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ɂɡ ɞɢɚɝɪɚɦɦɵ ɪɢɫ. 80 ɫɥɟɞɭɟɬ:
M
MM
M
T
ɉɪɢ
n o '
n. ɉɪɢ
ɫɪ
ɧɩ ɫɪ
(2) (1)
'!'.
ɫɪ ɫɪ
ɦ
()PMppo'n.
Ʉɢɧɟɬɢɤɚ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ
ɍɪɚɜɧɟɧɢɟ ɦɚɫɫɨɩɟɪɟɞɚɱɢ 1-ɝɨ ɩɟɪɢɨɞɚ ɫɭɲɤɢ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ (Ɍ
ɝɞɟ Ʉ =
' – ɫɪɟɞɧɹɹ ɞɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɨɰɟɫɫɚ ɩɨ ɫɭɲɢɥɶɧɨɦɭ ɚɝɟɧɬɭ, ɝɞɟ
' .
M
ɫɪ
M
E
– ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɨɬɞɚɱɢ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɬɚɤɬɚ ɜ ɝɚɡɨɜɭɸ ɮɚɡɭ;
ɫɚ
''
ɧɤ
2
*
M
ɫɚ
WKF
'
ɦɫɪ
, (262)
1
ɉɟɪɜɵɣ ɩɟɪɢɨɞ ɫɭɲɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɸ ɜɥɚɠɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɨɬ
ɞɨ
ZZ
ɧɤɪ
.
ɉɪɢ
ZZ
ɧɚɫɬɭɩɚɟɬ 2-ɨɣ ɩɟɪɢɨɞ ɫɭɲɤɢ.
ɤɪ
ɍɪɚɜɧɟɧɢɟ ɦɚɫɫɨɩɟɪɟɞɚɱɢ 2-ɝɨ ɩɟɪɢɨɞɚ ɫɭɲɤɢ ɫ ɭɦɟɧɶɲɚɸɳɟɣɫɹ ɫɤɨɪɨ-
ɫɬɶɸ (Ɍ
ɝɞɟ Ʉ – ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɩɟɪɟɞɚɱɢ ɨɬ ɦɚɬɟɪɢɚɥɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɬɚɤɬɚ ɮɚɡ;
):
2
Ȧ
'
ɫɪ
ɫɚ Ȧ
WKF ',
ɦɫɪ
ZZ
''
ɧɤ
2
Z
;
' .
*
ZZ
ȼɬɨɪɨɣ ɩɟɪɢɨɞ ɫɭɲɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɸ ɜɥɚɠɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɨɬ
ɞɨ ɢɥɢ
ZZ Z
ɤɪ ɤ
*
.
Ʉɪɢɜɚɹ ɫɤɨɪɨɫɬɢ ɫɭɲɤɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 82.
):
Ɋɢɫ. 82. Ʉɪɢɜɚɹ ɫɤɨɪɨɫɬɢ ɫɭɲɤɢ
91
ȼɨɡɦɨɠɧɵ ɫɥɟɞɭɸɳɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɩɟɪɢɨɞɨɜ ɫɭɲɤɢ:
Ɍ
= Ɍ1;
ɫɭɲɤɢ
= Ɍ2;
Ɍ
ɫɭɲɤɢ
Ɍ
= Ɍ1 + Ɍ2.
ɫɭɲɤɢ
ɉɪɢ ɚɧɚɥɢɡɟ ɪɚɜɧɨɜɟɫɢɹ ɦɵ ɪɚɫɫɦɨɬɪɟɥɢ ɩɪɨɰɟɫɫ ɫɭɲɤɢ, ɯɚɪɚɤɬɟɪɢɡɭɸ-
ɳɢɣɫɹ ɩɟɪɜɵɦ ɩɟɪɢɨɞɨɦ ɢ ɭɪɚɜɧɟɧɢɟɦ ɦɚɫɫɨɩɟɪɟɞɚɱɢ.
Ƚɚɡɨɨɛɪɚɡɧɨɟ ɬɨɩɥɢɜɨ G
ɩɨɞɚɟɬɫɹ ɫ ɩɟɪɜɢɱɧɵɦ ɜɨɡɞɭɯɨɦ Gɩɜ ɱɟɪɟɡ ɝɨɪɟɥ-
ɬ
ɤɢ ɜ ɬɨɩɤɭ 1, ɝɞɟ ɫɠɢɝɚɟɬɫɹ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ.
Ɏɨɪɦɢɪɨɜɚɧɢɟ ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɫɦɟɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɟ 2,
ɤɭɞɚ ɩɨɞɚɟɬɫɹ ɜɬɨɪɢɱɧɵɣ ɜɨɡɞɭɯ G
.
ɜɜ
ȼɥɚɠɧɵɣ ɦɚɬɟɪɢɚɥ ɩɨɞɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɞɨɡɚɬɨɪɚ 7 ɜ ɫɭ-
ɲɢɥɶɧɵɣ ɛɚɪɚɛɚɧ 3. Ȼɚɪɚɛɚɧ ɧɚɤɥɨɧɧɨ ɪɚɫɩɨɥɨɠɟɧ ɢ ɜɪɚɳɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
4–5 ɨɛ/ɦɢɧ, ɬɚɤ ɱɬɨ ɦɚɬɟɪɢɚɥ ɩɟɪɟɦɟɳɚɟɬɫɹ ɜɞɨɥɶ ɛɚɪɚɛɚɧɚ ɢ ɜɵɫɭɲɢɜɚɟɬɫɹ ɤ
ɦɨɦɟɧɬɭ ɩɨɩɚɞɚɧɢɹ ɜ ɛɭɧɤɟɪ 4 ɞɨ ɨɩɪɟɞɟɥɟɧɧɨɣ ɜɥɚɠɧɨɫɬɢ Z
.
ɫɦ
Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ
ɋɯɟɦɚ ɛɚɪɚɛɚɧɧɨɣ ɫɭɲɢɥɤɢ ɩɪɹɦɨɬɨɱɧɨɝɨ ɞɟɣɫɬɜɢɹ (ɪɢɫ. 83).
Ɋɢɫ. 83. ɋɯɟɦɚ ɛɚɪɚɛɚɧɧɨɣ ɫɭɲɢɥɤɢ ɩɪɹɦɨɬɨɱɧɨɝɨ ɞɟɣɫɬɜɢɹ:
1 – ɬɨɩɤɚ, 2 – ɫɦɟɫɢɬɟɥɶɧɚɹ ɤɚɦɟɪɚ, 3 – ɫɭɲɢɥɶɧɵɣ ɛɚɪɚɛɚɧ, 4, 5 – ɰɢɤɥɨɧ, 6 – ɜɟɧɬɢɥɹɬɨɪ
ɋɭɯɨɣ ɦɚɬɟɪɢɚɥ G
Ɉɬɪɚɛɨɬɚɧɧɵɣ ɫɭɲɢɥɶɧɵɣ ɚɝɟɧɬ G
ɨɬɝɪɭɠɚɟɬɫɹ ɢɡ ɛɭɧɤɟɪɚ 4 ɚɜɬɨɦɚɬɢɱɟɫɤɢɦ ɞɨɡɚɬɨɪɨɦ 7.
ɫɦ
ɜ ɰɢɤɥɨɧɟ 5 ɨɱɢɳɚɟɬɫɹ ɨɬ ɩɵɥɢ ɢ ɜɟɧ-
ɫɚ
ɬɢɥɹɬɨɪɨɦ 6 ɜɵɜɨɞɢɬɫɹ ɢɡ ɩɪɨɰɟɫɫɚ.
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ – ɜɥɚɠɧɨɫɬɶ ɫɭɯɨɝɨ ɦɚɬɟɪɢɚɥɚ
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ – ɩɨɞɞɟɪɠɚɧɢɟ
Z
ɡɞ
=
Z
ɫɦ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ
.
ɫɦ
Z
ɫɦ
ɬɨɩɤɢ ɢ ɫɦɟɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɵ (ɪɢɫ. 84).
92
.
Ɋɢɫ. 84. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɬɨɩɤɢ ɢ ɫɦɟɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɵ
Z
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɝɚɡɨɜɨɣ ɮɚɡɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɜɯ
VM dP
ɫɚ ɫɚ ɫɚ
ɜɯ
R
dt
T
ɫɚ
GG G GɊ
ɬɩɜɜɜɫɚ
ɜɯ
. (263)
()
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɜɯ
ɬɩɜɜɜɫɚ
. (264)
()GG G GɊ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɜɯ
d
T
UTTT
cV GqGc Gc Gc
ɫɚ ɫɚ
ɪɫɚ ɬ ɬ ɬ ɪɬ ɬ ɩɜ ɪɩɜ ɩɜ ɜɜ ɪɜɜ ɜɜ
ɫɚ
dt
ɜɯ ɜɯ
Gc
ɫɚ ɪɫɚ ɫɚ
ɜɯ
T
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
Gq Gc G c G c
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɬɨɩɤɢ ɢ ɫɦɟɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɵ (ɪɢɫ. 85).
ɬ ɬ ɬ ɪɬ ɬ ɩɜ ɪɩɜ ɩɜ ɜɜ ɪɜɜ ɜɜ
ɜɯ
TTT
ɜɯ ɜɯ
T
Gc
ɫɚ ɪɫɚ ɫɚ
. (266)
. (265)
Ɋɢɫ. 85. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɬɨɩɤɢ ɢ ɫɦɟɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɵ:
(,)
fc q – ɜɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ,
ɪi
ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ,
,,GG G – ɜɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ
ɬɩɜɜɜ
93
,,
TT T
ɬɩɜɜɜ
– ɜɨɡɦɨɠɧɵɟ
ȼɵɜɨɞɵ ɩɨ ɚɧɚɥɢɡɭ ɬɨɩɤɢ ɢ ɫɦɟɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɵ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ:
f
M
ɜɯ ɜɯ
() (,,)PG fGGG ;
ɫɚ ɫɚ ɬ ɩɜ ɜɜ
ɜɯ
(, , )
T
GG G
.
ɫɚ ɬ ɩɜ ɜɜ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɫɭɲɢɥɶɧɨɝɨ ɛɚɪɚɛɚɧɚ (ɪɢɫ. 86).
Ɋɢɫ. 86. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɫɭɲɢɥɶɧɨɝɨ ɛɚɪɚɛɚɧɚ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɬɜɟɪɞɨɣ ɮɚɡɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɦ
SGGW
U
ɦɚɩɩ ɜɦ ɫɦ ɦ
, (267)
dt
ɫɚ
ɝɞɟ hɦ – ɜɵɫɨɬɚ ɫɥɨɹ ɦɚɬɟɪɢɚɥɚ ɜ ɛɚɪɚɛɚɧɟ;
– ɫɟɱɟɧɢɟ ɚɩɩɚɪɚɬɚ;
S
ɚɩɩ
U
– ɩɥɨɬɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ;
ɦ
ɫɚ
W
– ɤɨɥɢɱɟɫɬɜɨ ɜɥɚɝɢ, ɭɞɚɥɹɟɦɨɣ ɜ ɩɪɨɰɟɫɫɟ ɫɭɲɤɢ ɢɡ ɦɚɬɟɪɢɚɥɚ ɜ ɟɞɢɧɢɰɭ
ɦ
ɜɪɟɦɟɧɢ, ɤɝ/ɫ.
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɇɚ ɨɫɧɨɜɚɧɢɢ (262) ɢ (263) ɦɨɠɧɨ ɩɪɢɧɹɬɶ:
GGW . (268)
ɜɦ ɫɦ ɦ
(,)hfGG .
ɦɜɦɫɦ
ȼ ɬɢɩɨɜɨɣ ɫɯɟɦɟ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɫɬɚɛɢɥɢɡɢɪɭɸɬ G
ɟɬ ɬɚɤɠɟ ɫɬɚɛɢɥɢɡɚɰɢɸ h
.
ɦ
ɫɚ
ɢ Gɫɦ, ɱɬɨ ɨɛɟɫɩɟɱɢɜɚ-
ɜɦ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɝɚɡɨɜɨɣ ɮɚɡɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɛ
ɝɞɟ
P – ɪɚɡɪɟɠɟɧɢɟ ɜ ɛɚɪɚɛɚɧɟ, ɉɚ;
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ ɜ ɛɚɪɚɛɚɧɟ ɤɝ/ɦɨɥɶ;
ɫɚ
ɛ
ɫɚ
ɛɛ ɛ
VM dP
ɫɚ ɫɚ ɫɚ
ɛ
dt
R
T
ɫɚ
ɜɯ ɜɵɯ ɫɚ
, (269)
GG W
ɫɚ ɫɚ ɦ
94
ɛ
T
– ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɛɚɪɚɛɚɧɟ (ɩɨ ɝɚɡɨɜɨɣ ɮɚɡɟ), Ʉ;
ɫɚ
ɛ
V – ɨɛɴɟɦ ɝɚɡɨɜɨɣ ɮɚɡɵ ɜ ɛɚɪɚɛɚɧɟ, ɦ3.
ɫɚ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
ɇɚ ɨɫɧɨɜɚɧɢɢ (269) ɢ (270) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
ɜɵɯ ɜɯ ɫɚ
GGW . (270)
ɫɚ ɫɚ ɦ
ɛɜɯɜɵɯ
(, )PfGG .
ɫɚ ɫɚ ɫɚ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɵɦ ɭɩɪɚɜɥɹɸɳɢɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɹɜɥɹɟɬɫɹ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɜ ɫɭɲɢɥɶɧɨɦ ɛɚɪɚɛɚɧɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
UTTT
ɫɚ ɫɚ ɪɫɚ ɫɚ ɪɫɚ ɫɚ ɜɦ ɪɜɦ ɜɦ ɫɚ ɪɫɚ ɫɚ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ȼ ɜɵɪɚɠɟɧɢɹɯ (273) ɢ (272) ɩɪɢɧɢɦɚɟɦ:
ɜɯ ɜɯ ɜɵɯ ɜɵɯ ɫɚ
Gc Gc G c Gc W r
ɫɚ ɪɫɚ ɫɚ ɜɦ ɪɜɦ ɜɦ ɫɚ ɪɫɚ ɫɚ ɫɦ ɪɫɦ ɫɦ ɦ
d
T
ɜɯ ɜɯ ɜɵɯ ɜɵɯ
ɛ
Vc G c G c G c
TT T T
dt
d
T
ɛ
dt
T
Gc W r
ɫɦ ɪɫɦ ɫɦ ɦ
0
:
ɫɚ
. (272)
ɜɵɯ
TT
,
ɛɫɚ
r – ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɜɥɚɝɢ, Ⱦɠ/ɤɝ.
ɇɚ ɨɫɧɨɜɚɧɢɢ (271) ɢ (274) ɦɨɠɧɨ ɩɪɢɧɹɬɶ:
ɝɞɟ
ɛɜɯɜɵɯ
(, ,,)fG G G G
T
, (273)
ɫɚ ɫɚ ɫɚ ɜɦ ɫɦ
ɜɯ
(, , )GfGGG
ɫɚ ɬ ɩɜ ɜɜ
. (274)
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɤɨɥɢɱɟɫɬɜɭ ɜɥɚɝɢ ɜ ɦɚɬɟɪɢɚɥɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
ɂɡ ɜɵɪɚɠɟɧɢɣ (275) ɢ (276) ɫɥɟɞɭɟɬ, ɱɬɨ:
ɫɚ
ɝɞɟ
W – ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɦɚɫɫɨɩɟɪɟɞɚɱɢ.
ɦ
d
Z
ɫɦ
VGGW
UZZ
ɫɦ ɫɦ ɜɦ ɜɦ ɫɦ ɫɦ ɦ
d
Z
dt
ZZ
. (275)
dt
ɫɦ
0
:
GGW
ZZ
. (276)
ɜɦ ɜɦ ɫɦ ɫɦ ɦ
(,,, )fG G W
ɫɦ ɜɦ ɫɦ ɜɦ ɦ
ɫɚ
ɫɚ
95
ɜɵɯ
.
G
ɫɚ
. (271)
ɫɚ
, (277)
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɤɨɥɢɱɟɫɬɜɭ ɜɥɚɝɢ ɜ ɫɭɲɢɥɶɧɨɦ ɚɝɟɧɬɟ
M
M
M
U
ɪ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
ɂɡ ɜɵɪɚɠɟɧɢɣ (278) ɢ (279) ɫɥɟɞɭɟɬ, ɱɬɨ:
d
UMM
VGG W
ɫɚ ɫɚ ɫɚ ɫɚ ɫɚ ɫɚ ɦ
dt
d
ɫɚ
dt
GWG
ɜɵɯ ɜɯ ɜɵɯ ɜɯ ɫɚ
MM
ɫɚ ɫɚ ɫɚ ɫɚ ɦ
ɜɯ ɜɯ ɜɵɯ ɜɵɯ ɫɚ
ɫɚ
. (278)
0
:
ɜɯ ɜɯ ɫɚ ɜɵɯ ɜɵɯ
. (279)
ɫɚ ɫɚ ɦ ɫɚ ɫɚ
(, ,, )fG G W
. (280)
M
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɨɛɳɟɦɭ ɤɨɥɢɱɟɫɬɜɭ ɜɥɚɝɢ ɜ ɩɪɨɰɟɫɫɟ ɫɭɲɤɢ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
d
Z
ɝɞɟ
ZZZZMMM M
.
ɜɦ ɧ ɫɦ ɤ ɫɚ ɧ ɫɚ ɤ
ɫɦ ɫɦ ɜɦ ɜɦ ɫɚ ɫɚ ɫɦ ɫɦ ɫɚ ɫɚ
; ; ;
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɜɵɪɚɠɟɧɢɣ (281) ɢ (282) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
ɉɪɢ ɚɧɚɥɢɡɟ ɬɨɩɤɢ ɦɵ ɩɨɥɭɱɢɥɢ:
ɫɦ
VGGGG
dt
d
GGGG
ZMZ M
ɜɦ ɜɦ ɫɚ ɫɚ ɫɦ ɫɦ ɫɚ ɫɚ
ZMZ M
, (281)
ɜɯ ɜɵɯ
Z
ɫɦ
0
:
dt
ɜɯ ɜɯ ɜɵɯ ɜɵɯ
. (282)
Z
. (283)
ɫɦ ɜɦ ɫɦ ɫɚ ɫɚ
ɜɯ
ɫɚ ɬ ɩɜ ɜɜ
ɜɯ ɜɯ ɜɵɯ ɜɵɯ
(,, , )fG G G G
ɜɯ ɜɵɯ
(, , )GfGGG . (284)
ɂɡ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɭɩɪɚɜɥɹɸɳɢɯ ɜɨɡɞɟɣɫɬɜɢɣ, ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜ ɜɵɪɚɠɟ-
ɧɢɹɯ (283) ɢ (284), ɞɥɹ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɤɨɧɟɱɧɨɣ ɜɥɚɠɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɧɚɢɛɨɥɟɟ
ɢɧɮɨɪɦɚɬɢɜɧɵɦ ɹɜɥɹɟɬɫɹ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ G
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
ȼɨɡɦɨɠɧɵɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ɜɦ ɫɦ ɫɚ ɬ ɩɜ ɜɜ ɫɚ
ZMM TT
ɜɦ ɫɚ ɫɚ ɫɚ ɜɦ
ɜɯ ɜɵɯ
,,(,,),GGGGGG G .
ɜɯ ɜɵɯ ɜɯ
, , , ,
WC.
.
ɬ
.
ɫɚ
,
i
ɦ
96
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
ZTT
ɫɦ ɛ ɫɚ ɛ ɫɚ
ɛɛ
, ( ), ( )PP
.
ɋɭɲɢɥɶɧɵɣ ɛɚɪɚɛɚɧ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɦɧɨɝɨɫɜɹɡɧɵɦ ɨɛɴɟɤɬɨɦ.
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɫɭɲɢɥɶɧɨɝɨ ɛɚɪɚɛɚɧɚ (ɪɢɫ. 87).
Ɋɢɫ. 87. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɫɭɲɢɥɶɧɨɝɨ ɛɚɪɚɛɚɧɚ
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ (ɪɢɫ. 88).
Ɋɢɫ. 88. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ
97
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ:
J
ɪɟɝɭɥɢɪɨɜɚɧɢɟ
Z
ɩɨ ɩɨɞɚɱɟ ɬɨɩɥɢɜɚ Gɬ – ɤɚɤ ɩɨɤɚɡɚɬɟɥɹ ɷɮɮɟɤɬɢɜɧɨ-
ɫɦ
ɫɬɢ ɩɪɨɰɟɫɫɚ ɫɭɲɤɢ;
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɪɚɫɯɨɞɨɜ ɬɨɩɥɢɜɚ G
ɩɨ ɩɨɞɚɱɟ ɩɟɪɜɢɱɧɨɝɨ ɜɨɡɞɭɯɚ
ɯɚ G
ɩɜ
GG
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨ-
ɩɜ ɬ
ɢ ɩɟɪɜɢɱɧɨɝɨ ɜɨɡɞɭ-
ɬ
ɫɬɢ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ;
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ ɧɚ ɜɯɨɞɟ ɜ ɛɚɪɚɛɚɧ
ɩɨ ɩɨɞɚɱɟ ɜɬɨɪɢɱɧɨɝɨ ɜɨɡɞɭɯɚ G
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɪɚɡɪɟɠɟɧɢɹ ɜ ɛɚɪɚɛɚɧɟ
ɜɵɯ
G
ɫɭɲɢɥɶɧɨɝɨ ɚɝɟɧɬɚ
– ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɝɚɡɨɜɨɣ
ɫɚ
;
ɜɜ
ɛ
Ɋɩɨ ɨɬɛɨɪɭ ɨɬɪɚɛɨɬɚɧɧɨɝɨ
ɫɚ
T
ɫɚɜɯ
ɮɚɡɟ.
ɋɬɚɛɢɥɢɡɚɰɢɹ ɪɚɫɯɨɞɨɜ ɜɥɚɠɧɨɝɨ ɢ ɫɭɯɨɝɨ ɦɚɬɟɪɢɚɥɚ G
ɜɦ
ɢ G
ɚɜɬɨɦɚɬɢ-
ɫɦ
ɱɟɫɤɢɦɢ ɞɨɡɚɬɨɪɚɦɢ – ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɬɜɟɪɞɨɣ ɮɚɡɟ.
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ – G
ɬɟɦɩɟɪɚɬɭɪɵ –
ɪɚɡɪɟɠɟɧɢɟ – Ɋ
ɜɥɚɠɧɨɫɬɶ –
, Gɩɜ, Gɜɜ, Gɜɦ, Gɫɦ;
ɬ
ɜɯ ɜɵɯ
,,;
TT T
ɫɚ ɫɚ ɛ
;
ɛ
Z
(
Z
.
)
ɫɦ
ɤ
ɋɢɝɧɚɥɢɡɚɰɢɹ:
ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɹ Z
ɡɧɚɱɢɬɟɥɶɧɨɟ ɩɨɜɵɲɟɧɢɟ
T
ɫɚ
ɨɬ Zɡɞ;
ɫɦ
ɜɯ
.
ɇɟɡɚɩɥɚɧɢɪɨɜɚɧɧɨɟ ɨɬɤɥɸɱɟɧɢɟ ɩɪɢɜɨɞɚ, ɩɪɢ ɷɬɨɦ ɮɨɪɦɢɪɭɟɬɫɹ ɫɢɝɧɚɥ
«ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ».
ɋɢɫɬɟɦɚ ɡɚɳɢɬɵ.
ɉɨ ɫɢɝɧɚɥɭ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ» – ɩɪɟɤɪɚɬɢɬɶ ɩɨɞɚɱɭ ɦɚɬɟɪɢɚɥɚ ɢ ɬɨɩɥɢɜɚ ɜ
ɫɭɲɢɥɶɧɵɣ ɚɝɪɟɝɚɬ.
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ (ɱ. 1)
Ⱦɢɚɝɪɚɦɦɚ ɪɚɜɧɨɜɟɫɢɹ «ș – x – y» ɩɪɢ Ɋ = const (ɪɢɫ. 89).
ɋɦɟɫɶ ɞɜɭɯɤɨɦɩɨɧɟɧɬɧɚɹ: ɤɨɦɩɨɧɟɧɬ Ⱥ – ɧɢɡɤɨɤɢɩɹɳɢɣ; ɤɨɦɩɨɧɟɧɬ
ȼ – ɜɵɫɨɤɨɤɢɩɹɳɢɣ.
Ⱦɢɚɝɪɚɦɦɚ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɹɬɶ:
ș
ɢ șy – ɞɥɹ ɥɸɛɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɦɟɫɢ ɩɪɢ ɡɚɞɚɧɧɨɦ Ɋ;
x
x ɢ y – ɞɥɹ ɥɸɛɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɦɟɫɢ.
98
Ɋɢɫ. 89. Ⱦɢɚɝɪɚɦɦɚ ɪɚɜɧɨɜɟɫɢɹ «ș – x – y» ɩɪɢ Ɋ = const
ɉɨ ɞɚɧɧɵɦ ɞɢɚɝɪɚɦɦɵ «ș – x – y» ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɞɢɚɝɪɚɦɦɚ ɪɚɜɧɨ-
ɜɟɫɢɹ «x – y» ɩɪɢ Ɋ = const.
Ⱦɢɚɝɪɚɦɦɚ ɪɚɜɧɨɜɟɫɢɹ «x – y» ɩɪɢ Ɋ = const (ɪɢɫ. 90).
Ɋɢɫ. 90. Ⱦɢɚɝɪɚɦɦɚ ɪɚɜɧɨɜɟɫɢɹ «x – y» ɩɪɢ Ɋ = const
ɇɚ ɨɫɹɯ y ɢ x ɨɬɤɥɚɞɵɜɚɸɬ ɡɧɚɱɟɧɢɹ y
ɢ xȺ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ 100 % ɫɨ-
Ⱥ
ɞɟɪɠɚɧɢɸ ɤɨɦɩɨɧɟɧɬɚ Ⱥ ɜ ɩɚɪɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɚɯ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; ɞɢɚɝɨ-
99
= xȺ.
Ⱥ
ɧɚɥɶ ɈȺ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɨɫɬɚɜɚɦ ɫɦɟɫɢ y
Ɋɚɫɩɨɥɨɠɟɧɢɟ ɪɚɜɧɨɜɟɫɧɨɣ ɥɢɧɢɢ ɜɵɲɟ ɞɢɚɝɨɧɚɥɢ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɚɪɵ ɨɛɨ-
f
f
x
ɝɚɳɟɧɵ ɧɢɡɤɨɤɢɩɹɳɢɦ ɤɨɦɩɨɧɟɧɬɨɦ.
ɑɟɦ ɛɥɢɠɟ ɥɢɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɤ ɞɢɚɝɨɧɚɥɢ, ɬɟɦ ɦɟɧɶɲɟ ɪɚɡɧɢɰɚ ɫɨɫɬɚɜɨɜ
ɠɢɞɤɨɣ ɢ ɩɚɪɨɜɨɣ ɮɚɡ ɢ ɬɟɦ ɬɪɭɞɧɟɟ ɪɚɡɞɟɥɹɟɬɫɹ ɫɦɟɫɶ ɩɪɢ ɪɟɤɬɢɮɢɤɚɰɢɢ.
ɋɯɟɦɚ ɤɨɥɨɧɧɵ ɪɟɤɬɢɮɢɤɚɰɢɢ ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɪɚɛɨɱɢɯ ɥɢ-
ɧɢɣ ɩɪɨɰɟɫɫɚ (ɪɢɫ. 91).
Ɋɢɫ. 91. ɋɯɟɦɚ ɤɨɥɨɧɧɵ ɪɟɤɬɢɮɢɤɚɰɢɢ ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɪɚɛɨɱɢɯ
ɥɢɧɢɣ ɩɪɨɰɟɫɫɚ
Ɉɛɨɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɰɟɫɫɚ:
, Gɮɥ, Gɞ, G
G
f
, xɞ, xɤ – ɦɨɥɹɪɧɵɟ ɫɨɫɬɚɜɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɨɬɨɤɨɜ;
x
f
R = G
ɮɥ
– ɪɚɫɯɨɞɵ ɩɢɬɚɧɢɹ, ɮɥɟɝɦɵ, ɞɢɫɬɢɥɥɹɬɚ, ɤɭɛɚ;
ɤ
/ Gɞ – ɮɥɟɝɦɨɜɨɟ ɱɢɫɥɨ.
Ɋɚɫɱɟɬ ɪɚɛɨɱɟɝɨ ɮɥɟɝɦɨɜɨɝɨ ɱɢɫɥɚ.
y
ɞ
R
min
yx
– ɡɚɞɚɧɧɵɣ ɫɨɫɬɚɜ ɠɢɞɤɨɣ ɮɚɡɵ ɩɨɬɨɤɚ ɩɢɬɚɧɢɹ;
ɝɞɟ x
f
– ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɟɦɭ ɪɚɜɧɨɜɟɫɧɵɣ ɫɨɫɬɚɜ ɩɚɪɨɜɨɣ ɮɚɡɵ ɩɨɬɨɤɚ ɩɢɬɚɧɢɹ.
y
f
Ɋɚɛɨɱɟɟ ɮɥɟɝɦɨɜɨɟ ɱɢɫɥɨ ɧɚɯɨɞɹɬ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ:
R = 1,3R
+ 0,3 ɢɥɢ R = ıR
min
,
f
,
min
ɝɞɟ ı = 1,2–2,5 – ɤɨɷɮɮɢɰɢɟɧɬ ɢɡɛɵɬɤɚ ɮɥɟɝɦɵ.
100
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