ
:
dt
Gc Gc G c G c . (246)
ɝ ɝ ɚ ɚ ɨɝ ɨɝ ɧɚ ɧɚ
ɨɝ ɝɨɝɚɧɚ
Gc G c
0
ɨɝ
dt
ɚɚ ɧɚɧɚ
(, , , )cfGGGG
. (245)
. (247)
84
Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ:
P
U
(, , , )cfGGGG . (248)
ɧɚ ɝ ɨɝ ɚ ɧɚ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
U
ɧɚ ɚɩɩ ɚ ɝ ɧɚ
ɇɚ ɨɫɧɨɜɚɧɢɢ (249) ɢ (250):
ɧɚ
SG
. (249)
dt
G Ɇ G . (250)
ɧɚ
ɚɝ ɧɚ
(, )hfGG . (251)
ɧɚ ɚ ɧɚ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɝɚɡɨɜɨɣ ɮɚɡɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
VM dP
ɝɞɟ Ɇ
Ɋ
T
V
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɨɛɟɞɧɟɧɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ, ɤɝ/ɦɨɥɶ;
ɨɝ
– ɞɚɜɥɟɧɢɟ ɜ ɤɨɥɨɧɧɟ, ɉɚ;
ɨɝ
– ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɤɨɥɨɧɧɟ (ɩɨ ɝɚɡɨɜɨɣ ɮɚɡɟ), Ʉ;
ɨɝ
– ɨɛɴɟɦ ɝɚɡɨɜɨɣ ɮɚɡɵ ɜ ɤɨɥɨɧɧɟ, ɦ3.
ɨɝ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɨɝ ɨɝ ɨɝ
R
T
ɨɝ
ɇɚ ɨɫɧɨɜɚɧɢɢ (252) ɢ (253) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
GG Ɇ
dt
GG Ɇ . (253)
ɨɝ ɝ ɨɝ
ɝɨɝ ɝ
ɝɨɝ ɝ
(, )
fG G
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɜ ɚɛɫɨɪɛɟɪɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɞɥɹ ɯɨɥɨɞɢɥɶɧɢɤɚ 1:
Vc Gc G c Gc G c
ɝɝɪɝ ɝ ɪɝɝ ɯɥ1 ɪɯɥ11 ɝɪɝɝ ɯɥ1 ɪɯɥ1 ɯɥ1
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
0
d
T
ɝ
dt
Gc Gc G c G c
TT T T
ɝɪɝɝ ɝɪɝɝ ɯɥ1 ɪɯɥ1 ɯɥ1 ɯɥ1 ɪɯɥ1 ɯɥ1
TTTT
0
d
T
ɝ
0
:
dt
0 ɜɵɯ ɜɯ
ɧɚ
Ɇ G
ɧɚ
, (252)
ɧɚ
. (254)
ɨɝ.
ɜɯ
ɯɥ
0 ɜɵɯ
. (255)
. (256)
85
ɇɚ ɨɫɧɨɜɚɧɢɢ (255) ɢ (256) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
U
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
0
(, )fG G
T
. (257)
ɝɝɯɥ1
ɯɥ1.
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɞɥɹ ɯɨɥɨɞɢɥɶɧɢɤɚ 2.
0
d
T
Vc Gc Gc Gc Gc
ɚ ɚ ɪɚ ɚ ɪɚ ɚ ɯɥ2 ɪɯɥ2 ɯɥ2 ɚɪɚɚ ɯɥ2 ɪɯɥ2 ɯɥ2
ɚ
TTTT
dt
ɜɯ 0 ɜɵɯ
ɇɚ ɨɫɧɨɜɚɧɢɢ (258) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
0
T
ɚ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ
),(
GGf
. (259)
ɯɥ2ɚ
G
.
ɯɥ2
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɞɥɹ ɭɫɬɚɧɨɜɤɢ ɫ ɩɨɤɚɡɚɬɟɥɟɦ ɷɮɮɟɤɬɢɜɧɨɫɬɢ
(ɪɢɫ. 74).
. (258)
ɫ
ɨɝ
Ɋɢɫ. 74. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɞɥɹ ɭɫɬɚɧɨɜɤɢ ɫ ɩɨɤɚɡɚɬɟɥɟɦ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫɨɝ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
,,,GG G G
ɝɨɝɚ ɧɚ
ȼɨɡɦɨɠɧɵɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
,,ɫ hP
ɨɝ ɧɚ ɨɝ
,ɫ c .
ɝɚ
Ɇ .
ɝ
ɧɚ
.
.
ɋɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ ɩɪɢ ɩɨɤɚɡɚɬɟɥɟ
ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
ɨɝ (ɪɢɫ. 75).
86
Ɋɢɫ. 75. ɋɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ
ɩɪɢ ɩɨɤɚɡɚɬɟɥɟ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
ɨɝ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɞɥɹ ɭɫɬɚɧɨɜɤɢ ɫ ɩɨɤɚɡɚɬɟɥɟɦ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
ɧɚ (ɪɢɫ. 76).
Ɋɢɫ. 76. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɞɥɹ ɭɫɬɚɧɨɜɤɢ ɫ ɩɨɤɚɡɚɬɟɥɟɦ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
,,ɫ hP
ɧɚ ɧɚ ɨɝ
.
ɋɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ ɩɪɢ ɩɨɤɚɡɚɬɟɥɟ
ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
Ɋɢɫ. 77. ɋɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ
(ɪɢɫ. 77).
ɧɚ
ɩɪɢ ɩɨɤɚɡɚɬɟɥɟ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
ɧɚ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ, ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɢ ɧɟɤɨɧɬɪɨɥɢɪɭ-
ɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ ɬɟ ɠɟ, ɱɬɨ ɢ ɜ ɫɢɫɬɟɦɟ ɫ ɩɨɤɚɡɚɬɟɥɟɦ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɫ
87
ɧɚ
.
ɨɝ
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ (ɪɢɫ. 78).
Ɋɢɫ. 78. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ:
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɫ
ɩɨ ɩɨɞɚɱɟ ɚɛɫɨɪɛɟɧɬɚ Gɚ – ɤɚɤ ɩɨɤɚɡɚɬɟɥɹ ɷɮɮɟɤɬɢɜ-
ɨɝ
ɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ;
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɞɚɜɥɟɧɢɹ ɜɟɪɯɚ ɤɨɥɨɧɧɵ Ɋ
ɝɚɡɨɜɨɣ ɫɦɟɫɢ G
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɭɪɨɜɧɹ h
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɝɚɡɨɜɨɣ ɮɚɡɟ;
ɨɝ
ɩɨ ɨɬɛɨɪɭ ɧɚɫɵɳɟɧɧɨɝɨ ɚɛɫɨɪɛɟɧɬɚ G
ɧɚ
ɜ
ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ;
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɢɫɯɨɞɧɵɯ ɦɚɬɟɪɢɚɥɶɧɵɯ ɩɨɬɨɤɨɜ ɝɚɡɚ
0
ɚɛɫɨɪɛɟɧɬɚ
ɩɨ ɩɨɞɚɱɟ ɯɥɚɞɨɚɝɟɧɬɨɜ G
T
ɚ
ɯɥ1
ɢ G
ɯɥ2,
ɩɟɱɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɭɫɬɚɧɨɜɤɢ.
ɋɬɚɛɢɥɢɡɚɰɢɹ ɪɚɫɯɨɞɚ ɢɫɯɨɞɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ G
ɞɚɧɧɨɣ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɭɫɬɚɧɨɜɤɢ.
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ – G
ɬɟɦɩɟɪɚɬɭɪɵ –
ɞɚɜɥɟɧɢɟ – Ɋ
ɭɪɨɜɟɧɶ ɧɚɫɵɳɟɧɧɨɝɨ ɚɛɫɨɪɛɟɧɬɚ – h
ɤɨɧɰɟɧɬɪɚɰɢɹ – ɫ
, Gɚ, Gɨɝ, Gɧɚ, G
ɝ
ɯ 00
,,,, , ,,,
TT TT T T TTT
ɝɨɝɚɧɚɯɥ1 ɯɥ2 ɝɚɚɩɩ
, Ɋɧ, 'Ɋ;
ɜ
.
ɨɝ
ɯɥ1
, G
ɯɥ2
;
;
ɧɚ
ɋɢɝɧɚɥɢɡɚɰɢɹ:
ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɋ
ɡɧɚɱɢɬɟɥɶɧɨɟ ɩɨɜɵɲɟɧɢɟ Ɋ
ɨɬ
ɨɝ
n > Ɋ
ɜ
ɡɞ
ɋ ;
ɨɝ
, ɩɪɢ ɷɬɨɦ ɮɨɪɦɢɪɭɟɬɫɹ ɫɢɝɧɚɥ
ɩɪɟɞ
«ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ».
88
= Ɋ
ɩɨ ɨɬɛɨɪɭ ɨɛɟɞɧɟɧɧɨɣ
ɨɝ
– ɞɥɹ
ɧɚ
T
ɝ0 ɢ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, – ɞɥɹ ɨɛɟɫ-
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɡɚ-
ɝ
;
ɋɢɫɬɟɦɚ ɡɚɳɢɬɵ.
UMU
M
ɉɨ ɫɢɝɧɚɥɭ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ» – ɨɬɤɪɵɜɚɟɬɫɹ ɦɚɝɢɫɬɪɚɥɶ G
ɡɚɤɪɵɜɚɸɬɫɹ
ɨɝ,
ɜɫɟ ɨɫɬɚɥɶɧɵɟ ɦɚɝɢɫɬɪɚɥɢ.
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ ɢ ɦɚɬɟɪɢɚɥɚ, ɤɚɤ ɜɥɚɝɨɧɨɫɢɬɟɥɟɣ.
M
Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɭɪɚɜɧɟɧɢɹ Ɇɟɧɞɟɥɟɟɜɚ – Ʉɥɚɩɟɣɪɨɧɚ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ:
ɩ
. (260)
ɧ
P
ɩ
M
. (261)
P
ɧ
:
Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ Z – ɬɨ ɨɬɧɨɲɟɧɢɟ ɦɚɫɫɵ ɜɥɚɝɢ Ɇ
ɤ ɨɛɳɟɣ ɦɚɫɫɟ ɜɥɚɠɧɨɝɨ ɦɚɬɟɪɢɚɥɚ Ɇ = Ɇ
ɝɨ ɦɚɬɟɪɢɚɥɚ Ɇ
.
ɫɦ
+ Ɇɜɥ, ɢɥɢ ɤ ɦɚɫɫɟ ɚɛɫɨɥɸɬɧɨ ɫɭɯɨ-
ɫɦ
ȼɥɚɠɧɨɫɬɶ, ɨɬɧɟɫɟɧɧɚɹ ɤɨ ɜɫɟɦɭ ɜɟɳɟɫɬɜɭ:
M
ɜɥ
Z
100, %
,
ɝɞɟ Ɇ = var.
ȼɥɚɠɧɨɫɬɶ, ɨɬɧɟɫɟɧɧɚɹ ɤ ɦɚɫɫɟ ɚɛɫɨɥɸɬɧɨ ɫɭɯɨɝɨ ɦɚɬɟɪɢɚɥɚ:
M
ɋ
ɜɥ
100, %
,
M
ɫɦ
ɝɞɟ Ɇ
= const.
ɫɦ
Z
Ⱦɢɚɝɪɚɦɦɵ ɪɚɜɧɨɜɟɫɢɹ ɩɪɢ ɫɭɲɤɟ
ɦ
)(
T
Ⱦɢɚɝɪɚɦɦɚ
ɩ
fP ɩɪɢ
Z
= Z* (ɪɢɫ. 79).
ɜɥ
Ɋɢɫ. 79. Ⱦɢɚɝɪɚɦɦɚ
ɦ
()Pf
T
ɩɪɢ
ɩ
Z
= Z*.
Z
* >
1
Z
* >
Z
*
2
3
89
ɂɡ ɞɢɚɝɪɚɦɦɵ ɫɥɟɞɭɟɬ:
ɦ
Ɋ
ɉɪɢ
ɉɪɢ
Ⱦɢɚɝɪɚɦɦɚ
p o Z*p – ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɫɭɲɤɢ ɩɨɜɵɲɚɟɬɫɹ.
ɩ
T
no Z* p – ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɫɭɲɤɢ ɩɨɜɵɲɚɟɬɫɹ.
Z
1 – ɞɢɚɝɪɚɦɦɚ ɩɪɢ
ɉɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ
ɂɡ ɞɢɚɝɪɚɦɦɵ ɫɥɟɞɭɟɬ:
ɉɪɢ
ɉɪɢ
Ⱦɢɚɝɪɚɦɦɚ
ɬɨɤɟ G
TZ
MZ
ɢ G
ɦ
*
no p
ɦ *
()P
ppop.
ɩ
Z–M
(ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ) ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 81.
ɫɚ
* = f (M ) ɩɪɢ T = const (ɪɢɫ. 80).
Z
Ɋɢɫ. 80. Ⱦɢɚɝɪɚɦɦɚ
T
, 2 – ɞɢɚɝɪɚɦɦɚ ɩɪɢ
1
T
<
T
<
T
1
2
3
* = f (M ) ɩɪɢ T = const:
.
T
3 – ɞɢɚɝɪɚɦɦɚ ɩɪɢ
2,
T
3
.
ɪɚɜɧɨɜɟɫɧɨɣ ɢ ɪɚɛɨɱɟɣ ɥɢɧɢɣ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ ɩɪɢ ɩɪɹɦɨ-
Ɋɢɫ. 81. Ⱦɢɚɝɪɚɦɦɚ
1 – ɪɚɜɧɨɜɟɫɧɚɹ ɥɢɧɢɹ
Z–M
ɪɚɜɧɨɜɟɫɧɨɣ ɢ ɪɚɛɨɱɟɣ ɥɢɧɢɣ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ ɩɪɢ ɩɪɹɦɨɬɨɤɟ Gɦ
ɢ G
(ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɢ
ɫɚ
Z
= f (M ) ɩɪɢ
T
, 2 – ɪɚɜɧɨɜɟɫɧɚɹ ɥɢɧɢɹ Z = f (M ) ɩɪɢ
1
3 – ɪɚɛɨɱɚɹ ɥɢɧɢɹ
Z–M
T
>
T
):
2
1
90
T
,
2
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