Готман В.И. Короткие замыкания и несимметричные режимы в электроэнергетических системах
Подождите немного. Документ загружается.
201
2
1
21,4 1,03 1,78 2,47 1,27 16,0
Ma
jj
ªº
«»
¬¼
U aa +a
ɤȼ;
22
2
1,03 1,78 2,47 1,27 5,37
Ma
j
ªº
«»
¬¼
U aa +a
ɤȼ;
2
0
1,27 16 1,27 5,37 7,95 10,7
M
jj j
ªº
¬¼
U aa
ɤȼ.
Ⱥɧɚɥɨɝɢɱɧɨ ɞɥɹ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɬɨɱ-
ɤɟ N ɩɨɥɭɱɚɟɦ:
1
0,55 17,28
Na
j U
ɤȼ;
2
0,55 4,12
Na
j U
ɤȼ;
0
10,9 10,7
N
j U
ɤȼ.
ɇɚɯɨɞɢɦ ɮɚɡɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɭɡɥɟ Ɇ:
x ɧɟɩɨɜɪɟɠɞɟɧɧɨɣ ɮɚɡɵ Ⱥ:
120
99,5
1,27 16 1,27 5,37
7,95 10,7 5,4 32,1 32,5 ɤȼ;
MA Ma Ma M
j
jj
jje
UU U U
D
x ɡɚɦɤɧɭɜɲɟɣ ɮɚɡɵ ȼ:
22
120
1,27 16 1,27 5,37
7,95 10,7 0;
MB Ma Ma M
jj
j
UUUUaa a a
x ɧɟɩɨɜɪɟɠɞɟɧɧɨɣ ɮɚɡɵ ɋ:
22
120
1,27 16 1,27 5,37
7,95 10,7 18,44ɤȼ.
MC Ma Ma M
jj
j
UU UUaa a a
Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɪɚɫɫɱɢɬɵɜɚɟɦ ɨɫɬɚɬɨɱɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɮɚɡ
Ⱥ ɢ ȼ ɜ ɬɨɱɤɟ N:
73
33,5 ɤȼ,
j
NA
e U
D
22,85 ɤȼ,
NB
U
0.
NC
U
Ɉɬɦɟɬɢɦ, ɱɬɨ
00
00
10,9 10,7 7,95 10,7 =18,85
= 1,03 18,1 =18,7 ɤȼ.
NM
MMN
jj
jx j j
|
|
UU
I
8.6. ɉɟɨɩɯɛɢɨɩɠ Ʌɂ ɬ ɫɛɢɫɶɝɩɧ ɯɛɢɶ
Ɋɚɫɫɦɚɬɪɢɜɚɟɦ ɫɟɬɶ ɫ ɡɚɡɟɦɥɟɧɧɨɣ ɧɟɣɬɪɚɥɶɸ. ɋɱɢɬɚɟɦ, ɱɬɨ ɩɪɨ-
ɢɫɯɨɞɢɬ ɪɚɡɪɵɜ ɨɞɧɨɣ ɮɚɡɵ (Ⱥ), ɩɪɢ ɷɬɨɦ ɨɞɢɧ ɤɨɧɟɰ ɩɪɨɜɨɞɚ ɷɬɨɣ ɮɚɡɵ
ɡɚɡɟɦɥɹɟɬɫɹ, ɨɛɪɚɡɭɹ ɨɞɧɨɮɚɡɧɨɟ ɄɁ, ɚ ɞɪɭɝɨɣ ɨɫɬɚɟɬɫɹ ɢɡɨɥɢɪɨɜɚɧɧɵɦ
(ɫɦ. ɪɢɫ. 8.16).
Ⱦɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨ
ɧɢɱɧɵɟ ɭɫɥɨɜɢɹ:
ɞɥɹ ɨɞɧɨɮɚɡɧɨɝɨ ɄɁ
–
0, 0,
K
BKC KA
IIU
ɞɥɹ ɨɛɪɵɜɚ ɮɚɡɵ –
0, 0,
L
ALBLC
' 'IUU
ɗɬɢɦ ɝɪɚɧɢɱɧɵɦ ɭɫɥɨ
ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɫɥɟɞɭɸɳ
ɢ
ɨɬɧɨɲɟɧɢɹ:
120
;
Ka Ka K
III
120
0
Kɚ Kɚ K
UUU
120
0;
LL L
III
12
0
Lɚ Lɚ L
' ' 'UUU
Ⱦɨɩɨɥɧɢɦ ɷɬɢ ɫɨɨɬ
ɧ
(8.3) ɢ ɪɟɲɢɦ ɩɨɥɭɱɟɧɧɭɸ
1
Kɚ
U
La
'U
Ɂɞɟɫɶ
KK
x
x
2
2
LL
L
L
x
x
x
xx
ɝɞɟ
2,K
x
0K
x
–
ɪ
ɟɚɤɬɢɜɧɨ
ɫ
ɧɨɫɬɟɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤ
ɢ
2, 0LL
xx
– ɬɨ ɠɟ ɨɬɧɨɫɢ
ɬ
2, 0KL KL
xx
– ɜɡɚɢɦɧɵɟ ɪ
ɟ
ɪ
ɵɜɚ ɜ ɫɯɟɦɚɯ ɫɨɨɬɜɟɬɫɬɜɭ
ɸ
Ⱦɥɹ ɭɫɥɨɜɢɣ ɫɨɜɩɚɞɟɧ
ɢ
ɧɚɥɢɱɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɫɜ
ɹ
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɹ
ɦ
ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɜ ɮɨɪɦɟ
ɫɹɬ ɬɨɥɶɤɨ ɨɬ
ɪ
ɟɚɤɬɢɜɧɨɫɬ
ɟ
ɉɪɟɨɛɪɚɡɭɟɦ ɭɪɚɜɧɟ
ɧ
ɧɢɯ ɞɜɚ ɨɞɢɧɚɤɨɜɵɯ, ɧɨ
ɩ
ɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɩ
ɧɵɦ ɩɨɥɨɠɢɬɟɥɶɧɨɦɭ ɧɚɩ
ɪ
202
ɝɨ ɫɥɭɱɚɹ ɞɜɨɣɧɨɣ ɧɟɫɢɦɦɟɬɪɢɢ ɢɦ
ɟ
–
0;
0
.
ɜɢɹɦ
ɢ
ɟ cɨ-
0
;
0
.
ɧ
ɨɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹɦɢ (6.12), (6.13)
,
ɫɢɫɬɟɦɭ ɨɬɧɨɫɢɬɟɥɶɧɨ
1Kɚ
U
ɢ
1
Lɚ
'U
1
11
;
KKa KLLa
jx jx II
111
.
a
LK Ka L La
jx jx II
2
20
20
20
()
KL KL
K
K
LL
xx
x
xx
;
0
0
L
L
x
,
20 02
20
KL L KL L
KL
LL
xx xx
x
xx
,
ɫ
ɬɢ ɫɯɟɦ ɨɛɪɚɬɧɨɣ ɢ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞ
ɢ
ɄɁ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɪɚɡɪɵɜɚ ɫɯɟɦɵ ɜ
ɬ
ɟɥɶɧɨ ɦɟɫɬɚ ɪɚɡɪɵɜɚ ɩɪɢ ɨɬɫɭɬɫɬ
ɜ
ɟ
ɚɤɬɢɜɧɨɫɬɢ ɦɟɠɞɭ ɬɨɱɤɨɣ ɄɁ ɢ ɦɟɫ
ɬ
ɸ
ɳɢɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ.
ɢ
ɹ ɨɫɨɛɵɯ ɮɚɡ ɬɨɱɟɤ ɧɟɫɢɦɦɟɬɪɢɢ
K
ɹ
ɡɢ ɦɟɠɞɭ ɧɢɦɢ ɫɩɪɚɜɟɞɥɢɜɨ
K
L
xx
ɦ
(8.44) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɬɨɱɧɚɹ ɷɥɟɤɬ
ɪ
ɬɪɟɯɥɭɱɟɜɨɣ ɡɜɟɡɞɵ, ɷɥɟɦɟɧɬɵ ɤɨɬɨ
ɪ
ɟ
ɣ ɨɛɪɚɬɧɨɣ ɢ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶ
ɧ
ɧ
ɢɹ (8.44), ɜɜɟɞɹ ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɤɚ
ɠ
ɩ
ɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɩɨ ɡɧɚɤɭ ɫɥɚɝɚɟɦɵ
ɯ
ɚɞɟɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢɧ
ɹ
ɬɨ ɩɪɨɬɢ
ɜ
ɪ
ɚɜɥɟɧɢɸ ɬɨɤɚ):
Ɋɢɫ. 8.16. Ɉɞɧɨɮɚɡɧɨɟ ɄɁ
ɨɞɧɨɜɪɟɦɟɧɧɵɦ ɪɚɡɪɵɜɨɦ ɮ
ɚ
ɟ
ɟɦ ɝɪɚ-
,
(8.2) ɢ
1
:
(8.44)
ɞ
ɨɜɚɬɟɥɶ-
ɬɨɱɤɟ L;
ɜ
ɢɢ ɄɁ;
ɬ
ɨɦ ɪɚɡ-
K
ɢ
L
ɢ
LK
x
[6].
ɪ
ɢɱɟɫɤɚɹ
ɪ
ɨɣ ɡɚɜɢ-
ɧ
ɨɫɬɟɣ.
ɠ
ɞɨɝɨ ɢɡ
ɯ (ɩɨɥɨ-
ɜ
ɨɩɨɥɨɠ-
ɫ
ɚ
ɡɵ
ɩ
ɧ
ɜ
ɫ
ɩ
(
ɢ
ɬ
ɞ
ɷ
ɧ
ɫ
ɫ
ɂ
ɥ
ɜ
ɧ
ɩ
ɩ
ɬ
ɫ
ɬ
ɜ
ɦ
ɩ
ɪ
ɧɵ
ɜ
ɚ
ɬ
ɫ
ɯ
ɟ
ɩ
ɨ
(
ɪ
ɢ
ɢ
ɬ
ɟ
ɥ
ɞ
ɚ
ɷ
ɤ
ɜ
ɧɢ
ɫ
ɬ
ɫ
ɥ
ɟ
(
ɂɧ
ɥ
ɨ
ɜ
ɚ
ɬ
ɧɵ
ɩ
ɪ
ɩ
ɨ
ɬ
ɨ
ɥ
ɫ
ɜ
ɹ
ɬ
ɟ
ɥ
ɜ
ɦ
ɦɵ
ɋ
ɯ
ɚɜ
ɥ
ɵ
ɧ
ɬ
ɟ
ɥ
ɟ
ɦ
ɫɥ
ɢ
ɫ.
ɧ
ɚ
ɥ
ɶ
ɧ
ɧ
ɜ
ɢ
ɜ
ɢ
ɹ
ɜ
ɬ
ɨ
ɱ
ɟ
ɞ
ɨ
K
x
ɧ
ɵ
ɦ
ɷ
ɤ
ɬ
ɟ
ɥ
ɵ
ɯ
ɩ
ɨɜ
ɤ
ɨ
ɥ
ɶ
ɤ
ɹ
ɡ
ɢ
ɥ
ɶ
ɧ
ɦ
ɟ
ɫ
ɵ
ɤ
ɚ
ɯ
ɟ
ɦ
ɥ
ɟ
ɧ
ɧ
ɚ
ɪ
ɥ
ɶ
ɧ
ɦ
ɭ
ɟɞ
8
.
ɚ
ɩ
ɪ
ɧ
ɨ
ɫ
ɟɫ
ɢ
ɜ
ɚ
ɥ
ɜ
ɮ
ɱ
ɤ
ɚ
ɨ
ɜ
ɚ
)
K
L
ɦɢ
ɤ
ɜ
ɢ
ɥ
ɶ
ɧ
ɋ
ɩ
ɪ
ɟɪ
ɨ
ɧ
ɬ
j
Ⱦ
ɤ
ɨ
ɢ
G
ɧ
ɭ
ɸ
ɫ
ɬ
ɨ
Ʉ
ɚ
ɧ
ɢ
U
'
ɦɚ
ɧɢ
ɪ
ɢ
ɧ
ɨ
ɫ
ɷɤ
ɨɜ
.
1
7
ɪ
ɹ
ɠ
ɫ
ɬ
ɢ
ɢɦ
ɥ
ɟ
ɧ
ɮ
ɢ
ɤ
ɚ
ɦ
ɢ
ɚ
ɬ
ɟ
)
,
ɢ
ɫ
ɥ
ɢ
ɜ
ɚ
ɧ
ɨ
ɫ
ɋ
ɩ
ɪ
ɟɨ
ɢ
ɦ
ɬ
ɭ
ɪ
(
jx
Ⱦ
ɥ
ɹ
ɩ
ɪ
G
ɸ
ɨ
ɪ
Ʉ
ɚ
ɤ
ɢ
ɹ
K
U
'
U
ɚ
ɡ
ɢ
ɹ
ɬ
ɫ.
ɫ
ɬ
ɢ
ɜ
ɢ
ɚɬ
7
)
ɫ
ɠɟ
ɢ
ɞ
ɦ
ɦ
ɟ
ɧ
ɬ
ɧ
ɤ
ɬ
ɢ
ɢ
K
ɟ
ɥ
ɶ
x
ɥ
ɨ
ɚ
ɥ
ɟ
ɫ
ɬ
ɢ
ɪ
ɚ
ɜ
ɛ
ɪ
ɦ
ɪ
ɪ
ɭ
K
x
ɹ
ɩ
ɪ
ɨ
ɞ
F
ɪɟ
ɚɡ
ɪ
ɤ
ɩ
ɜ
ɦ
1
K
ɚ
L
ɚ
U
ɡ
ɚ
ɦ
ɬ
ɨ
ɤ
8.
1
ɢ
ɜ
ɢ
ɜ
ɚ
ɟɥ
ɶ
ɫ
ɥ
ɟ
ɟ
ɧ
ɢ
ɞ
ɥ
ɹ
ɟ
ɬ
ɪ
ɧ
ɨ
ɝ
ɢ
ɜ
ɧ
K
1
ɶ
ɧ
ɨ
K
x
ɜɚ
ɟ
ɧ
ɬ
ɢ
.
ɜ
ɟ
ɞ
ɪ
ɚɡ
ɨ
ɪ
ɚɫ
ɱ
G
K
I
ɩ
ɪ
ɞ
ɨ
ɥ
F
(
ɚɤ
ɬ
ɪɵ
ɩ
ɪ
ɚ
ɦɟ
1
ɚ
ɦ
ɟ
ɳ
ɤ
ɨ
ɜ
1
7
.
ɜ
ɚ
ɥɟ
ɶ
ɧ
ɟ
ɞ
ɭ
ɢ
ɣ
ɹ
ɪ
ɪ
ɢ
ɢ
ɝ
ɨ
ɧ
ɨ
ɢ
ɨ
ɫ
ɬ
K
ɦ
ɢ
ɬ
ɧ
ɨ
ɞ
ɥ
ɢ
ɨ
ɜ
ɚ
ɱ
ɟ
ɬ
,
F
1
K
ɚ
ɢɜ
ɥ
ɶ
ɧ
K
x
ɬ
ɢ
ɵ
ɜ
ɚ
ɚ
ɜ
ɢ
ɟ
ɫɬ
jx
j
j
ª
¬
ɳ
ɟ
ɜ
,
.
ȿ
ɬɨ
ɧ
ɬ
ɨɫ
ɭ
ɟ
ɬ
ɩ
ɪ
ɚ
ɫ
ɢ
ɫ
ɬ
ɪ
ɣ
ɬ
L
1
ɬ
ɢ
K
x
ɢ
,
ɫ
ɨ
ɫ
ɬ
ɢ
ɜ
ɨ
ɚ
ɧ
ɢ
ɬ
ɨ
ɦ
,
FL
U
x
ɟɞ
ɧ
ɨ
K
ɜ
ɧ
ɚ
;
ɩ
ɢ
ɥ
ɨ
ɟ
ɩ
K
K
x
x
I
(
K
j
x
ª
¬
ɧ
ɢ
ɫɨ
ȿ
ɟ
ɩ
ɱ
ɤ
ɬ
ɧ
ɭ
ɬ
ɢ
ɬ
,
ɩ
ɪ
ɹ
ɫ
ɫ
ɦ
ɫ
ɜ
ɨ
ɪ
ɟ
ɯ
ɬ
ɨ
ɱ
1
ɫ
K
L
ɫ
ɨ
ɛ
ɬ
ɢ
ɨ
ɫ
ɬ
ɢɣ
ɦ
ɩ
1
L
ɫ
L
U
K
x
ɞ
ɟ
ɧ
ɣ
ɧ
f
ɧ
ɨɫ
ɩ
ɪ
ɢ
ɨ
,
ɧ
ɩ
ɨ
ɜ
K
K
I
K
L
j
x
I
ɢ
ɹ,
ɨɬ
ɩɪ
ɤ
ɚ
ɯ
ɭ
ɸ
ɢ
.
ɂ
ɱ
ɬ
ɹ
ɦ
ɨ
ɦ
ɚ
ɬ
ɨ
ɞ
ɢ
ɯ
ɮ
ɚ
ɱ
ɤ
ɟ
ɫ
ɯ
ɟ
ɪ
ɛ
ɥ
ɸ
ɩ
ɪ
ɬ
ɶ
ɣ
ɭ
ɪ
ɩ
ɨ
ɫ
ɯ
ɟ
1a
K
L
I
ɧ
ɧ
ɨ
ɧ
ɟ
ɫ
f
;
ɬɶ
ɢ
ɷ
ɬ
ɧ
ɚ
ɢ
ɜ
ɪ
ɟ
1
K
ɚ
x
K
KL
x
I
ɩ
ɜɟ
ɬ
ɪ
ɢ
ɫ
ɯ
K
ɬ
ɨ
ɂ
ɡ
ɬ
ɨ
ɪ
ɨɣ
ɬ
ɪ
ɢ
ɢ
ɬ
ɫ
ɚ
ɡ
ɧ
ɟ
G
ɟ
ɦ
ɵ
ɪ
ɟ
ɚ
ɢ
ɸɞ
ɪ
ɹ
ɦ
ɨ
ɪ
ɚ
ɜ
ɬɟ
ɧ
ɟ
ɦ
ɵ
j
L
a
I
ɨ
ɣ
ɫ
ɢ
ɦ
K
I
ɞ
ɥ
ɬ
ɨ
ɦ
ɢ
ɛ
ɨ
ɟɠ
K
L
j
x
1
)
K
ɚ
L
ɩ
ɚ
ɪ
ɬ
ɫ
ɬ
ɫ
ɨ
ɟ
K
ɨ
ɤ
ɚ
ɷ
ɬ
ɪ
ɚ
ɣ
ɩ
ɢ
ɜ
ɚ
ɫ
ɹ
ɧ
ɨ
ɝ
G
,
ɵ
ɩ
ɚ
ɤ
ɬ
ɞ
ɚ
ɟ
ɦ
ɨ
ɣ
ɨ
ɫ
ɭ
ɜ
ɧ
ɟ
ɧ
ɰ
ɵ
:
(
jx
1
)
a
ɫ
ɯ
ɦɦ
1
K
ɚ
ɥ
ɹ
ɦ
x
ɨ
ɥ
ɶ
ɠ
ɞɟ
L
j
x
I
K
j
I
ɪ
ɚ
ɦ
ɬ
ɜ
ɭ
ɟ
ɞ
ɢ
ɢ
ɚ
ɦ
ɬ
ɨ
ɣ
ɫɱ
ɩ
ɨ
ɚ
ɟ
ɦ
ɤ
ɝ
ɨ
ɫ
ɜ
ɩ
ɪ
ɹ
ɬ
ɢ
ɜ
L
x
ɟ
ɬɫ
ɣ
ɩ
ɭɳ
ɟ
ɧ
ɢ
ɰ
ɢ
ɚ
K
x
j
ɯ
ɟ
ɦ
ɦ
ɟ
ɬ
ɩ
ɪ
L
x
ɶɲ
ɧ
ɢ
K
L
K
I
1
K
ɚ
j
x
ɦ
ɟ
ɬ
ɭɸ
ɢ
ɧ
ɟ
L
ɩ
ɣ
ɟɬ
ɫɥ
ɦ
ɨ
ɪ
ɚ
ɡ
ɚ
ɜ
ɹ
ɡ
ɹ
ɦ
ɜ
ɧ
ɨ
L
ɹ
ɩ
ɩ
ɨ
ɳ
ɟɫ
ɬ
ɢɣ
ɚ
ɥ
ɚ
K
(
jx
ɦɵ
ɬ
ɪ
ɢ
0
)
ɪ
ɨ
ɞ
L
ɫ
ɨ
ɲ
ɢ
ɣ
ɢ
ɹ
ɮ
1
LL
ɚ
I
1
L
I
ɬ
ɪ
ɵ
ɸ
ɳ
ɟ
ɧ
ɢ
L
ɞ
ɩ
ɪ
ɹ
ɫɯ
ɬ
ɨ
ɟɞ
ɝɨ
ɚ
ɫ
ɱ
ɚ
ɦ
ɵ
ɡ
ɚ
ɧ
ɨ
ɣ
ɨ
ɫ
ɬ
K
x
ɩ
ɪ
ɫɥ
ɬ
ɜ
ɥ
ɣ
(
8
ɚ
U
K
x
K
x
ɵ
ɪ
ɢ
ɢ.
.
ȼ
ɞ
ɨ
ɥ
ɨ
ɨ
ɬ
ɣ
ɢ
ɮɚ
2
0
1
(
L
a
L
a
L
I
ɵ
ɢɟ
ɢ
ɟ
ɞ
ɚ
ɟ
ɹ
ɦ
ɨ
ɟ
ɦ
ɨ
ɤ
ɨ
ɨɜ
ɜ
ɢ
ɱ
ɟ
ɬ
ɵɤ
ɧ
ɧ
ɨ
ɣ
ɩ
ɨ
ɬ
ɹ
ɦ
K
L
ɚɜ
ɢ
ɟɞ
ɨ
ɥ
ɟ
ɧ
8
.4
4
La
U
)
K
L
K
L
I
ɪ
ɚ
ɫ
Ɉ
ȼ
ɟ
ɬ
ɥ
ɶ
ɧ
ɬ
ɜ
ɟ
ɢ
ɧ
ɬ
ɚ
ɡ
ɵ
0
3
( j
1
1
a
L
ɚ
ɟɟ
ɭ
ɪ
ɤ
ɟ
ɬ
ɨ
ɣ
ɦ
ɵ
ɨ
ɜ
ɚ-
ɢ
-
ɬ
ɭ
ɤ
ɚ-
ɨ
ɣ
ɨ
-
ɦ
ɢ
.
ɢ
-
ɨ
-
ɧ
-
4
)
1
a
)
K
I
K
a
ɫ
ɫ
ɦ
Ɉ
ɬ
ɫ
ɬ
ɜ
ɶ
ɧ
ɨ
ɣ
ɟ
ɬ
ɫ
ɬ
ɟ
ɪ
ɵ
.
ȿ
K
jx
j
x
1
j
º
¼
ɷ
ɪ
ɚ
ɜ
ɢ
ɫ
1
K
ɚ
1
a
ɦ
ɨ
ɬ
ɫ
ɭ
ɬ
ɶ
L
ɣ
ɧ
ɫ
ɬ
ɜ
ɪ
ɟ
ɫ
ȿ
ɫ
ɥ
K
L
KL
x
K
x
º
¼
ɥɟ
ɜ
ɧ
ɟ
ɫ
ɯ
ɨ
1
x
ɬ
ɪ
ɢ
ɬ
ɫɬ
ɜ
1
L
c
–
ɧ
ɟ
ɫ
ɜ
ɭ
ɟ
ɫ
ɩ
ɪ
ɥ
ɢ
Ɋ
ɬ
)
LK
L
I
K
L
j
I
ɦ
ɟ
ɟ
ɧ
ɢ
ɨ
ɞ
ɧ
(
j
L
x I
ɢ
ɦ
ɜ
ɢ
–
F
ɫ
ɢ
ɦ
ɟ
ɬ
ɪ
ɪ
ɟ
ɞ
ɜ
ɫ
Ɋ
ɢ
ɬ
ɨ
ɤ
K
a
K
I
L
a
L
x
I
ɟ
ɧ
ɬ
ɢ
ɹ
ɧ
ɨ
ɣ
(
L
x
L
a
I
ɱ
ɸ
–
L
ɦɦ
ɪ
ɚ
ɡ
ɞ
ɫ
ɬ
ɫ
ɟ
ɩ
ɢ
ɫ.
8
ɤ
ɚ
ɦ
ɫ
ɬ
1
1
K
ɚ
1
a
L
ɬ
ɨ
ɜ
ɦ
ɣ
ɫ
L
1
)
a
ɱ
ɚɫ
ɬ
Ʉ
Ɂ
1
L
ɦ
ɟ
ɬ
ɡ
ɪ
ɵ
ɬ
ɚ
ɜ
ɩ
ɪ
8
.
1
ɦ
ɩ
ɬɢ
ɫ
jx
I
K
j
x
ɜ
,
(8
.
ɫ
ɯ
ɟ
K
x
ɬ
ɧ
Ɂ
ɫ
ɩ
ɪ
ɬ
ɪ
ɢ
ɵ
ɜ
ɜ
ɥ
ɹ
ɢ
ɜ
1
7.
ɩ
ɪ
ɹ
ɢ
ɞ
ɥ
ɫ
ɪ
K
L
x
I
K
K
L
j
x
ɩ
ɨ
.
4
5
ɟ
ɦ
ɟ
KL
K
U
ɵ
ɣ
ɫ
ɨ
ɨ
ɪ
ɟ
ɞ
ɢ
ɢ
ɭ
ɨ
ɹ
ɟ
ɬ
ɜ
ɟ
ɞ
ɋ
ɯ
ɹ
ɦ
ɨ
ɥ
ɹ
ɨ
ɪ
ɚɡ
ɪ
1
K
L
ɚ
I
K
L
I
I
ɨ
ɥ
ɨ
5
),
ɟ
ɩ
)
L
I
K
ɚ
ɣ
ɫ
ɨ
ɬ
ɜ
ɞ
ɫ
ɬ
(
x
ɨ
ɞ
ɧ
ɬ
ɬ
ɞ
ɟ
ɧ
ɯ
ɟ
ɦ
ɨ
ɣ
ɩ
ɨ
ɞ
ɧ
ɪɵ
;
K
ɚ
L
L
a
I
ɨ
ɠ
ɢ
(8
ɩ
ɪ
ɹ
L
a
1
ɫ
ɥ
ɭ
ɜ
ɟ
ɬ
ɬ
ɚ
ɜ
L
x
)
ɧ
ɨ
ɣ
ɬ
ɨ
ɤ
ɧ
ɧ
ɵ
ɦ
ɚ
ɷ
ɩ
ɨ
ɫ
ɧ
ɨ
ɮ
ɵ
ɜɨ
ɦ
1
ɚ
1
1
.
ɚ
a
ɢ
ɬ
.4
6
ɹ
ɦ
ɨ
1
a
ɭ
ɱ
ɚ
ɬ
ɫɬ
ɜ
ɥ
ɹ
)
,
ɜ
ɣ
ɮ
ɤ
ɤ
ɨ
ɵ
ɟ
ɷ
ɤ
ɜ
ɫ
ɥ
ɟ
ɮ
ɚ
ɦ
ɮ
ɟɥ
6
),
ɨ
ɣ
'
U
ɚ
ɣ
:
ɜ
ɭ
ɹ
ɟɬ
ɜ
ɤ
ɥ
ɮ
ɚ
ɡ
ɨ
ɪ
ɨ
ɗ
Ⱦ
ɜ
ɢ
ɜ
ɟ
ɞ
ɨ
ɡɧ
ɨ
ɮɚ
ɶ
ɧ
ɩ
ɪ
ɩ
ɨ
L
U
:
ɧ
ɭ
ɟɬ
ɞ
ɨ
ɥ
ɸ
ɡ
ɵ
ɨ
ɬ
ɤ
Ⱦɋ
ɜ
ɚ
ɥ
ɨ
ɜ
ɚ
ɨ
ɝ
ɨ
ɚ
ɡ
ɵ
(
(
ɧ
ɵ
ɟ
ɪ
ɢ
ɜ
ɨ
ɫ
ɥ
1
L
ɚ
ɧ
ɚ
ɥ
ɪ
ɚ
ɨ
ɩ
ɨ
ɱɟ
ɧ
.
ɤ
ɨ
ɝ
ɋ
ɢ
ɥ
ɟɧ
ɚ
ɬ
ɟ
ɨ
Ʉ
ɵ
(
8.
(
8.
ɟ
ɧ
ɜ
ɟ
ɞ
ɥ
ɟ
ɞ
.
ɥ
ɢ
ɱ
ɚ
ɡ
ɪ
ɨ
ɥ
ɧ
ɧɧ
ɝ
ɨ
ɢ
ɫɬ
ɬɧ
ɟ
ɥ
ɶ
Ʉ
Ɂ
+
45
4
6
ɧ
ɚ
-
ɞ
ɟ
-
ɞ
ɨ
-
ɱ
ɢ
ɟ
ɪ
ɵ
ɜ
ɧ
ɢ
ɧ
ɭ
ɸ
ɡ
ɚ
ɨ
ɱ
ɧ
ɚ
ɹ
ɶ
ɧɨ
+
)
6
)
-
-
-
ɟ
ɜ
ɢ
-
ɸ
ɚ
-
ɱ
-
ɹ
-
204
ɧɢɤɨɜ ɪɚɜɧɵ ɦɟɠɞɭ ɫɨɛɨɣ, ɚ ɬɚɤɠɟ ɪɚɜɧɵ ɪɟɚɤɬɚɧɫɵ (ɷɥɟɦɟɧɬɨɜ ɜ ɫɯɟ-
ɦɚɯ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ), ɬɨ ɬɨɤ
1
K
a
I
ɜ ɦɟɫɬɟ ɤɨ-
ɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɩɪɢ ɨɞɧɨɜɪɟɦɟɧɧɨɦ ɪɚɡɪɵɜɟ ɡɚɦɤɧɭɜɲɟɣ ɮɚɡɵ ɨɩ-
ɪɟɞɟɥɢɬɫɹ ɩɨ ɜɵɪɚɠɟɧɢɸ
1
1
Ka
L
jx x
D
E
I
, (8.47)
ɝɞɟ
1
10
2
x
xx
66
, ɚ
1
x
6
ɢ
0
x
6
– ɪɟɡɭɥɶɬɢɪɭɸɳɢɟ ɪɟɚɤɬɢɜɧɨɫɬɢ ɩɪɢ
ɨɞɧɨɮɚɡɧɨɦ ɤɨɪɨɬɤɨɦ ɡɚɦɵɤɚɧɢɢ ɜ ɬɨɱɤɟ K ɢ ɨɬɫɭɬɫɬɜɢɢ ɪɚɡɪɵɜɚ ɮɚɡɵ,
2
01
01
2
KL KL
LL
x
x
xx
D
§·
¨¸
©¹
,
10
10
2
LL
L
L
L
xx
x
x
x
,
12
L
L
x
x
ɢ
12
K
LKL
xx
.
Ɂɞɟɫɶ ɪɟɚɤɬɢɜɧɨɫɬɢ ɢɦɟɸɬ ɬɨɬ ɠɟ ɫɦɵɫɥ, ɱɬɨ ɢ ɜ ɜɵɪɚɠɟɧɢɹɯ (8.44).
Ɍɨɤ ɄɁ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɢɡɜɟɫɬɧɨɦɭ ɫɨɨɬɧɨɲɟɧɢɸ
1
3.
K
Kɚ
II
ɋɪɚɜɧɟɧɢɟ ɜɵɪɚɠɟɧɢɣ (8.47) ɢ (7.16) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɨɞɧɨɜɪɟɦɟɧ-
ɧɨɟ ɤɨɪɨɬɤɨɟ ɡɚɦɵɤɚɧɢɟ ɫ ɪɚɡɪɵɜɨɦ ɮɚɡɵ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɬɨɤɚ
ɄɁ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɥɭɱɚɹ ɨɬɫɭɬɫɬɜɢɹ ɪɚɡɪɵɜɚ.
Ⱦɥɹ ɦɧɨɝɨɤɪɚɬɧɨɣ ɧɟɫɢɦɦɟɬɪɢɢ, ɩɨɞɨɛɧɨ ɨɞɧɨɤɪɚɬɧɨɣ, ɬɚɤɠɟ
ɦɨɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɤɨɦɩɥɟɤɫɧɨɣ ɫɯɟɦɨɣ ɡɚɦɟɳɟɧɢɹ. Ɉɞɧɚɤɨ ɩɪɢ ɫɨ-
ɟɞɢɧɟɧɢɢ ɫɯɟɦ ɨɬɞɟɥɶɧɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɩɨ ɦɟɫɬɭ ɩɨɜɪɟɠɞɟɧɢɣ
ɢɦɟɸɬɫɹ ɨɫɨɛɟɧɧɨɫɬɢ. ɗɥɟɤɬɪɢɱɟɫɤɢ ɫɨɟɞɢɧɟɧɢɟ ɫɯɟɦ ɜɨɡɦɨɠɧɨ
ɥɢɲɶ
ɩɨ ɤɚɤɨɣ-ɥɢɛɨ ɨɞɧɨɣ ɬɨɱɤɟ ɧɟɫɢɦɦɟɬɪɢɢ, ɚ ɩɨ ɜɬɨɪɨɣ ɬɨɱɤɟ ɩɨɜɪɟɠɞɟ-
ɧɢɹ ɫɨɟɞɢɧɟɧɢɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɵ.
ɗɬɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ɞɨɥɠɧɵ ɢɦɟɬɶ ɧɢɱɬɨɠɧɨɟ ɪɚɫɫɟɹɧɢɟ ɢ ɨɱɟɧɶ
ɛɨɥɶɲɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. ɋ ɬɚɤɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ ɤ
ɬɪɚɧɫɮɨɪɦɚɬɨɪɚɦ ɫɜɹɡɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɨɦɩɥɟɤɫɧɵɯ ɫɯɟɦ ɜɨɡɦɨɠɧɨ ɧɚ
ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɬɟɯɧɢɤɟ.
Ʌɩɨɭɫɩɦɷɨɶɠ ɝɩɪɫɩɬɶ
1. Ƚɞɟ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɤɥɟɦɦɵ ɧɚɱɚɥɚ ɢ ɤɨɧɰɚ
ɫɯɟɦ ɡɚɦɟɳɟɧɢɹ
ɪɚɡɥɢɱɧɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɩɪɢ ɩɪɨɞɨɥɶɧɨɣ ɧɟɫɢɦɦɟɬɪɢɢ?
2. ȼ ɱɟɦ ɨɫɨɛɟɧɧɨɫɬɶ ɪɚɫɱɟɬɚ ɪɟɡɭɥɶɬɢɪɭɸɳɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ
ɫɯɟɦ ɡɚɦɟɳɟɧɢɹ ɩɪɹɦɨɣ, ɨɛɪɚɬɧɨɣ ɢ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɩɪɢ
ɩɪɨɞɨɥɶɧɨɣ ɧɟɫɢɦɦɟɬɪɢɢ?
3. ȼ ɱɟɦ ɡɚɤɥɸɱɚɟɬɫɹ ɨɬɥɢɱɢɟ ɨɩɪɟɞɟɥɟɧɢɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɗȾɋ
ɜ ɩɪɨɞɨɥɶɧɨɣ ɧɟɫɢɦɦɟɬɪɢɢ ɨɬ ɩɨɩɟɪɟɱɧɨɣ?
4. ɑɬɨ ɩɨɧɢɦɚɟɬɫɹ ɩɨɞ ɬɟɪɦɢɧɨɦ «ɫɥɨɠɧɵɟ ɜɢɞɵ ɧɟɫɢɦɦɟɬɪɢɢ»?
205
Ⱦɦɛɝɛ 9
ɂȻɇɖɅȻɈɃɚ Ƚ Ɍɀɍɚɐ Ɍ ɃɂɉɆɃɋɉȽȻɈɈɉɄ ɈɀɄɍɋȻɆɗə
Ƀ ɘɆɀɅɍɋɉɎɌɍȻɈɉȽɅȻɐ ȿɉ 1 ɅȽ
9.1. ɉɜɴɣɠ ɢɛɧɠɲɛɨɣɺ
ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɫɟɬɢ ɧɚɩɪɹɠɟɧɢɟɦ 6…35 ɤȼ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ
ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɦɢ, ɩɨɫɤɨɥɶɤɭ ɩɨ ɧɢɦ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɷɥɟɤɬɪɨɫɧɚɛ-
ɠɟɧɢɟ ɛɨɥɶɲɢɧɫɬɜɚ ɩɨɬɪɟɛɢɬɟɥɟɣ. ɇɚɞɟɠɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ ɫɟ-
ɬɟɣ ɫɭɳɟɫɬɜɟɧɧɨ ɧɢɠɟ, ɱɟɦ ɫɟɬɟɣ ɛɨɥɟɟ ɜɵɫɨɤɨɝɨ ɤɥɚɫɫɚ ɧɚɩɪɹɠɟɧɢɣ.
ɇɚ ɞɨɥɸ ɩɟɪɜɵɯ ɩɪɢɯɨɞɢɬɫɹ 70…75 % ɨɛɳɟɝɨ ɱɢɫɥɚ ɩɨɜɪɟɠɞɟɧɢɣ ɜ
ɷɧɟɪɝɨɫɢɫɬɟɦɚɯ.
ɉɪɢ ɚɧɚɥɢɡɟ ɪɟɠɢɦɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ
ɪɹɞ ɯɚɪɚɤɬɟɪɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ, ɩɪɢɫɭɳɢɯ
ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɦ ɫɟɬɹɦ.
1. ɋɟɬɢ 6…35 ɤȼ ɭɞɚɥɟɧɵ ɨɬ ɫɢɫɬɟɦɧɵɯ ɝɟɧɟɪɢɪɭɸɳɢɯ ɢɫɬɨɱɧɢ-
ɤɨɜ ɞɜɭɦɹ–ɬɪɟɦɹ ɫɬɭɩɟɧɹɦɢ ɬɪɚɧɫɮɨɪɦɚɰɢɢ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɩɟɪɟɯɨɞ-
ɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɭɤɚɡɚɧɧɵɯ ɫɟɬɹɯ ɫɥɚɛɨ ɜɥɢɹɸɬ ɧɚ ɪɟɠɢɦɵ ɝɟɧɟɪɚɬɨɪɨɜ
ɢ ɫɢɫɬɟɦɨɨɛɪɚɡɭɸɳɢɯ ɫɟɬɟɣ. ɉɨɷɬɨɦɭ ɩɪɢ ɄɁ ɜ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ ɫɟ-
ɬɹɯ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɜɵɫɲɟɣ ɫɬɨɪɨɧɟ ɩɢɬɚɸɳɟɝɨ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ
ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɵɦ. Ɇɟɫɬɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ
ɫɬɚɧɰɢɢ, ɤɪɭɩ-
ɧɵɟ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɢ ɫɢɧɯɪɨɧɧɵɟ ɤɨɦɩɟɧɫɚɬɨɪɵ, ɧɚɯɨɞɹɳɢɟɫɹ ɜ ɪɚɫ-
ɩɪɟɞɟɥɢɬɟɥɶɧɨɣ ɫɟɬɢ, ɭɱɢɬɵɜɚɸɬɫɹ ɢɧɞɢɜɢɞɭɚɥɶɧɨ.
2. ȼ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ ɫɟɬɹɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜɨɡɞɭɲɧɵɟ ɢ ɤɚɛɟɥɶ-
ɧɵɟ ɥɢɧɢɢ ɫɪɚɜɧɢɬɟɥɶɧɨ ɦɚɥɵɯ ɫɟɱɟɧɢɣ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɧɟɨɛɯɨɞɢɦɨ-
ɫɬɢ ɭɱɟɬɚ ɚɤɬɢɜɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɪɢ ɪɚɫɱɟɬɟ ɪɟɠɢɦɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚ-
ɦɵɤɚɧɢɹ.
3. Ɋɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɟ ɫɟɬɢ 6…35 ɤȼ ɢɦɟɸɬ ɢɡɨɥɢɪɨɜɚɧɧɭɸ ɢɥɢ
ɤɨɦɩɟɧɫɢɪɨɜɚɧɧɭɸ ɧɟɣɬɪɚɥɶ (ɡɚɡɟɦɥɟɧɢɟ
ɧɟɣɬɪɚɥɢ ɱɟɪɟɡ ɛɨɥɶɲɨɟ ɢɧ-
ɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ). ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ, ɩɪɢ ɨɞɧɨɮɚɡɧɨɦ ɡɚɦɵɤɚ-
ɧɢɢ ɧɚ ɡɟɦɥɸ, ɬɨɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɟɦɤɨɫɬɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ ɡɞɨɪɨɜɵɯ
ɮɚɡ ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɟɦɥɢ. Ɉɧ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɬɨɤɚ ɨɞɧɨɮɚɡɧɨɝɨ ɄɁ ɜ
ɫɟɬɢ ɫ ɝɥɭɯɨɡɚɡɟɦɥɟɧɧɨɣ ɧɟɣɬɪɚɥɶɸ. ɉɨɷɬɨɦɭ ɫɟɬɢ ɫ ɢɡɨɥɢɪɨɜɚɧɧɨɣ
ɧɟɣɬɪɚɥɶɸ ɦɨɝɭɬ ɞɥɢɬɟɥɶɧɨ ɪɚɛɨɬɚɬɶ ɜ ɪɟɠɢɦɟ ɨɞɧɨɮɚɡɧɨɝɨ ɄɁ. ɗɬɨ
ɩɨɡɜɨɥɹɟɬ ɨɛɫɥɭɠɢɜɚɸɳɟɦɭ ɩɟɪɫɨɧɚɥɭ
ɫɨɡɞɚɜɚɬɶ ɜɪɟɦɟɧɧɵɟ ɫɯɟɦɵ
ɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɹ ɩɨɬɪɟɛɢɬɟɥɟɣ ɛɟɡ ɢɯ ɨɬɤɥɸɱɟɧɢɹ.
4. ɉɪɢ ɞɥɢɬɟɥɶɧɵɯ ɪɟɠɢɦɚɯ ɄɁ (t = 0,4…0,6 ɫ) ɜɫɥɟɞɫɬɜɢɟ ɩɨɜɵ-
ɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɨɜɨɞɧɢɤɚ ɩɪɨɢɫɯɨɞɢɬ ɭɜɟɥɢɱɟɧɢɟ ɟɝɨ ɚɤɬɢɜɧɨɝɨ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ. ɗɬɨ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɦɨɠɟɬ ɜɵɡɜɚɬɶ ɡɚɦɟɬɧɨɟ ɫɧɢɠɟɧɢɟ
ɬɨɤɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɢ ɧɚɡɵɜɚɟɬɫɹ ɷɮɮɟɤɬɨɦ ɬɟɩɥɨɜɨɝɨ ɫɩɚɞɚ ɬɨ-
ɤɚ ɄɁ. ɍɱɟɬ ɷɬɨɝɨ ɮɚɤɬɨɪɚ ɢɡɥɨɠɟɧ
ɜ [1, 12, 14].
5. ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɭɫ
ɬ
ɥɟɧɧɨɫɬɶ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɫ
ɜɵɫɲɟɣ ɫɬɨɪɨɧɟ ɬɪɚɧɫ
ɮ
Ʉɪɨɦɟ ɬɨɝɨ, ɡɞɟɫɶ ɧɟɨɛɯ
ɨ
ɫɤɢɟ ɨɫɨɛɟɧɧɨɫɬɢ (ɩɟɪɟɯɨ
ɞ
ɟɞɢɧɟɧɢɣ ɷɥɟɦɟɧɬɨɜ ɫɯɟɦ
ɵ
ɧɢɠɟ.
9.2. ɉȿɈɉɏȻɂɈ
ɉ
Ɍ Ƀɂɉ
Ɇ
Ɂɚɦɵɤɚɧɢɟ ɮɚɡɵ ɧɚ
ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɩɪɨɫ
ɬ
ɬɪɟɯɮɚɡɧɭɸ ɫɟɬɶ, ɜ ɤɨɬɨ
ɪ
(ɪɢɫ. 9.1). ȿɦɤɨɫɬɢ, ɪɚɫɩɪ
ɟ
ɬɟɥɶɧɨ ɡɟɦɥɢ, ɩɪɟɞɫɬɚɜɥɟ
ɧ
C
C
). Ɇɟɠɮɚɡɧɵɟ ɟɦɤɨɫɬɢ
ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɢ ɧɚ
ɪ
Ɋɢɫ. 9.1. Ɋɚɫɩɪɟɞɟɥɟɧɢ
ȿɦɤɨɫɬɧɚɹ ɩɪɨɜɨɞɢ
ɦ
ɪ
ɨɬɤɢɦ ɡɚɦɵɤɚɧɢɟɦ; ɩɪɢ
ɥ
ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɬɨɤ ɱɟɪɟɡ
ɭ
ɫɥɨɜɥɟɧ ɫɭɦɦɨɣ ɟɦɤɨɫɬɧɵ
ɯ
ɧɨ ɧɚ ɪɢɫ. 9.1.
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ
ɞ
ɞɥɹ ɨɞɧɨɮɚɡɧɨɝɨ ɄɁ ɜ ɫɟɬ
ɹ
206
ɬ
ɚɧɨɜɤɢ ɞɨ 1000 ȼ ɢɦɟɸɬ ɟɳɟ ɛɨɥɶ
ɲ
ɩɨɥɧɵɦ ɨɫɧɨɜɚɧɢɟɦ ɫɱɢɬɚɬɶ ɧɚɩɪɹ
ɠ
ɮ
ɨɪɦɚ, ɩɢɬɚɸɳɟɝɨ ɷɬɭ ɫɟɬɶ, ɩɨɫ
ɬ
ɨ
ɞɢɦɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɭɱɢɬɵɜɚɬɶ ɫɩ
ɟ
ɞ
ɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɦɟɫɬɚɯ ɤɨɧɬɚɤ
ɬ
ɵ
, ɜ ɦɟɫɬɟ ɄɁ ɢ ɞɪ.), ɤɨɬɨɪɵɟ ɪɚɫɫɦɚɬ
ɪ
ɉ
ɀ ɂȻɇɖɅȻɈɃɀ ɈȻ ɂɀɇɆə Ƚ ɌɀɍɃ
Ɇ
ɃɋɉȽȻɈɈɉɄ ɈɀɄɍɋȻɆɗə
ɡɟɦɥɸ ɜ ɫɟɬɢ ɫ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɧɟ
ɣ
ɬ
ɵɦ ɡɚɦɵɤɚɧɢɟɦ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨ
ɫ
ɪ
ɨɣ ɩɪɨɢɡɨɲɥɨ ɩɪɨɫɬɨɟ ɡɚɦɵɤɚɧɢɟ
ɟ
ɞɟɥɟɧɧɵɟ ɜɞɨɥɶ ɥɢɧɢɢ ɤɚɠɞɨɣ ɮɚɡɵ
ɧ
ɵ ɞɥɹ ɩɪɨɫɬɨɬɵ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɦɢ
(
ɧɟ ɨɤɚɡɵɜɚɸɬ ɨɳɭɬɢɦɨɝɨ ɜɥɢɹɧɢɹ ɧ
ɪ
ɢɫ. 9.1 ɧɟ ɨɬɪɚɠɟɧɵ.
ɟ ɬɨɤɨɜ ɩɪɢ ɩɪɨɫɬɨɦ ɡɚɦɵɤɚɧɢɢ ɧɚ ɡɟɦ
ɥ
ɦ
ɨɫɬɶ ɩɨɜɪɟɠɞɟɧɧɨɣ ɮɚɡɵ ɡɚɲɭɧɬɢɪɨ
ɥ
ɨɠɟɧɧɨɟ ɤ
A
C
ɧɚɩɪɹɠɟɧɢɟ ɪɚɜɧɨ
ɧ
ɭ
ɤɚɡɚɧɧɭɸ ɟɦɤɨɫɬɶ ɧɟ ɩɪɨɬɟɤɚɟɬ. Ɍɨɤ
ɯ
ɬɨɤɨɜ ɮɚɡ ȼ ɢ ɋ, ɢ ɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢ
ɟ
ɞ
ɥɹ ɩɪɨɫɬɨɝɨ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ ɬɟ
ɠ
ɹ
ɯ ɫ ɡɚɡɟɦɥɟɧɧɨɣ ɧɟɣɬɪɚɥɶɸ, ɩɨɷɬɨɦ
ɭ
ɲ
ɭɸ ɭɞɚ-
ɠ
ɟɧɢɟ ɧɚ
ɬ
ɨɹɧɧɵɦ.
ɟ
ɰɢɮɢɱɟ-
ɬ
ɧɵɯ ɫɨ-
ɪ
ɢɜɚɸɬɫɹ
ɣɬɪɚɥɶɸ
ɫ
ɬɟɣɲɭɸ
ɮɚɡɵ Ⱥ
ɨɬɧɨɫɢ-
(
A
C
,
B
C
,
ɚ ɪɟɠɢɦ
ɥ
ɸ
ɜɚɧɚ
ɤ
ɨ-
ɧ
ɭɥɸ, ɢ,
ɄɁ ɨɛɭ-
ɟ
ɩɨɤɚɡɚ-
ɠ
ɟ, ɱɬɨ ɢ
ɭ
ɪɚɫɱɟɬ-
ɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɩɨɥɭɱɟɧɧ
ɵ
ɫɦɚɬɪɢɜɚɟɦɵɯ ɭɫɥɨɜɢɣ ɫ ɭ
ɱ
x ɟɦɤɨɫɬɧɵɟ ɫɨɩɪɨ
ɬ
ɳɟɫɬɜɟɧɧɨ ɩɪɟɜɵɲɚɸɬ ɚɤ
ɬ
ɬɨɜ ɫɯɟɦɵ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ
ɩ
x ɩɨɫɤɨɥɶɤɭ ɬɨɤɢ
Ʉ
ɬɨɱɧɢɤɚ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧ
ɧ
Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɪɚɫ
ɱ
ɫɯɟɦɟ (ɪɢɫ. 9.2, ɚ) ɢ ɤɨɦɩ
ɥ
ɩɨɦɢɦɨ ɟɦɤɨɫɬɧɨɝɨ ɫɨɩɪ
ɨ
ɜɜɟɞɟɧɨ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩ
ɪ
ɜɫɟɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ,
ɧɢɹ ɧɟɡɧɚɱɢɬɟɥɶɧɵ ɢ ɩɪɢɧ
ɢ
Ɋɢɫ. 9.2.
ɉ
ɪɨɫɬɨɟ ɡɚɦ
ɛ – ɤɨ
ɦ
207
ɵ
ɟ ɪɚɧɟɟ ɜ ɪɚɡɞ. 7.3, ɫɩɪɚɜɟɞɥɢɜɵ ɢ
ɱ
ɟɬɨɦ ɪɹɞɚ ɨɫɨɛɟɧɧɨɫɬɟɣ:
ɬ
ɢɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɯ ɢ ɤɚɛɟɥɶɧɵɯ ɥ
ɢ
ɬ
ɢɜɧɵɟ ɢ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ
ɩ
ɨɫɥɟɞɧɢɦɢ ɩɪɟɧɟɛɪɟɱɶ;
Ʉ
Ɂ ɦɚɥɵ, ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚɩɪɹɠ
ɟ
ɧ
ɵɦ.
ɱ
ɟɬɧɵɯ ɜɵɪɚɠɟɧɢɣ ɨɛɪɚɬɢɦɫɹ ɤ ɩɪɨ
ɥ
ɟɤɫɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ (ɪɢɫ. 9.2,
ɛ
ɨ
ɬɢɜɥɟɧɢɹ ɜɨɡɞɭɲɧɨɣ ɥɢɧɢɢ, ɫɢɦɜ
ɨ
ɪ
ɨɬɢɜɥɟɧɢɟ ɷɬɨɣ ȼɅ ɢ ɬɪɚɧɫɮɨɪɦɚ
ɬ
ɯɨɬɹ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɷɬɢ ɫɨɩ
ɪ
ɢ
ɦɚɸɬɫɹ ɪɚɜɧɵɦɢ ɧɭɥɸ.
ɵɤɚɧɢɟ ɧɚ ɡɟɦɥɸ
: ɚ – ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟ
ɦ
ɦ
ɩɥɟɤɫɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ
ɞɥɹ ɪɚɫ-
ɢ
ɧɢɣ ɫɭ-
ɹ
ɷɥɟɦɟɧ-
ɟ
ɧɢɟ ɢɫ-
ɫɬɟɣɲɟɣ
ɛ
). Ɂɞɟɫɶ,
ɨ
ɥɢɱɟɫɤɢ
ɬ
ɨɪɚ ɞɥɹ
ɪ
ɨɬɢɜɥɟ-
ɦ
ɚ;
208
ɉɨɫɤɨɥɶɤɭ ɜ ɫɯɟɦɚɯ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɟɦ-
ɤɨɫɬɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ȼɅ (
1ɋ
x
,
2ɋ
x
) ɡɚɲɭɧɬɢɪɨɜɚɧɵ ɦɚɥɵɦɢ ɫɨɩɪɨ-
ɬɢɜɥɟɧɢɹɦɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ (
Ɍ 1 Ɍ 2
0xx |
), ɬɨ ɷɬɨ ɩɨɡɜɨɥɹɟɬ ɩɪɢɧɹɬɶ
12
0xx
66
. ɋɱɢɬɚɹ ɪɟɚɤɬɨɪ ɜ ɧɟɣɬɪɚɥɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɨɬɫɭɬɫɬɜɭɸ-
ɳɢɦ (ɩɨɤɚɡɚɧ ɩɭɧɤɬɢɪɨɦ), ɢɦɟɟɦ
00ɋ
xx
66
.
ɉɪɢ ɩɪɢɧɹɬɵɯ ɭɫɥɨɜɢɹɯ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (7.16) ɢ
(7.17), ɬɨɤ ɩɪɢ ɦɟɬɚɥɥɢɱɟɫɤɨɦ ɡɚɦɵɤɚɧɢɢ ɧɚ ɡɟɦɥɸ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ
ɜɵɪɚɠɟɧɢɟɦ
ɮ.ɫɪ
ɡɮ.ɫɪ 0
0Ȉ
3
3
C
j
C
jx
Z
6
U
IU
, (9.1)
ɝɞɟ
ɋ0
x
6
– ɪɟɡɭɥɶɬɢɪɭɸɳɟɟ ɟɦɤɨɫɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɧɭɥɟɜɨɣ ɩɨɫɥɟ-
ɞɨɜɚɬɟɥɶɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɢ ɤɚɛɟɥɶɧɵɯ ɥɢɧɢɣ, ɷɥɟɤɬɪɢɱɟɫɤɢ ɫɜɹɡɚɧɧɵɯ
ɫ ɬɨɱɤɨɣ ɡɚɦɵɤɚɧɢɹ;
ɮ.ɫɪ
U
– ɫɪɟɞɧɟɟ ɮɚɡɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɬɭɩɟɧɢ ɄɁ.
Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ (9.1), ɬɨɤ ɩɪɨɫɬɨɝɨ ɡɚɦɵɤɚɧɢɹ ɪɚɜɟɧ ɭɬɪɨɟɧɧɨɣ ɜɟ-
ɥɢɱɢɧɟ ɟɦɤɨɫɬɧɨɝɨ ɬɨɤɚ ɨɞɧɨɣ ɮɚɡɵ ɜ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ. ɉɨɷɬɨɦɭ
ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɟ ɫɟɬɢ 6…35 ɤȼ ɧɚɡɵɜɚɸɬɫɹ ɫɟɬɹɦɢ ɫ ɦɚɥɵɦɢ ɬɨɤɚɦɢ
ɡɚɦɵɤɚɧɢɹ.
ȼ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɚɯ ɜɨɡɦɨɠɧɚ ɝɪɭɛɚɹ ɨɰɟɧɤɚ ɜɟɥɢɱɢɧɵ ɬɨɤɚ
ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ ɩɨ ɜɵɪɚɠɟɧɢɸ
ɮ.ɫɪ ɫɪ.ɧɨɦ
ɡ
3UU
ILL
NN
(Ⱥ),
ɝɞɟ
ɫɪ.ɧɨɦ
U
– ɫɪɟɞɧɟɟ ɧɨɦɢɧɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɬɭɩɟɧɢ ɄɁ, ɤȼ; N –
ɤɨɷɮɮɢɰɢɟɧɬ, ɩɪɢɧɢɦɚɟɦɵɣ ɞɥɹ ɜɨɡɞɭɲɧɵɯ ɥɢɧɢɣ ɪɚɜɧɵɦ 350, 10 – ɞɥɹ
ɤɚɛɟɥɶɧɵɯ; L – ɫɭɦɦɚɪɧɚɹ ɞɥɢɧɚ ɜɨɡɞɭɲɧɵɯ ɢɥɢ ɤɚɛɟɥɶɧɵɯ ɥɢɧɢɣ,
ɷɥɟɤɬɪɢɱɟɫɤɢ ɫɜɹɡɚɧɧɵɯ ɫ ɬɨɱɤɨɣ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ, ɤɦ.
Ɉɬɦɟɬɢɦ, ɱɬɨ ɜɟɥɢɱɢɧɚ ɬɨɤɚ ɡɚɦɵɤɚɧɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ
ɦɟɫɬɚ ɡɚɦɵɤɚɧɢɹ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɭɦɦɚɪɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ (ɞɥɢɧɨɣ)
ɥɢɧɢɣ, ɷɥɟɤɬɪɢɱɟɫɤɢ
ɫɜɹɡɚɧɧɵɯ ɫ ɬɨɱɤɨɣ ɡɚɦɵɤɚɧɢɹ.
Ⱦɥɹ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ
ɩɪɢɧɹɬɵɦɢ ɞɨɩɭɳɟɧɢɹɦɢ, ɢɦɟɟɦ:
111ɮKa Ka
jx
66
U ȿ IU
; (9.2)
222
00
K
aKa
jx
6
#UI
; (9.3)
0Ȉ
000 ɮɮ
0Ȉ
0
C
KK
C
jx
jx
jx
6
UI UU. (9.4)
ɇɚ ɪɢɫ. 9.3 ɩɪɢɜɟɞɟ
ɧ
ɜ ɦɟɫɬɟ ɩɪɨɫɬɨɝɨ ɡɚɦɵɤɚɧ
ɢ
ɪ
ɚɧɟɟ ɩɪɢɧɹɬɵɯ ɞɨɩɭɳɟɧɢ
ɣ
1Ka
U
U
ȼɟɤɬɨɪɵ
1a
U
,
1b
U
,
U
ɠɟɧɢɣ ɧɨɪɦɚɥɶɧɨɝɨ ɪɟɠɢ
ɜɟɤɬɨɪɨɦ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞ
ɨ
ɫɥɟɞɭɟɬ ɢɡ ɞɢɚɝɪɚɦɦɵ, ɜ
ɪ
ɧɵɯ ɮɚɡ ȼ ɢ ɋ ɭɜɟɥɢɱɢɜɚ
ɸ
ɧɚɩɪɹɠɟɧɢɹ. ɉɪɢ ɷɬɨɦ «ɬ
ɪ
ɛɟɡ ɢɡɦɟɧɟɧɢɣ, ɤɚɤ ɢ ɜ ɧɨ
ɪ
ɫɬɜɢɢ ɫ ɩɟɪɟɦɟɳɟɧɢɟɦ ɰɟ
ɧ
ɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟɦ ɧɭɥɟɜɨ
ɣ
ɫɬɢ «ɬɪɟɭɝɨɥɶɧɢɤɚ» ɥɢɧɟɣ
ɧ
ɩɥɭɚɬɚɰɢɨɧɧɵɣ ɪɟɠɢɦ ɩɪ
ɢ
Ɋɢɫ. 9.3. ȼɟɤɬɨɪɧɵɟ
ɩɪɨɫ
ɬ
ȿɦɤɨɫɬɧɵɟ ɬɨɤɢ ɡɞɨ
ɪ
(ɪɢɫ. 9.3) ɢ ɩɨ ɦɨɞɭɥɸ ɨɩɪ
ɟ
B
I
Ɍɨɤ ɡɟɦɥɢ ɩɪɟɞɫɬɚɜ
ɥ
ɟɬ ɜɵɪɚɠɟɧɢɸ (9.1).
209
ɧ
ɵ ɜɟɤɬɨɪɧɵɟ ɞɢɚɝɪɚɦɦɵ ɧɚɩɪɹɠɟɧɢ
ɣ
ɢ
ɹ ɧɚ ɡɟɦɥɸ ɮɚɡɵ Ⱥ. Ɉɧɢ ɩɨɫɬɪɨɟɧɵ
c
ɣ
, ɩɪɢ ɤɨɬɨɪɵɯ
ɮ
U
,
2
0
Ka
#U
,
0 ɮK
UU
.
1c
U
ɨɛɪɚɡɭɸɬ ɫɢɦɦɟɬɪɢɱɧɭɸ «ɡɜɟɡɞɭ
»
ɦɚ. Ƚɟɨɦɟɬɪɢɱɟɫɤɚɹ ɫɭɦɦɚ ɷɬɢɯ ɜɟ
ɤ
ɨ
ɜɚɬɟɥɶɧɨɫɬɢ ɞɚɟɬ ɮɚɡɧɵɟ ɧɚɩɪɹɠɟ
ɧ
ɪ
ɟɠɢɦɟ ɄɁ ɮɚɡɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɧɟɩɨ
ɜ
ɸ
ɬɫɹ ɜ
3
ɪɚɡ, ɩɪɢɧɢɦɚɹ ɡɧɚɱɟɧɢɟ ɦɟ
ɠ
ɪ
ɟɭɝɨɥɶɧɢɤ» ɥɢɧɟɣɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
ɪ
ɦɚɥɶɧɨɦ ɪɟɠɢɦɟ, ɢ ɩɟɪɟɦɟɳɚɟɬɫɹ ɜ
ɧ
ɬɪɚ ɬɹɠɟɫɬɢ, ɩɨɥɨɠɟɧɢɟ ɤɨɬɨɪɨɝɨ ɨ
ɩ
ɣ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ. Ȼɥɚɝɨɞɚɪɹ ɧɟ
ɢ
ɧ
ɵɯ ɧɚɩɪ
ɹ
ɠɟɧɢɣ ɢ ɜɨɡɦɨɠɟɧ ɞɥɢɬɟɥɶ
ɧ
ɢ
ɩɪɨɫɬɨɦ ɡɚɦɵɤɚɧɢɢ.
ɞɢɚɝɪɚɦɦɵ ɧɚɩɪɹɠɟɧɢɣ ɢ ɬɨɤɨɜ ɜ ɦɟɫɬ
ɟ
ɬ
ɨɝɨ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ
ɪ
ɨɜɵɯ ɮɚɡ ɨɩɟɪɟɠɚɸɬ ɢɯ ɧɚɩɪɹɠɟɧɢɹ
ɧ
ɟ
ɞɟɥɹɸɬɫɹ ɬɚɤ:
ɮ 0
3
B
C
IUɋ
Z
6
.
ɥ
ɹɟɬ ɢɯ ɝɟɨɦɟɬɪɢɱɟɫɤɭɸ ɫɭɦɦɭ ɢ ɫɨɨ
ɬ
ɣ
ɢ ɬɨɤɨɜ
c
ɭɱɟɬɨɦ
» ɧɚɩɪɹ-
ɤ
ɬɨɪɨɜ ɫ
ɧ
ɢɹ. Ʉɚɤ
ɜ
ɪɟɠɞɟɧ-
ɠ
ɮɚɡɧɨɝɨ
ɨɫɬɚɟɬɫɹ
ɫɨɨɬɜɟɬ-
ɩ
ɪɟɞɟɥɹ-
ɢ
ɡɦɟɧɧɨ-
ɧ
ɵɣ ɷɤɫ-
ɟ
ɧ
ɚ
90
D
ɬ
ɜɟɬɫɬɜɭ-
9.3. Ʌɩɧɪɠɨɬɛɱɣɺ
ɉɪɢ ɧɟɛɨɥɶɲɨɣ ɩɪ
ɨ
ɬɨɤ ɡɚɦɵɤɚɧɢɹ ɮɚɡɵ ɧɚ ɡ
ɟ
ɚɦɩɟɪ. Ⱦɭɝɚ ɩɪɢ ɷɬɢɯ ɭɫɥ
ɨ
ɦɨɫɬɨɹɬɟɥɶɧɨ. ɍɜɟɥɢɱɟɧɢ
ɟ
ɤ ɪɨɫɬɭ ɬɨɤɚ ɡɚɦɵɤɚɧɢɹ ɧ
ɚ
ɬɚɤɢɯ ɬɨɤɚɯ ɦɨɠɟɬ ɝɨɪɟɬ
ɶ
ɩɪɟɜɪɚɳɚɹ ɨɞɧɨɮɚɡɧɨɟ ɡɚ
ɦ
ɥɢɤɜɢɞɚɰɢɹ ɞɭɝɢ ɞɨɫɬɢɝɚɟ
ɬ
ɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ ɩɨɫɪɟ
ɞ
ɱɟɪɟɡ ɢɧɞɭɤɬɢɜɧɭɸ ɤɚɬɭ
ɲ
ȼɟɥɢɱɢɧɚ ɢɧɞɭɤɬɢɜɧɨɫɬɢ
ɬ
ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫ
ɬ
ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɩɨɥɧɨɦɭ
ɢ
ɧɟɛɪɟɝɚɹ ɢɧɞɭɤɬɢɜɧɵɦɢ ɫ
ɨ
ɯɨɞɢɦ, ɱɬɨ
ɪ
ɟɡɨɧɚɧɫ ɧɚɫɬɭ
ɩ
ɬɨɤ ɨɞɧɨɮɚɡɧɨɝɨ ɡɚɦɵɤɚɧ
ɢ
ɬɨɱɧɨ ɞɥɹ ɩɨɝɚɲɟɧɢɹ ɞɭɝɢ
ȼ ɧɨɪɦɚɥɶɧɨɦ ɪɟɠ
ɢ
ɢɦɟɟɬɫɹ ɧɟɛɨɥɶɲɨɟ ɫɦɟɳɟ
ɧ
ɱɟɧ ɨɬ ɧɭɥɹ. ɗɬɨ ɫɦɟɳɟɧɢ
ɟ
ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɩɚɫɧɨɫɬ
ɢ
ɧɟɣɬɪɚɥɶ ɟɟ ɩɨɬɟɧɰɢɚɥ ɦɨ
ɠ
ɷɬɨɝɨ ɮɚɤɬɨɪɚ ɨɛɪɚɬɢɦɫɹ
ɤ
ɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɤɨɬɨɪɨɣ
Ɋɢɫ. 9.4.
Ʉ
ɨɩɪɟɞɟɥɟɧ
ɢ
ɫɯɟɦɚ ɡɚɦɟɳɟɧɢ
ɹ
210
ɠɧɥɩɬɭɨɩɞɩ ɭɩɥɛ ɪɫɩɬɭɩɞɩ ɢɛɧɶɥɛɨɣɺ
ɨ
ɬɹɠɟɧɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɢ ɤɚɛɟɥɶɧɵ
ɯ
ɟ
ɦɥɸ ɜ ɫɟɬɹɯ 3…20 ɤȼ ɫɨɫɬɚɜɥɹɟɬ ɧ
ɟ
ɨ
ɜɢɹɯ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɣ ɢ ɝ
ɚ
ɟ
ɧɚɩɪɹɠɟɧɢɹ ɢ ɩɪɨɬɹɠɟɧɧɨɫɬɢ ɫɟɬɢ
ɩ
ɚ
ɡɟɦɥɸ ɞɨ ɞɟɫɹɬɤɨɜ ɢ ɫɨɬɟɧ ɚɦɩɟɪ.
Ⱦ
ɶ
ɞɥɢɬɟɥɶɧɨ ɢ ɩɟɪɟɯɨɞɢɬɶ ɧɚ ɫɨɫɟɞɧ
ɢ
ɦ
ɵɤɚɧɢɟ ɜ ɞɜɭɯ- ɢɥɢ ɬɪɟɯɮɚɡɧɨɟ.
ɇ
ɬ
ɫɹ ɡɚ ɫɱɟɬ ɤɨɦɩɟɧɫɚɰɢɢ ɟɦɤɨɫɬɧɨɝɨ
ɞ
ɫɬɜɨɦ ɡɚɡɟɦɥɟɧɢɹ ɧɟɣɬɪɚɥɢ ɬɪɚɧɫɮ
ɨ
ɲ
ɤɭ (ɩɨɤɚɡɚɧɚ ɩɭɧɤɬɢɪɨɦ ɧɚ ɫɯɟɦɟ
ɪ
ɬ
ɚɤɨɣ ɤɚɬɭɲɤɢ ɜɵɛɢɪɚɟɬɫɹ ɬɚɤ, ɱɬɨɛ
ɵ
ɬ
ɢ ɜɨɡɧɢɤ ɪɟɡɨɧɚɧɫ ɬɨɤɨɜ. ɉɪɢ ɷɬɨɦ
x
ɢ
ɫɱɟɡɧɨɜɟɧɢɸ ɬɨɤɚ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦ
ɥ
ɨ
ɩɪɨɬɢɜɥɟɧɢɹɦɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɢ ɥ
ɢ
ɩ
ɚɟɬ ɩɪɢ
Ɋ C0Ȉ
3xx
. Ȼɥɚɝɨɞɚɪɹ ɪɟɚɤ
ɬ
ɢ
ɹ ɫɧɢɠɚɟɬɫɹ ɜ ɞɟɫɹɬɤɢ ɪɚɡ, ɱɬɨ ɜɩɨɥ
ɧ
ɜ ɦɟɫɬɟ ɡɚɦɵɤɚɧɢɹ.
ɢ
ɦɟ ɫɟɬɢ ɢɡ-ɡɚ ɧɟɫɢɦɦɟɬɪɢɢ ɮɚɡ ȼ
Ʌ
ɧ
ɢɟ ɧɟɣɬɪɚɥɢ, ɬ. ɟ. ɩɨɬɟɧɰɢɚɥ ɧɟɣɬɪɚ
ɥ
ɟ
ɫɨɫɬɚɜɥɹɟɬ 3…4 % ɮɚɡɧɨɝɨ ɧɚɩɪɹɠ
ɟ
ɢ
. ɉɪɢ ɜɤɥɸɱɟɧɢɢ ɞɭɝɨɝɚɫɹɳɟɝɨ ɪɟ
ɚ
ɠ
ɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɭɜɟɥɢɱɢɬɶɫɹ. Ⱦɥɹ ɩ
ɨ
ɤ
ɨɞɧɨɥɢɧɟɣɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ ɫɟ
ɬ
ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 9.4, ɚ.
ɢ
ɸ ɩɨɬɟɧɰɢɚɥɚ ɧɟɣɬɪɚɥɢ:
ɚ – ɬɪɟɯɥɢɧɟɣɧ
ɚ
ɹ
; ɛ – ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ
ɯ
ɥɢɧɢɣ
ɟ
ɫɤɨɥɶɤɨ
ɚ
ɫɧɟɬ ɫɚ-
ɩ
ɪɢɜɨɞɢɬ
Ⱦ
ɭɝɚ ɩɪɢ
ɢ
ɟ ɮɚɡɵ,
ɇ
ɚɞɟɠɧɚɹ
ɬɨɤɚ ɡɚ-
ɨ
ɪɦɚɬɨɪɚ
ɪ
ɢɫ. 9.2).
ɵ
ɜ ɫɯɟɦɟ
0
x
6
= f,
ɥ
ɸ. ɉɪɟ-
ɢ
ɧɢɢ, ɧɚ-
ɬɨɪɚɦ
ɧ
ɟ ɞɨɫɬɚ-
Ʌ
ɜɫɟɝɞɚ
ɥ
ɢ ɨɬɥɢ-
ɟ
ɧɢɹ, ɱɬɨ
ɚ
ɤɬɨɪɚ ɜ
ɨ
ɹɫɧɟɧɢɹ
ɬ
ɢ, ɩɪɢɧ-
ɚ
ɹ