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Ɇɚɫɫɚɨɞɧɨɝɨɦɟɬɪɚɤɚɧɚɬɚɨɩɪɟɞɟɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
J
V
z
ɝɞɟ
–ɡɚɩɚɫɩɪɨɱɧɨɫɬɢɜɧɢɠɧɟɦɫɟɱɟɧɢɢɤɚɧɚɬɚ
ɧ
ɉɨɡɧɚɱɟɧɢɸm
ɤ.ɪɚɫ.
m
ɢ
ɪɚɫɤ
ɜɵɛɢɪɚɟɬɫɹɤɚɧɚɬɫɦɩɭɧɤɬɢɩɪɨɜɟɪɹɟɬɫɹ
ɜ
zmm
ɨɧɫɝ
V
ɜ
ɤɝɦ
z
ɧ
ɧɚɮɚɤɬɢɱɟɫɤɭɸɩɪɨɱɧɨɫɬɶɜɧɢɠɧɟɦɢɜɟɪɯɧɟɦɫɟɱɟɧɢɹɯ
Ɂɚɩɚɫɩɪɨɱɧɨɫɬɢɜɧɢɠɧɟɦɫɟɱɟɧɢɢɤɚɧɚɬɚ
F
z
ɮɧ
GQ
ɪɚɡ
t
z
ɧ
Ɂɚɩɚɫɩɪɨɱɧɨɫɬɢɜɜɟɪɯɧɟɦɫɟɱɟɧɢɢɤɚɧɚɬɚ
F
z
ɮɜ
ɪɚɡ
ɇpGQ
ɤ
t
Z
ɜ
Ɏɚɤɬɢɱɟɫɤɢɟɡɚɩɚɫɵɩɪɨɱɧɨɫɬɢɞɨɥɠɧɵɛɵɬɶɧɟɧɢɠɟɡɚɩɚɫɨɜɩɪɨɱɧɨɫɬɢ
ɨɛɭɫɥɨɜɥɟɧɧɵɯɉȻ ɞɥɹ ɤɚɧɚɬɨɜɝɪɭɡɨɩɨɞɴɟɦɧɵɯɭɫɬɚɧɨɜɨɤɤɚɤɭɤɚɡɚɧɨɜ ɮɨɪ
ɦɭɥɚɯ
ȼɵɛɨɪɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵ
ɉɪɨɦɵɲɥɟɧɧɨɫɬɶɸɜɵɩɭɫɤɚɸɬɫɹɛɨɥɶɲɢɟ ɩɨɞɴɟɦɧɵɟ ɦɚɲɢɧɵ ɫɰɢɥɢɧ
ɞɪɢɱɟɫɤɢɦɢ ɛɚɪɚɛɚɧɚɦɢ ɩɨ ȽɈɋɌɢ ȽɈɋɌ ɞɜɭɯɛɚɪɚɛɚɧɧɵɟ
ɬɢɩɚ2ɐ-Ⱦ
ɧɵɟɫɪɚɡɪɟɡɚɧɧɵɦɛɚɪɚɛɚɧɨɦɢɦɚɥɵɟɩɨɞɴɟɦɧɵɟɦɚɲɢɧɵɐ-Ⱦ
ȼɆɉȻ-Ⱦɛ-ȼ-ȼɚɬɚɤɠɟɐɊ-Ⱦ
u
ɛ
ȼ/ȼ1ɆɉȻ-Ⱦɛ×-ȼ-ȼ1 ɨɞɧɨɛɚɪɚɛɚɧ
u
ɛ
ȼ ɨɞɧɨɛɚɪɚ
u
ɛ
ɛɚɧɧɵɟ Ⱦɚɧɧɵɟ ɭɤɚɡɚɧɧɵɯ ɦɚɲɢɧ ɩɪɢɜɟɞɟɧɵ ɜ ɩɪɢɥɨɠɟɧɢɢ Ⱥ ɬɚɛɥ Ⱥ
ȺȺȺ
ɉɟɪɜɚɹɛɨɥɶɲɚɹ ɩɨɞɴɟɦɧɚɹɦɚɲɢɧɚ ɬɢɩɚ ɐî ɢɡɝɨɬɨɜɥɟɧɧɚɹ ɇɨɜɨ
Ʉɪɚɦɚɬɨɪɫɤɢɦ ɦɚɲɢɧɨɫɬɪɨɢɬɟɥɶɧɵɦ ɡɚɜɨɞɨɦ ɞɥɹ ɲɚɯɬɵ ©ɋ Ɉɪɞɠɟɧɢɤɢɞɡɟª
ɉɈ©Ɇɚɤɟɟɜɭɝɨɥɶªɜɝɛɵɥɚɪɚɫɫɱɢɬɚɧɚɞɥɹɩɨɞɴɟɦɚɬɨɧɧɝɨɪɧɨɣɦɚɫɫɵ
ɫɝɥɭɛɢɧɵɦȼɝɨɫɜɨɟɧɜɵɩɭɫɤɩɨɞɴɟɦɧɵɯɦɚɲɢɧɫɰɢɥɢɧɞɪɢɱɟɫɤɢ
ɦɢɪɚɡɪɟɡɧɵɦɢɛɚɪɚɛɚɧɚɦɢ
Ɇɚɪɤɢɪɨɜɤɚ ɜɫɟɯ ɩɨɞɴɟɦɧɵɯ ɦɚɲɢɧ ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦɢ ɛɚɪɚɛɚɧɚɦɢ
ɨɡɧɚɱɚɟɬ
M ±ɦɚɲɢɧɚ
ɉ ±ɩɨɞɴɟɦɧɚɹ
Ȼ ±ɛɚɪɚɛɚɧɧɚɹ
Ⱦɛ ±ɞɢɚɦɟɬɪɛɚɪɚɛɚɧɚɦ
ȼ ±ɨɛɳɚɹɲɢɪɢɧɚɛɚɪɚɛɚɧɚɦɤɨɥɢɱɟɫɬɜɨ ɛɭɤɜ ȼ ɭɤɚɡɵɜɚɟɬ ɤɨɥɢɱɟɫɬɜɨ
ɛɚɪɚɛɚɧɨɜ
ȼ1 ±ɲɢɪɢɧɚɨɬɪɟɡɧɨɣɱɚɫɬɢɛɚɪɚɛɚɧɚɦ
Ɋ ±ɨɬɪɟɡɧɨɣɛɚɪɚɛɚɧ
ɐ ±ɰɢɥɢɧɞɪɢɱɟɫɤɚɹɦɚɲɢɧɚ
ɐɢɮɪɚ 2 ±ɤɨɥɢɱɟɫɬɜɨɛɚɪɚɛɚɧɨɜ
Ɉɩɪɟɞɟɥɟɧɢɟɨɫɧɨɜɧɵɯɩɚɪɚɦɟɬɪɨɜɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵ
ɞɢɚɦɟɬɪɛɚɪɚɛɚɧɚ
Ⱦɛdɤɦɦ
ɦɚɤɫɢɦɚɥɶɧɨɟɫɬɚɬɢɱɟɫɤɨɟɧɚɬɹɠɟɧɢɟɤɚɧɚɬɚ
F
Q + G + ɪɤ Â ɇ0ɇ
ɫɬ.mɚɯ
ɪɚɡɧɨɫɬɶɫɬɚɬɢɱɟɫɤɢɯɧɚɬɹɠɟɧɢɣɜɟɬɜɟɣɤɚɧɚɬɨɜ
ɞɥɹɧɟɭɪɚɜɧɨɜɟɲɟɧɧɨɝɨɩɨɞɴɟɦɚq
¨F
ɝɞɟ ɇ
–ɜɵɫɨɬɚɩɨɞɴɟɦɚɫɦɪɢɫɭɧɨɤ
ɩ
ɇ
= Q + ɪɤ Â ɇnɇ
ɫm
= ɇɲ + hɭ + hɛ + h'ɦ,
ɩ
ɞɥɹɭɪɚɜɧɨɜɟɲɟɧɧɨɝɨɩɨɞɴɟɦɚq pɤ
¨F = Qɇ
ɝɞɟ q – ɜɟɫ ɨɞɧɨɝɨ ɦɟɬɪɚ ɭɪɚɜɧɨɜɟɲɢɜɚɸɳɟɝɨ ɤɚɧɚɬɚ ɩɪɢɧɢɦɚɟɬɫɹ ɛɥɢɡɤɢɦ
ɨɞɧɨɦɭɦɟɬɪɭɝɨɥɨɜɧɨɝɨɤɚɧɚɬɚɩɪɢɥɨɠɟɧɢɟȺɬɚɛɥȺ
ɉɨȾɛF
ɢ¨Fɫmɩɨ ȽɈɋɌ ɜɵɛɢɪɚɟɬɫɹɩɨɞɴɟɦɧɚɹ ɦɚɲɢɧɚ ɫ ɛɥɢɠɚɣ
ɫɬ.mɚɯ
ɲɢɦ ɛɨɥɶɲɢɦ ɫɬɚɧɞɚɪɬɧɵɦ ɞɢɚɦɟɬɪɨɦ ɛɚɪɚɛɚɧɚ ɉɪɢ ɷɬɨɦ ɡɧɚɱɟɧɢɟ ɭɫɢɥɢɣ
F
ɢ ¨ Fcm, ɭɤɚɡɚɧɧɵɟ ɜ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɞɨɥɠɧɵ ɛɵɬɶ ɛɨɥɶɲɟ ɢɥɢ ɪɚɜɧɵ
ɫɬ.mɚɯ
ɪɚɫɫɱɟɬɧɵɦɡɧɚɱɟɧɢɹɦ
ɉɨɫɥɟɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨɜɵɛɨɪɚɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɟɟɛɚɪɚɛɚɧɩɪɨɜɟɪɹ
ɟɬɫɹɧɚ ɤɚɧɚɬɨɟɦɤɨɫɬɶ ɉɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶɱɬɨɧɚɝɥɚɜɧɵɯɩɨɞɴ
ɟɦɧɵɯɭɫɬɚɧɨɜɤɚɯɜɟɫɶɤɚɧɚɬɧɚɛɚɪɚɛɚɧɟɞɨɥɠɟɧɪɚɫɩɨɥɚɝɚɬɶɫɹɜɨɞɢɧɫɥɨɣ
Ɏɚɤɬɢɱɟɫɤɚɹɲɢɪɢɧɚɛɚɪɚɛɚɧɚɡɚɧɢɦɚɟɦɚɹ ɤɚɧɚɬɨɦ ɞɥɹ ɦɚɲɢɧɬɢɩɚ2ɐ-
Ⱦ
ȼɆɉȻ-Ⱦɛ-ȼ-ȼ, ɨɩɪɟɞɟɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
u
ɛ
ɝɞɟ
§
A
H
n
¨
ȼ
ɪɚɫ
¨
Ⱦ
S
ɛ
©
A
±ɡɚɩɚɫɤɚɧɚɬɚɧɚɩɟɪɢɨɞɢɱɟɫɤɢɟɢɫɩɵɬɚɧɢɹɦ,
·
¸
ɤomp
¸
¹
ȼdnn
d
H
ɦ
A
ɦ
Ⱦɛ– ɩɪɢɧɹɬɵɣɫɬɚɧɞɚɪɬɧɵɣɪɚɡɦɟɪɞɢɚɦɟɬɪɚɛɚɪɚɛɚɧɚɦ
n
H
– ɱɢɫɥɨɜɢɬɤɨɜɬɪɟɧɢɹn
mɪ.
ɞɥɹɧɟɮɭɬɟɪɨɜɚɧɧɵɯɢɥɢn
mɪ.
ɞɥɹɮɭ
mɪ.
ɬɟɪɨɜɚɧɧɵɯɛɚɪɚɛɚɧɨɜ
no– ɱɢɫɥɨɜɢɬɤɨɜɞɥɹɪɚɡɦɟɳɟɧɢɹɞɨɩɨɥɧɢɬɟɥɶɧɨɣɞɥɢɧɵɤɚɧɚɬɚɢɡɡɚɟɝɨ
ɭɞɥɢɧɟɧɢɹ no
–ɡɚɡɨɪɦɟɠɞɭɫɨɫɟɞɧɢɦɢɜɢɬɤɚɦɢɤɚɧɚɬɚɦɦ,H ɦɦ
ȿɫɥɢ ɤɚɧɚɬ ɧɟ ɩɨɦɟɳɚɟɬɫɹ ɧɚ ɛɚɪɚɛɚɧɟ ɜ ɨɞɢɧ ɫɥɨɣ ɪɚɫɱɟɬɧɚɹ ɲɢɪɢɧɚ
ɛɨɥɶɲɟɱɟɦɭɤɚɡɚɧɚɜɤɚɬɚɥɨɝɟɩɪɢɧɢɦɚɟɬɫɹɩɨɞɴɟɦɧɚɹɦɚɲɢɧɚɛɨɥɶɲɟɣɲɢ
ɪɢɧɵɟɫɥɢɬɚɤɚɹ ɩɪɟɞɭɫɦɨɬɪɟɧɚ ɢɥɢ ɫɛɚɪɚɛɚɧɨɦɛɨɥɶɲɟɝɨ ɞɢɚɦɟɬɪɚ ɢ ɫɧɨɜɚ
ɜɵɩɨɥɧɹɟɬɫɹɩɪɨɜɟɪɤɚɧɚɤɚɧɚɬɨɟɦɤɨɫɬɶ
Ɏɚɤɬɢɱɟɫɤɚɹɲɢɪɢɧɚɛɚɪɚɛɚɧɚ ɡɚɧɢɦɚɟɦɚɹ ɤɚɧɚɬɨɦɞɥɹɦɚɲɢɧ ɫ ɪɚɡɪɟɡ
ɧɵɦɛɚɪɚɛɚɧɨɦɬɢɩɚɐɊ-Ⱦ
ȼ/ȼ1ɢɆɉȻ-Ⱦɛ-ȼ-B1ɜɵɱɢɫɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
u
ɛ
§
H
A
n
¨
ȼ
ɪɚɫ
¨
Ⱦ
S
©
ɛ
·
¸
ɤomɪ
¸
¹
ȼȼdnn
d
H
ɦ
ȿɫɥɢ ɤɚɧɚɬ ɧɟ ɩɨɦɟɳɚɟɬɫɹ ɩɨ ɲɢɪɢɧɟ ɛɚɪɚɛɚɧɚ ȼ-B1 ɜ ɨɞɢɧ ɫɥɨɣ ɬɨ
ɩɪɢɧɢɦɚɟɬɫɹɦɚɲɢɧɚɫɛɨɥɶɲɢɦɡɧɚɱɟɧɢɟɦȾɛ,ɢɟɟɛɚɪɚɛɚɧɫɧɨɜɚɩɪɨɜɟɪɹɟɬɫɹ
ɧɚɤɚɧɚɬɨɟɦɤɨɫɬɶ
ɉɨɫɥɟ ɜɵɛɨɪɚ ɩɨɞɴɟɦɧɨɣ ɦɚɲɢɧɵ ɤɨɬɨɪɚɹ ɨɬɜɟɱɚɟɬ ɜɫɟɦ ɬɪɟɛɨɜɚɧɢɹɦ
ɞɚɟɬɫɹɟɟɯɚɪɚɤɬɟɪɢɫɬɢɤɚɩɪɢɥɨɠɟɧɢɟȺɬɚɛɥȺȺȺȺ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɨɞɴɟɦɧɨɣ ɦɚɲɢɧɵ
Ɍɢɩ±Ⱦɛȼȼ1ȼ2F
ɫɬ.mɚɯ
¨FɫɬV
U1U2U3(GȾ2)ɛ,
mɚɯ
ɝɞɟ ȼ2– ɪɚɫɫɬɨɹɧɢɟɦɟɠɞɭɧɚɜɢɜɨɱɧɵɦɢɩɨɜɟɪɯɧɨɫɬɹɦɢɛɚɪɚɛɚɧɨɜɦɚɲɢɧɬɢ
ɩɚɆɉȻ Ⱦɛ-ȼ-ȼ1ɢɥɢ2ɐ-Ⱦ
ȼ, ɦ
u
ɛ
U1U2U3±ɜɨɡɦɨɠɧɵɟɩɟɪɟɞɚɬɨɱɧɵɟɱɢɫɥɚɪɟɞɭɤɬɨɪɨɜ
(GȾ2)ɛ–ɦɚɯɨɜɵɣɦɨɦɟɧɬɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɤɇāɦ
ȼɵɛɨɪɤɨɩɪɨɜɵɯɲɤɢɜɨɜ
Ⱦɢɚɦɟɬɪɲɤɢɜɚɞɨɥɠɟɧɭɞɨɜɥɟɬɜɨɪɹɬɶɬɪɟɛɨɜɚɧɢɸ
Ⱦ
ɉɨɩɨɥɭɱɟɧɧɨɦɭɡɧɚɱɟɧɢɸ Ⱦ
ɲɟɝɨ ɛɨɥɶɲɟɝɨ ɞɢɚɦɟɬɪɚ ɢ ɜɵɩɢɫɵɜɚɟɬɫɹ ɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɢɩ ± Ⱦ
(GȾ2)
ɫɦɩɪɢɥɨɠɟɧɢɟȺɬɚɛɥȺ
ɲ.ɤ
79Âdɤ , ɦɦ
ɲ.ɤ.
ɩɨɤɚɬɚɥɨɝɭɜɵɛɢɪɚɸɬɫɹ ɲɤɢɜɵ ɛɥɢɠɚɣ
ɲ.ɤ.
ɲ.ɤ.
ȿɫɥɢ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɤɚɧɚɬɨɟɦɤɨɫɬɢ ɛɚɪɚɛɚɧɚ ɛɵɥɚ ɩɪɢɧɹɬɚ ɦɚɲɢɧɚɫ
ɛɨɥɶɲɢɦɞɢɚɦɟɬɪɨɦɬɨɠɟɥɚɬɟɥɶɧɨ ɢ ɞɢɚɦɟɬɪ ɤɨɩɪɨɜɵɯɲɤɢɜɨɜɩɪɢɧɹɬɶɬɨɝɨ
ɠɟɞɢɚɦɟɬɪɚɱɬɨɦɨɠɟɬɭɩɪɨɫɬɢɬɶɦɨɞɟɪɧɢɡɚɰɢɸɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
H
Ɋɚɫɩɨɥɨɠɟɧɢɟɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɨɬɧɨɫɢɬɟɥɶɧɨɭɫɬɶɹɫɬɜɨɥɚ
ɗɥɟɦɟɧɬɵɪɚɫɩɨɥɨɠɟɧɢɹɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɨɬɧɨɫɢɬɟɥɶɧɨɫɬɜɨɥɚɭɤɚɡɚ
ɧɵ ɧɚ ɪɢɫɭɧɤɟ ɝɞɟ ɢɫɩɨɥɶɡɨɜɚɧɵ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ ɜ – ɨɬɧɨɫ ɨɫɢ
ɦɚɲɢɧɵɨɬɜɟɪɬɢɤɚɥɶɧɨɣɨɫɢɫɬɜɨɥɚɦ
ɜ = 0,6 ɇ
+ Ⱦɛ + (7÷10)ɦ.
ɤ
Ⱦɥɢɧɚɫɬɪɭɧɵɤɚɧɚɬɚɦ
Ⱦ
ɝɞɟ c±ɩɪɟɜɵɲɟɧɢɟɨɫɢɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɧɚɞɭɫɬɶɟɦɫɬɜɨɥɚ, ±ɦ
ɤɫmɪ
ɜɫɇL
ɤɲ
d
ɦ
ɍɝɨɥɧɚɤɥɨɧɚɫɬɪɭɧɵɤɚɧɚɬɚɤɝɨɪɢɡɨɧɬɭɝɪɚɞ
ɫɇ
arctg
ɤ
Ⱦ
ɤɲ
ɜ
DD
dd
EE
ɍɝɥɵɨɬɤɥɨɧɟɧɢɹɤɚɧɚɬɚɭɝɥɵɞɟɜɢɚɰɢɢ
Į1±ɜɧɟɲɧɢɣɭɝɨɥɨɬɤɥɨɧɟɧɢɹɝɪɚɞ
Į2 ± ɜɧɭɬɪɟɧɧɢɣɭɝɨɥɨɬɤɥɨɧɟɧɢɹɝɪɚɞ
ɉɪɢɩɪɢɦɟɧɟɧɢɢɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɬɢɩɚɆɉȻ-Ⱦɛ-ȼ-ȼ ɢɥɢ2ɐ-Ⱦ
S
ȼ
o
ȼ
D
arctg
L
ɫmɪ
H
dn
ɤmɪ
D
c
d
ɛ
ȼȼȼS
ɫmɪ
ɪɚɫo
D
c
d
arctg
D
L
ɉɪɢɩɪɢɦɟɧɟɧɢɢɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɬɢɩɚɆɉȻ-Ⱦɛ-ȼ-ȼɢɥɢɐɊ-Ⱦ
u
u
ɛ
ȼ
ȼ/ȼ1
dnSȼ
arctg
D
ɤmɪo
L
ɫmɪ
D
c
d
arctg
D
ɝɞɟ
±ɪɚɫɫɬɨɹɧɢɟɦɟɠɞɭɩɥɨɫɤɨɫɬɹɦɢɤɨɩɪɨɜɵɯɲɤɢɜɨɜɦ.
S
o
ɪɚɫ
Sȼȼ
D
O
L
ɫmɪ
c
d
Ɋɢɫɭɧɨɤ 2.1. ɗɥɟɦɟɧɬɵ ɨɬɜɟɫɚ ɤɚɧɚɬɚ ɢ ɪɚɫɩɨɥɨɠɟɧɢɹ ɩɨɞɴɟɦɧɨɣ ɦɚɲɢɧɵ
ɨɬɧɨɫɢɬɟɥɶɧɨ ɭɫɬɶɹ ɫɬɜɨɥɚ ɲɚɯɬɵ
Ʉɢɧɟɦɚɬɢɤɚɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
Ⱦɥɹ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɯ ɫɤɢɩɨɜɵɯ ɩɨɞɴɟɦɧɵɯ ɭɫɬɚɧɨɜɨɤ ɩɪɢɧɢɦɚɟɬɫɹ
ɲɟɫɬɢɩɟɪɢɨɞɧɚɹɞɢɚɝɪɚɦɦɚɫɤɨɪɨɫɬɢɤɨɬɨɪɚɹɩɨɤɚɡɚɧɚɧɚɪɢɫɭɧɤɟ
ɂɫɯɨɞɧɵɟɞɚɧɧɵɟɞɥɹɩɨɫɬɪɨɟɧɢɹɞɢɚɝɪɚɦɦɵɫɤɨɪɨɫɬɢ
ɜɵɫɨɬɚɩɨɞɴɟɦɚ– ɇnɦ
ɩɭɬɶɪɚɡɝɪɭɡɤɢɫɤɢɩɚ±h0 ɦ
ɫɤɨɪɨɫɬɶɫɤɢɩɚɧɚɜɵɯɨɞɟɢɡɪɚɡɝɪɭɡɨɱɧɵɯɤɪɢɜɵɯ±V0 ɦɫ
ɩɭɬɶɞɨɬɹɠɤɢɢɫɬɨɩɨɪɟɧɢɹ±hɞ h
h0 ɦ
ɫɬ
ɫɤɨɪɨɫɬɶɞɨɬɹɠɤɢ±Vɞ ɦɫ
ɡɚɦɟɞɥɟɧɢɟɫɬɨɩɨɪɟɧɢɹɚ
ɦɫ
ɫm
2.7.1. Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɫɤɢɩɚ
ȼɪɟɦɹɞɜɢɠɟɧɢɹɫɤɢɩɚɫ– Ɍ = Ɍɰ – tn = (3600Âmɝ/Ⱥ
ɝɞɟ Tɰ±ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɩɨɞɴɟɦɧɨɝɨɰɢɤɥɚɫ
tn ±ɩɪɢɧɹɬɨɟɡɧɚɱɟɧɢɟɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢɩɚɭɡɵF
) – tnɫ;
ɱɚɫ
Ⱦɥɹɫɤɢɩɨɜɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɶɸɞɨ ɬ ɩɪɢɧɢɦɚɬɶtn ɫɟɤɞɥɹɫɤɢɩɨɜ
Ɍ
S
ɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɶɸ ɛɨɥɟɟ ɬ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɚɭɡɵ ɜ ɫɟɤɭɧɞɚɯ ɱɢɫɥɟɧɧɨ
ɪɚɜɧɚɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɢɫɤɢɩɚɜɬɨɧɧɚɯ
ɋɪɟɞɧɹɹɫɤɨɪɨɫɬɶɩɨɞɴɟɦɚ
ɇ
ɩ
V
ɫɪ
, ɦɫ
Ɇɚɤɫɢɦɚɥɶɧɚɹɪɚɫɱɟɬɧɚɹɫɤɨɪɨɫɬɶɩɨɞɴɟɦɚ
= ĮÂVɫɪɦɫ
V
mɚɯ.ɪɚɫ
ɝɞɟ Į ±ɦɧɨɠɢɬɟɥɶɫɤɨɪɨɫɬɢĮ ɞɥɹɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɯɩɨɞɴɟɦɨɜ
Į
Ʉɨɪɪɟɤɬɢɪɨɜɤɚɦɚɤɫɢɦɚɥɶɧɨɣɫɤɨɪɨɫɬɢ
ɑɚɫɬɨɬɚɜɪɚɳɟɧɢɹɛɚɪɚɛɚɧɚɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵ
V
n
ɛ
ɪɚɫmɚɯ
ɦɢɧ
Ⱦ
S
ɛ
ɑɚɫɬɨɬɚɜɪɚɳɟɧɢɹɪɨɬɨɪɚɩɨɞɴɟɦɧɨɝɨɞɜɢɝɚɬɟɥɹ
n
= nɛÂU1; n
ɞɜ1
= nɛÂU2; n
ɞɜ2
= nɛÂU3ɦɢɧ
ɞɜ3
ɝɞɟ U1, U2, U3 ±ɩɟɪɟɞɚɬɨɱɧɵɟɱɢɫɥɚɪɟɞɭɤɬɨɪɨɜɨɞɢɧɢɡɤɨɬɨɪɵɯɩɨɫɥɟɜɵɛɨ
ɪɚɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɪɨɬɨɪɚɞɜɢɝɚɬɟɥɹ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚ ɩɨɞɴɟɦɧɨɣ
ɦɚɲɢɧɟ
Ɋɹɞɫɢɧɯɪɨɧɧɵɯɱɚɫɬɨɬɜɪɚɳɟɧɢɹɩɨɞɴɟɦɧɵɯɞɜɢɝɚɬɟɥɟɣ
nc ɦɢɧ
ɉɨɥɭɱɟɧɧɵɟɩɨ ɭɪɚɜɧɟɧɢɸ ɱɚɫɬɨɬɵɫɪɚɜɧɢɜɚɸɬɫɹɫɫɢɧɯɪɨɧɧɵɦɢ
ɚ ɡɚɬɟɦ ɢɡ ɫɢɧɯɪɨɧɧɨɝɨ ɪɹɞɚ ɱɚɫɬɨɬ ɩɪɢɧɢɦɚɟɬɫɹ ɛɥɢɠɚɣɲɚɹ ɛɨɥɶɲɚɹ ɢɡ
ɭɫɥɨɜɢɹɱɬɨɛɵɮɚɤɬɢɱɟɫɤɚɹɫɤɨɪɨɫɬɶɞɜɢɠɟɧɢɹɛɵɥɚɪɚɜɧɨɣɢɥɢɛɨɥɟɟɪɚɫɱɟɬ
ɧɨɣ
Ɏɚɤɬɢɱɟɫɤɚɹɫɤɨɪɨɫɬɶɞɜɢɠɟɧɢɹɫɤɢɩɚ
snȾ
V
ɮmɚɯ
cɛ
U
t
, ɦɫ
V
ɪɚɫmaɯ
ɝɞɟ nc, U± ɩɪɢɧɹɬɵɟ ɫɢɧɯɪɨɧɧɚɹɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹɢ ɩɟɪɟɞɚɬɨɱɧɨɟ
ɱɢɫɥɨɪɟɞɭɤɬɨɪɚ
s ±ɤɨɷɮɮɢɰɢɟɧɬɫɤɨɥɶɠɟɧɢɟɪɨɬɨɪɚɞɜɢɝɚɬɟɥɹ s
2.7.2. ȼɵɛɨɪ ɦɨɳɧɨɫɬɢ ɩɨɞɴɟɦɧɨɝɨ ɞɜɢɝɚɬɟɥɹ
K
K
K
K
Ɉɪɢɟɧɬɢɪɨɜɨɱɧɨɟɷɤɜɢɜɚɥɟɧɬɧɨɟɭɫɢɥɢɟ
= ɤÂQÂȟ,Âɇ,
F
ɷɤɜ.ɨɪ
ɝɞɟ ɤ ± ɤɨɷɮɮɢɰɢɟɧɬ ɭɱɢɬɵɜɚɸɳɢɣ ɜɪɟɞɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Ⱦɥɹ ɫɤɢɩɨɜɵɯ
ɩɨɞɴɟɦɧɵɯɭɫɬɚɧɨɜɨɤɤ
ȟ ±ɤɨɷɮɮɢɰɢɟɧɬɷɤɜɢɜɚɥɟɧɬɧɨɫɬɢɧɚɝɪɭɡɤɢɞɥɹɧɟɭɪɚɜɧɨɜɟɲɟɧɧɵɯɩɨɞɴ
ɟɦɨɜɩɪɢɧɢɦɚɟɬɫɹȟ ɞɥɹɭɪɚɜɧɨɜɟɲɟɧɧɵɯȟ
Ɉɪɢɟɧɬɢɪɨɜɨɱɧɚɹɦɨɳɧɨɫɬɶɞɜɢɝɚɬɟɥɹ
VF
ɮmaɯɨɪɷɤɜ
Ɋ
ɨɪɷɤɜ
, ɤȼɬ
K
ɪɟɞ
ɝɞɟ
± ɄɉȾ ɪɟɞɭɤɬɨɪɚɞɥɹɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ
ɪɟɞ
ɱɚɬɨɝɨ
ɪɟɞ
ɂɡɩɪɢɥɨɠɟɧɢɹ Ⱥɬɚɛɥ ȺȺ ɩɨ
ɞɥɹ ɞɜɭɯɫɬɭɩɟɧ
ɪɟɞ
ɢn
ɜɵɛɢɪɚɟɬɫɹ ɚɫɢɧɯɪɨɧ
ɫ
ɨɪɷɤɜɊ
ɧɵɣ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ ɛɥɢɠɚɣɲɟɣ ɛɨɥɶɲɟɣ ɢɥɢ ɪɚɜɧɨɣ ɦɨɳɧɨɫɬɢ ɡɚɬɟɦ ɩɪɢ
ɜɨɞɢɬɫɹɟɝɨɩɨɥɧɚɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɝɞɟ Ȗ
ɬɢɩ±Ɋ
ɬɚɛɥ
(GȾ2)
I
I
ɪɨɬ
Ʉɨɝɞɚ
ɧɨɦ
n
ɧɨɦ, Ȗɬɚɛɥ
(GȾ2)
ɪɨɬ
I
ɪɨɬ
Iɫɬȿ
ɪɨɬ
±ɬɚɛɥɢɱɧɵɣɤɨɷɮɮɢɰɢɟɧɬɩɟɪɟɝɪɭɡɨɱɧɨɣɫɩɨɫɨɛɧɨɫɬɢ
±ɦɚɯɨɜɵɣɦɨɦɟɧɬɪɨɬɨɪɚɞɜɢɝɚɬɟɥɹɤɇÂɦ
ɪɨɬ
±ɫɢɥɚɬɨɤɚɜɪɨɬɨɪɟɢɫɬɚɬɨɪɟȺ
ɫɬ
ɤȼɬɩɪɢɧɢɦɚɟɬɫɹɞɜɚ ɞɜɢɝɚɬɟɥɹ ɦɨɳɧɨɫɬɶ ɤɚɠɞɨɝɨɢɡ
Ɋ
ɧɨɦ
t
ɤɨɬɨɪɵɯɧɟɦɟɧɶɲɟɩɨɥɨɜɢɧɵɨɛɳɟɣɦɨɳɧɨɫɬɢ
2.7.3. ȼɵɛɨɪ ɪɟɞɭɤɬɨɪɚ
ɇɨɦɢɧɚɥɶɧɨɟɭɫɢɥɢɟɪɚɡɜɢɜɚɟɦɨɟɩɪɢɜɨɞɨɦɧɚɨɤɪɭɠɧɨɫɬɢɛɚɪɚɛɚɧɚ
Ɋ
F
ɧɨɦ
ɪɟɞɧɨɦ
V
ɇ
ɮmɚɯ
Ɇɚɤɫɢɦɚɥɶɧɵɣɤɪɭɬɹɳɢɣɦɨɦɟɧɬɧɚɜɵɯɨɞɧɨɦɜɚɥɭɪɟɞɭɤɬɨɪɚ
Ɇ
ɤɪ.mɚɯ
= 0,5ÂF
ɧɨɦÂȖɪɚɫÂȾɛ
, ɇāɦ
ɝɞɟ Ȗ
±ɪɚɫɱɟɬɧɵɣɤɨɷɮɮɢɰɢɟɧɬɩɟɪɟɝɪɭɡɤɢȖ
ɪɚɫ
āȖ
ɪɚɫ
ɬɚɛɥ
J
ɉɨɡɧɚɱɟɧɢɹɦɆ
ɢUɞɥɹɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɩɪɢɧɢɦɚɟɬɫɹɪɟɞɭɤɬɨɪɫ
ɤɪ.mɚɯ
ɛɥɢɠɚɣɲɢɦ ɛɨɥɶɲɢɦ ɤɪɭɬɹɳɢɦ ɦɨɦɟɧɬɨɦ ɢ ɜɵɛɪɚɧɧɵɦ ɡɧɚɱɟɧɢɟɦ U ɢ
ɩɪɢɜɨɞɢɬɫɹ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɢɩ Ɇ
ɤɪ.mɚɯ
U Ș
(GȾ2)
ɪɟɞ
ɩɪɢɥɨɠɟɧɢɟ Ⱥ
ɪɟɞ
ɬɚɛɥȺ
2.7.4. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɪɢɜɟɞɟɧɧɨɣ ɦɚɫɫɵ ɩɨɞɴɟɦɧɨɣ ɭɫɬɚɧɨɜɤɢ
ɉɪɢɜɟɞɟɧɧɚɹɦɚɫɫɚɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢɨɩɪɟɞɟɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
m
= mɝ + 2Âmɫ + 2ÂmɤÂL
nɪ
ª
GȾ
«
g
Ⱦ
«
ɤɲ
¬
GȾ
ɤɲ
ɛ
Ⱦ
ɛ
GȾ
+ m
ɝ.ɤ.
ɪɨɬ
Ⱦ
ɛ
ɭ.ɤÂLɭ.ɤ
ɩU
ɞ
GȾ
+
Ⱦ
º
ɪɟɞ
»
»
ɛ
¼
ɤɝ
ɝɞɟ L
±ɩɨɥɧɚɹɞɥɢɧɚɨɞɧɨɣɜɟɬɜɢɝɨɥɨɜɧɨɝɨɤɚɧɚɬɚɦ
ɝ.ɤ.
L
= ɇɨ + L
ɝ.ɤ.
L
±ɞɥɢɧɚɜɟɬɜɢɭɪɚɜɧɨɜɟɲɢɜɚɸɳɟɝɨɤɚɧɚɬɚ, L
ɭ.ɤ
+ Ɛ3 + ʌȾɛnmɪ, ɦ
ɫmɪ
= ɇɨɦ
ɭ.ɤ
ɩ – ɤɨɥɢɱɟɫɬɜɨɩɪɢɧɹɬɵɯɞɜɢɝɚɬɟɥɟɣɲɬ
2.7.5. Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ ɢ ɡɚɦɟɞɥɟɧɢɹ ɩɨɞɴɟɦɧɨɣ ɭɫɬɚɧɨɜɤɢ
Ɉɩɪɟɞɟɥɟɧɢɟɪɚɰɢɨɧɚɥɶɧɨɝɨɭɫɤɨɪɟɧɢɹɨɫɭɳɟɫɬɜɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
ɇqpQɤF
=
ɚ
1
m
ɩɪ
ɩɤɪɚɫɧɨɦ
, ɦɫ
ɍɫɤɨɪɟɧɢɟɞɨɥɠɧɨɛɵɬɶɜɩɪɟɞɟɥɚɯɚ1 ɦɫ
ȿɫɥɢɚ
!ɦɫɬɨɜɪɚɫɱɟɬɚɯɫɥɟɞɭɟɬɩɪɢɧɢɦɚɬɶɚ1 ɦɫ
1
ȿɫɥɢɚ1 ɦɫɬɨɧɭɠɧɨɜɡɹɬɶɞɜɢɝɚɬɟɥɶɛɨɥɶɲɟɣɦɨɳɧɨɫɬɢɩɪɢɬɨɣ
ɠɟɩɪɢɧɹɬɨɣɫɢɧɯɪɨɧɧɨɣɱɚɫɬɨɬɟɜɪɚɳɟɧɢɹ
Ɂɚɦɟɞɥɟɧɢɟɜɵɱɢɫɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
=
ɚ
3
HqɪQɤ
ɩɤ
m
ɩɪ
ɦɫ
Ɂɧɚɱɟɧɢɟɡɚɦɟɞɥɟɧɢɹɞɨɥɠɧɨɛɵɬɶɜɞɢɚɩɚɡɨɧɟɚ3ɦɫ
ȿɫɥɢ ɜɟɥɢɱɢɧɚ ɡɚɦɟɞɥɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɮɨɪɦɭɥɟ ɛɭɞɟɬɞɨ
ɦɫɬɨɜɪɚɫɱɟɬɚɯɫɥɟɞɭɟɬɩɪɢɧɢɦɚɬɶɚ3 ɦɫ
ȿɫɥɢɪɚɫɱɟɬɧɨɟɡɧɚɱɟɧɢɟɚ
!ɦɫɬɨɜɷɬɨɦɫɥɭɱɚɟɡɚɦɟɞɥɟɧɢɟɫɥɟɞɭ
3
ɟɬɨɩɪɟɞɟɥɢɬɶɩɨɮɨɪɦɭɥɟ
ɚ3 =
m
HqɪQɤ
ɩɤ
ɩɪ
ɦɫ
2.7.6. Ɋɚɫɱɟɬ ɞɢɚɝɪɚɦɦɵ ɫɤɨɪɨɫɬɢ
ȼɪɟɦɹɞɜɢɠɟɧɢɹɫɤɢɩɚɜɪɚɡɝɪɭɡɨɱɧɵɯɤɪɢɜɵɯɢɟɝɨɭɫɤɨɪɟɧɢɟɜɷɬɨɬɩɟ
ɪɢɨɞ
h
t
o
=
o
ɫ
V
o
ɚɨ =
V
o
, ɦɫ
t
o
ɝɞɟ V0±ɫɤɨɪɨɫɬɶɞɜɢɠɟɧɢɹɫɨɫɭɞɚɧɚɜɯɨɞɟɢɜɵɯɨɞɟɢɡɪɚɡɝɪɭɡɨɱɧɵɯɤɪɢɜɵɯ
ɋɨɝɥɚɫɧɨɬɪɟɛɨɜɚɧɢɹɦɛɟɡɨɩɚɫɧɨɫɬɢV0ɦɫ
ȼɪɟɦɹɭɫɤɨɪɟɧɧɨɝɨɞɜɢɠɟɧɢɹɫɤɢɩɚɢɩɭɬɶɩɪɨɣɞɟɧɧɵɣɜɷɬɨɬɩɟɪɢɨɞ
VV
t
1
a
oɮmaɯ
ɫ
h
VV
PD[
oɮ
ɦ
t
ȼɪɟɦɹɫɬɨɩɨɪɟɧɢɹɫɤɢɩɚɢɩɭɬɶɩɪɨɣɞɟɧɧɵɣɜɬɟɱɟɧɢɟɷɬɨɝɨɩɟɪɢɨɞɚ
V
ɞ
t
ɫɬ
ɫ
a
ɫɬ
hɫɬ = 0,5ÂVɞÂtɫɬɦ
ɝɞɟ Vɞ ± ɫɤɨɪɨɫɬɶ ɞɨɬɹɠɤɢ ɋɨɝɥɚɫɧɨ ɬɪɟɛɨɜɚɧɢɹɦ ɛɟɡɨɩɚɫɧɨɫɬɢ Vɞ ·
·ɦɫ
ɚɫɬ ± ɡɚɦɟɞɥɟɧɢɟ ɫɬɨɩɨɪɟɧɢɹ ɋɨɝɥɚɫɧɨ ɬɪɟɛɨɜɚɧɢɹɦ ɛɟɡɨɩɚɫɧɨɫɬɢ ɚɫɬ
ɦɫ
ɉɭɬɶɞɨɬɹɠɤɢɫɤɢɩɚɢɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɷɬɨɝɨɩɟɪɢɨɞɚ
h
h
= ho – hɫɬ, ɦ; tɞ =
ɞ
ɞ
, ɫ
V
ɞ
ȼɪɟɦɹɡɚɦɟɞɥɟɧɧɨɝɨɞɜɢɠɟɧɢɹɢɩɭɬɶɩɪɨɣɞɟɧɧɵɣɜɬɟɱɟɧɢɟɷɬɨɝɨɩɟɪɢ
ɨɞɚ
VV
t
3
=
ɚ
ɫ t
h
VV
ɞɮmaɯɞɮmaɯ
, ɦ
ɉɭɬɶ ɩɪɨɣɞɟɧɧɵɣ ɜɨ ɜɪɟɦɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɞɜɢɠɟɧɢɹ ɢ ɩɪɨɞɨɥɠɢɬɟɥɶ
ɧɨɫɬɶɷɬɨɝɨɩɟɪɢɨɞɚ
h
h
= Hɩ – (2ho + h1 + h3), ɦ t2 =
2
, ɫ
V
ɮmaɯ
Ɏɚɤɬɢɱɟɫɤɨɟɜɪɟɦɹɞɜɢɠɟɧɢɹɫɤɢɩɚ
= to + t1 + t2 + t3 + tɞ + tɫɬɫ
T
ɮ
Ɏɚɤɬɢɱɟɫɤɚɹɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɩɨɞɴɟɦɧɨɝɨɰɢɤɥɚ
ɝɞɟ t
± ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɩɪɢ ɡɚɩɭɫɤɟ
ɩ.ɩ
ɩɨɞɴɟɦɧɨɝɨɞɜɢɝɚɬɟɥɹ t
ɫ
n.ɩ
Ɍ
ɰ.ɮ=Ɍɮ+tn+tɩ.ɩ
,
Ɏɚɤɬɢɱɟɫɤɚɹɱɚɫɨɜɚɹɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
=
ɮɱɚɫȺ
ɮɰ
ɬɱɚɫ
ȺmɌt
ɱɚɫɝ
ɉɨɫɬɪɨɟɧɢɟɞɢɚɝɪɚɦɦɵɭɫɢɥɢɣ
ɍɫɢɥɢɟɤɨɬɨɪɨɟɞɟɣɫɬɜɭɟɬ ɧɚ ɛɚɪɚɛɚɧɟ ɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɜ ɥɸɛɨɣ ɦɨ
ɦɟɧɬɜɪɟɦɟɧɢɩɪɢɞɜɢɠɟɧɢɢɫɤɢɩɨɜɨɩɪɟɞɟɥɹɟɬɫɹɭɪɚɜɧɟɧɢɟɦɚɤɚɞɟɦɢɤɚɆɆ
Ɏɟɞɨɪɨɜɚɤɨɬɨɪɨɟɢɦɟɟɬɜɢɞ
ɞɥɹɧɟɭɪɚɜɧɨɜɟɲɟɧɧɵɯɩɨɞɴɟɦɨɜ
= ɤÂQ + (pɤ – q)Â(Hn – 2ɯ) ± mɩɪÂɚɿɇ
F
ɿ
ɞɥɹɭɪɚɜɧɨɜɟɲɟɧɧɵɯɩɨɞɴɟɦɨɜ
F
= ɤÂQ ± mɩɪÂɚɿɇ
ɿ
ɝɞɟ x ± ɤɨɨɪɞɢɧɚɬɚ ɩɨɥɨɠɟɧɢɹ ɩɨɞɧɢɦɚɸɳɟɝɨɫɹ ɫɤɢɩɚ Ɉɧɚ ɫɱɢɬɵɜɚɟɬɫɹ ɨɬ
ɭɪɨɜɧɹɨɤɨɥɨɫɬɜɨɥɶɧɨɝɨɞɜɨɪɚɦ
ɚɿ±ɭɫɤɨɪɟɧɢɟɿɝɨɩɟɪɢɨɞɚɦɫ
Ⱦɥɹɩɨɫɬɪɨɟɧɢɹɞɢɚɝɪɚɦɦɵɭɫɢɥɢɣɢɯ ɪɚɫɫɱɢɬɵɜɚɸɬ ɜ ɤɨɧɬɪɨɥɶɧɵɯ ɬɨɱ
ɤɚɯɜɨ ɜɫɟɯ ɭɪɚɜɧɟɧɢɹɯ ɟɞɢɧɢɰɚɢɡɦɟɪɟɧɢɹ ɭɫɢɥɢɣ ± ɇȾɥɹ ɧɟɭɪɚɜɧɨɜɟɲɟɧ
ɧɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
)
F ɤ QpqHɩɬ ɚ
F ɤ QpqHɩ h ɬɚ
F ɤ QpqHɩ h ɬɚ
F ɤ QpqHɩ hh ɬɚ
F ɤ QpqHɩ hh
F ɤ QpqHɩ hhh
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ɤɩɪ
ɤɩɪ
>@
ɤɩɪ
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