Федоров М.П. и др. Информационно-компьютерные технологии в строительстве. Использование программы SCAD для расчета сооружений из плоских элементов
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120
ɡɚɝɪɭɠɟɧɢɣ (ɪɢɫ. 2.3).
Ɋɢɫ. 2.2
56.16
145.98
481.71
70.25
178
4.7
121
Ɋɢɫ. 2.3
188.41
140.22.
210.34
174.28
Ɉ
112
112
53.25
53.25
71.0
122
Ɋɢɫ. 2.4
Ⱦɥɹ ɤɨɧɬɪɨɥɹ ɪɚɜɧɨɜɟɫɢɹ ɫɬɟɧɤɢ ɜɵɲɟ ɩɨɞɨɲɜɵ ɩɨɫɬɭɩɢɦ ɬɚɤɢɦ ɠɟ
ɨɛɪɚɡɨɦ, ɤɚɤ ɜ ɜɚɪɢɚɧɬɟ ɫ ɠɟɫɬɤɢɦ ɨɫɧɨɜɚɧɢɟɦ: ɨɩɪɟɞɟɥɢɦ ɭɫɢɥɢɹ ɜ ɭɡɥɚɯ ɩɨ
ɥɢɧɢɢ ɤɨɧɬɚɤɬɚ ɫɬɟɧɤɢ ɫ ɨɫɧɨɜɚɧɢɟɦ.
Ⱦɥɹ ɢɥɥɸɫɬɪɚɰɢɢ ɨɝɪɚɧɢɱɢɦɫɹ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɬɨɥɶɤɨ ɫɭɦɦɚɪɧɨɝɨ
271.36
244.52
5.76
244.57
53.25
53.25
71.0
66
107
123
ɡɚɝɪɭɠɟɧɢɹ (ɤɨɦɛɢɧɚɰɢɟɣ ɡɚɝɪɭɠɟɧɢɣ 1 ɢ 2).
ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɵɩɨɥɧɟɧɢɹ ɩɪɨɰɟɞɭɪɵ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚɝɪɭɡɤɢ ɨɬ ɮɪɚɝɦɟɧɬɚ
ɫɯɟɦɵ ɩɪɢ ɤɨɦɛɢɧɢɪɨɜɚɧɧɨɦ ɧɚɝɪɭɠɟɧɢɢ ɫɬɟɧɤɢ, ɩɨɥɭɱɢɦ ɜɟɪɬɢɤɚɥɶɧɵɟ (ɪɢɫ.
2.5,
ɚ) ɢ ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ (Ɋɢɫ. 2.5, ɛ) ɭɫɢɥɢɹ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɨɫɧɨɜɚɧɢɟ ɜ
ɭɡɥɚɯ ɫɟɬɤɢ Ʉɗ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɩɨ ɩɨɞɨɲɜɟ.
Ɋɢɫ. 2.5
Ɂɧɚɤɢ ɷɬɢɯ ɭɫɢɥɢɣ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɩɪɚɜɢɥɚɦ ɡɚɞɚɧɢɹ ɜɧɟɲɧɢɯ ɧɚɝɪɭɡɨɤ ɧɚ
ɮɪɚɝɦɟɧɬ ɫɯɟɦɵ, ɤɨɬɨɪɵɦ ɹɜɥɹɟɬɫɹ ɩɨɥɭɩɥɨɫɤɨɫɬɶ, ɩɪɢɧɹɬɵɦ ɜ ɩɪɨɝɪɚɦɦɟ
SCAD. ɇɚ ɫɬɟɧɤɭ ɷɬɢ ɭɫɢɥɢɹ ɞɟɣɫɬɜɭɸɬ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
ɉɪɨɜɟɪɢɦ ɜɵɩɨɥɧɟɧɢɟ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ (1.1) ɫɬɟɧɤɢ ɩɪɢ
ɤɨɦɛɢɧɚɰɢɢ ɨɛɨɢɯ ɡɚɝɪɭɠɟɧɢɣ ɫɬɟɧɤɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɚɟɦ:
Q
o
=
¦
12
1
i
i
xi
R = – 260 ɤɇ.
N
o
= G =
¦
12
1
i
i
zi
R = – 475.04 ɤɇ.
M
o
=
i
i
i
xi
hR
¦
12
1
= – 133.2 ɤɇ·ɦ.
ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɩɪɨɜɟɪɤɟ ɩɟɪɜɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɟ ɡɚɛɵɬɶ ɜ ɭɡɥɟ ɫ ɧɨɦɟɪɨɦ 386 ɤ
ɝɨɪɢɡɨɧɬɚɥɶɧɨɦɭ ɞɚɜɥɟɧɢɸ ɧɚ ɨɫɧɨɜɚɧɢɟ -12.58 ɤɇ ɞɨɛɚɜɢɬɶ ɜɧɟɲɧɸɸ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ
ɭɡɥɨɜɭɸ ɧɚɝɪɭɡɤɭ, ɪɚɜɧɭɸ – 19.49 ɤɇ (ɫɦ. ɩɪɢɦɟɱɚɧɢɟ ɧɚ ɫɬɪ. 109 ɞɚɧɧɨɝɨ ɍɆɄ).
Ʉɚɤ ɜɢɞɢɦ (ɫɦ. ɪɚɡɞɟɥ 1. 7), ɩɨɝɪɟɲɧɨɫɬɶ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɟɪɜɵɯ ɞɜɭɯ
ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɩɨɥɭɱɚɟɬɫɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɭɥɟɜɨɣ, ɚ ɞɥɹ ɬɪɟɬɶɟɝɨ
ɭɪɚɜɧɟɧɢɹ ɫɨɫɬɚɜɥɹɟɬ ɩɪɢɦɟɪɧɨ 9% : (119 – 87)·100/342 = 9.36%).
ȼɵɜɨɞɵ ɩɨ ɪɚɛɨɬɟ
Ɋɟɡɭɥɶɬɚɬɵ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɩɟɪɜɨɦ ɢ ɜɬɨɪɨɦ ɪɚɡɞɟɥɚɯ ɪɚɛɨɬɵ ɩɨɡɜɨɥɹɸɬ
ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ.
1. ɉɨɞɚɬɥɢɜɨɫɬɶ ɨɫɧɨɜɚɧɢɹ ɜɥɢɹɟɬ ɧɚ ɇȾɋ ɫɬɟɧɤɢ ɢ ɨɫɧɨɜɚɧɢɹ ɜ ɡɨɧɟ ɢɯ
ɤɨɧɬɚɤɬɚ, ɩɨɷɬɨɦɭ ɪɚɫɱɟɬ ɇȾɋ ɞɨɥɠɟɧ ɩɪɨɜɨɞɢɬɶɫɹ ɩɨ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ,
ɚ)
ɛ)
Ɉ
124
ɭɱɢɬɵɜɚɸɳɟɣ ɞɟɮɨɪɦɚɬɢɜɧɵɟ ɫɜɨɣɫɬɜɚ ɨɫɧɨɜɚɧɢɹ.
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɪɢ ɭɱɟɬɟ ɞɟɮɨɪɦɚɬɢɜɧɵɯ ɫɜɨɣɫɬɜ ɨɫɧɨɜɚɧɢɹ ɩɭɬɟɦ
ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɪɢɛɥɢɠɟɧɧɨɣ ɥɢɧɟɣɧɨ-ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
ɦɟɬɨɞɚ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɜ ɜɢɞɟ, ɩɪɢɜɟɞɟɧɧɨɦ ɧɚ ɪɢɫ. 1.1 ɪɚɛɨɬɵ,
ɧɟɨɛɯɨɞɢɦɨ ɡɚɞɚɜɚɬɶ ɪɚɡɥɢɱɧɵɟ ɠɟɫɬɤɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɨɧɟɱɧɵɯ
ɷɥɟɦɟɧɬɨɜ ɫɬɟɧɤɢ ɢ ɨɫɧɨɜɚɧɢɹ.
2. Ⱦɥɹ ɛɨɥɟɟ ɩɨɥɧɨɝɨ ɢɡɭɱɟɧɢɹ ɇȾɋ ɜ ɡɨɧɟ ɫɯɟɦɵ, ɩɪɢɦɵɤɚɸɳɟɣ ɤ
ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ,
ɧɟɨɛɯɨɞɢɦɨ ɭɦɟɧɶɲɚɬɶ ɪɚɡɦɟɪɵ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɤ ɩɨɞɨɲɜɟ.
Ɉɫɨɛɟɧɧɨ ɷɬɨ ɠɟɥɚɬɟɥɶɧɨ ɫɞɟɥɚɬɶ ɜɛɥɢɡɢ ɬɨɱɟɤ ɩɟɪɟɫɟɱɟɧɢɹ ɫɪɟɞɢɧɧɵɯ
ɩɥɨɫɤɨɫɬɟɣ ɫɥɨɹ ɫɬɟɧɤɢ ɢ ɫɥɨɹ ɨɫɧɨɜɚɧɢɹ, ɢɦɟɸɳɢɯ ɜ ɡɚɞɚɱɟ ɨ ɩɥɨɫɤɨɣ
ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɧɤɢ ɟɞɢɧɢɱɧɭɸ ɬɨɥɳɢɧɭ.
3. ɍɦɟɧɶɲɟɧɢɟ ɪɚɡɦɟɪɨɜ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɢ ɜɛɥɢɡɢ ɝɪɚɧɢɰ ɪɚɫɱɟɬɧɨɣ
ɫɯɟɦɵ ɩɨɡɜɨɥɢɬ ɛɨɥɟɟ ɬɨɱɧɨ ɭɞɨɜɥɟɬɜɨɪɢɬɶ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɩɥɨɫɤɨɣ ɡɚɞɚɱɢ
ɬɟɨɪɢɢ
ɭɩɪɭɝɨɫɬɢ.
4. ȼɵɱɢɫɥɟɧɢɟ ɧɨɪɦɚɥɶɧɵɯ
z
V (NZ) ɢ ɤɚɫɚɬɟɥɶɧɵɯ
zx
W (TZX) ɧɚɩɪɹɠɟɧɢɣ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨ ɮɨɪɦɭɥɟ ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ ɢ ɩɨ ɮɨɪɦɭɥɟ ɀɭɪɚɜɫɤɨɝɨ,
ɩɨɥɭɱɟɧɧɵɯ ɞɥɹ ɬɨɧɤɨɣ ɛɚɥɤɢ ɧɟ ɭɱɢɬɵɜɚɸɬ ɜɥɢɹɧɢɹ ɧɢ ɠɟɫɬɤɨɝɨ, ɧɢ
ɞɟɮɨɪɦɢɪɭɟɦɨɝɨ ɨɫɧɨɜɚɧɢɹ ɧɚ ɇȾɋ ɛɚɥɤɢ-ɫɬɟɧɤɢ ɜ ɡɨɧɟ ɤɨɧɬɚɤɬɚ ɫɬɟɧɤɢ ɫ
ɨɫɧɨɜɚɧɢɟɦ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɷɬɢɯ ɮɨɪɦɭɥ ɞɥɹ ɛɚɥɤɢ-ɫɬɟɧɤɢ, ɢɦɟɸɳɟɣ ɨɞɧɭ ɢɥɢ
ɞɜɟ ɧɚɤɥɨɧɧɵɟ ɝɪɚɧɢ, ɡɚɜɟɞɨɦɨ ɧɟ ɛɭɞɭɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ ɝɪɚɧɢɱɧɵɟ
ɭɫɥɨɜɢɹ
(ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɬɪɟɭɝɨɥɶɧɨɝɨ ɜɢɞɚ ɷɥɟɦɟɧɬɨɜ).
5. Ɉɞɧɚɤɨ
ɜɵɱɢɫɥɟɧɢɟ ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɨ ɮɨɪɦɭɥɟ
ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ ɩɨɥɟɡɧɨ, ɬɚɤ ɤɚɤ ɷɩɸɪɵ, ɩɨɫɬɪɨɟɧɧɵɟ ɫ ɩɨɦɨɳɶɸ
ɷɬɨɣ ɮɨɪɦɭɥɵ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɢɬɶ ɥɢɧɟɣɧɵɟ ɷɩɸɪɵ ɢɫɤɨɦɵɯ ɧɚɩɪɹɠɟɧɢɣ
z
V
(NZ), ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɤɨɧɬɪɨɥɹ ɤɪɢɜɨɥɢɧɟɣɧɵɯ
ɷɩɸɪ, ɩɨɥɭɱɟɧɧɵɯ ɜ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ ɫ ɭɱɟɬɨɦ ɜɥɢɹɧɢɹ ɨɫɧɨɜɚɧɢɹ.
ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɢ ɬɟ ɢ ɞɪɭɝɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɷɩɸɪɵ
ɢɧɬɟɝɪɚɥɶɧɨ ɞɚɸɬ ɩɪɨɞɨɥɶɧɭɸ ɫɢɥɭ N
o
. ɉɨɷɬɨɦɭ ɩɥɨɳɚɞɶ ɤɪɢɜɨɥɢɧɟɣɧɨɣ
ɷɩɸɪɵ, ɩɨɥɭɱɟɧɧɚɹ ɜ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ ɫ ɭɱɟɬɨɦ ɜɥɢɹɧɢɹ ɨɫɧɨɜɚɧɢɹ,
ɪɚɫɩɨɥɨɠɟɧɧɚɹ ɜɵɲɟ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɷɩɸɪɵ ɢ ɩɥɨɳɚɞɶ, ɪɚɫɩɨɥɨɠɟɧɧɚɹ
ɧɢɠɟ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɷɩɸɪɵ ɢɦɟɸɬ ɪɚɡɧɵɟ ɡɧɚɤɢ ɢ ɜ ɫɭɦɦɟ ɞɨɥɠɧɵ ɛɵɬɶ
ɪɚɜɧɵ ɧɭɥɸ.
6. Ɍɚɤɨɣ ɠɟ ɫɦɵɫɥ ɢɦɟɟɬ ɩɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɨ
ɮɨɪɦɭɥɟ ɀɭɪɚɜɫɤɨɝɨ. ɉɥɨɳɚɞɢ ɤɪɢɜɨɥɢɧɟɣɧɵɯ ɷɩɸɪ, ɩɨɥɭɱɟɧɧɵɯ ɪɚɫɱɟɬɨɦ ɩɨ
125
ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ, ɫ ɨɪɞɢɧɚɬɚɦɢ ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɜɵɲɟ ɢ ɧɢɠɟ
ɩɚɪɚɛɨɥɢɱɟɫɤɨɣ ɷɩɸɪɵ, ɩɨɫɬɪɨɟɧɧɨɣ ɩɨ ɮɨɪɦɭɥɟ ɀɭɪɚɜɫɤɨɝɨ, ɜ ɫɭɦɦɟ ɞɨɥɠɧɵ
ɛɵɬɶ ɪɚɜɧɵ ɧɭɥɸ.
ɋɩɢɫɨɤ ɭɱɟɛɧɵɯ ɩɨɫɨɛɢɣ ɤ ɪɚɛɨɬɟ (ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɤ ɍɆɄ)
1. Ʉɨɧɫɬɚɧɬɢɧɨɜ ɂ.Ⱥ., Ʌɚɥɢɧ ȼ.ȼ., Ʌɚɥɢɧɚ ɂ.ɂ. Ɍɟɨɪɢɹ ɭɩɪɭɝɨɫɬɢ. Ɋɚɫɱɟɬ ɩɥɨɫɤɢɯ
ɷɥɟɦɟɧɬɨɜ ɫɨɨɪɭɠɟɧɢɣ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD. ɍɱɟɛ. ɩɨɫɨɛɢɟ. ɂɡɞ-ɜɨ
ɉɨɥɢɬɟɯɧ. ɭɧ-ɬɚ. 2007. 87 ɫ.
2. Ʉɨɧɫɬɚɧɬɢɧɨɜ ɂ.Ⱥ., Ʌɚɥɢɧ ȼ.ȼ., Ʌɚɥɢɧɚ ɂ.ɂ
. ɋɬɪɨɢɬɟɥɶɧɚɹ ɦɟɯɚɧɢɤɚ. ɑɚɫɬɶ 1.
Ɋɚɫɱɟɬ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD:
ɍɱɟɛ. ɩɨɫɨɛɢɟ. ɋɉɛ: ɂɡɞ-ɜɨ ɉɨɥɢɬɟɯɧ. ɭɧ-ɬɚ, 2008. 260 ɫ.
3. ɍɱɟɛɧɵɟ ɡɚɞɚɧɢɹ ɩɨ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ. Ɇɚɲɢɧɨɩɢɫɧɵɣ ɬɟɤɫɬ ɢ ɷɥɟɤɬɪɨɧɧɚɹ ɮɨɪɦɚ
ɜ ɫɟɬɢ ɭɱɟɛɧɨɝɨ ɤɥɚɫɫɚ (ɚɭɞ. 404 ȽɄ-2 ɋɉɛȽɉɍ).
ɑȺɋɌɖ 4. ɉɊɂɆȿɊ ɂɋɉɈɅɖɁɈȼȺɇɂə ɉɊɈȽɊȺɆɆɕ SCAD
ȾɅə ȼɕɉɈɅɇȿɇɂə ɇȺɍɑɇɈ – ɂɋɋɅȿȾɈȼȺɌȿɅɖɋɄɈɃ ɊȺȻɈɌɕ
ɋɌɍȾȿɇɌȺ (ɇɂɊɋ)
ȼ ɭɱɟɛɧɨɦ ɩɪɨɰɟɫɫɟ ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɢɧɠɟɧɟɪɨɜ-ɫɬɪɨɢɬɟɥɟɣ ɜɚɠɧɨ ɞɚɬɶ
ɭɱɚɳɟɦɭɫɹ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɜɥɢɹɧɢɢ ɪɚɡɥɢɱɧɵɯ ɮɚɤɬɨɪɨɜ (ɧɚɩɪɢɦɟɪ,
ɢɡɦɟɧɟɧɢɹ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɨɨɪɭɠɟɧɢɹ, ɮɢɡɢɤɨ-ɦɟɯɚɧɢɱɟɫɤɢɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɦɚɬɟɪɢɚɥɚ ɢ ɬ.ɞ.) ɧɚ ɟɝɨ ɇȾɋ.
ɉɪɢɦɟɧɟɧɢɟ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɫɱɟɬɧɵɯ ɪɚɛɨɬ ɫɬɭɞɟɧɬɨɜ ɉɄ ɢ
ɫɨɜɪɟɦɟɧɧɵɯ ɉȼɄ, ɧɚɩɪɢɦɟɪ SCAD, ɩɨɡɜɨɥɹɟɬ ɷɬɨ ɫɞɟɥɚɬɶ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɨ.
Ⱦɥɹ ɷɬɨɝɨ ɦɨɠɧɨ ɜɜɟɫɬɢ ɜ
ɡɚɞɚɧɢɹ ɩɨ ɪɚɫɱɟɬɧɵɦ ɪɚɛɨɬɚɦ ɫɬɭɞɟɧɬɨɜ ɷɥɟɦɟɧɬ
ɧɚɭɱɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɤɚɤ ɷɬɨ (ɱɚɫɬɢɱɧɨ) ɛɵɥɨ ɫɞɟɥɚɧɨ ɜ ɩɪɟɞɵɞɭɳɟɦ
ɩɪɢɦɟɪɟ ɨɩɪɟɞɟɥɟɧɢɹ ɇȾɋ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ.
Ɇɨɠɧɨ, ɞɥɹ ɯɨɪɨɲɨ ɭɫɩɟɜɚɸɳɢɯ ɫɬɭɞɟɧɬɨɜ, ɫɪɚɡɭ ɜɵɞɚɬɶ ɡɚɞɚɧɢɟ ɧɚ
ɜɵɩɨɥɧɟɧɢɟ ɜ ɭɱɟɛɧɨɦ ɩɪɨɰɟɫɫɟ ɇɂɊɋ. Ⱦɚɥɟɟ ɩɪɢɜɟɞɟɧ ɩɪɢɦɟɪ ɜɵɩɨɥɧɟɧɢɹ
ɬɚɤɨɣ ɪɚɛɨɬɵ. ɉɨɫɬɚɜɥɟɧɚ ɡɚɞɚɱɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɥɢɹɧɢɹ ɧɚ ɇȾɋ ɛɟɬɨɧɧɨɣ
ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ, ɪɚɛɨɬɚɸɳɟɣ
ɜ ɭɫɥɨɜɢɹɯ ɩɥɨɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɤɚɤ ɛɚɥɤɚ –
ɫɬɟɧɤɚ [6], ɢɡɦɟɧɟɧɢɹ ɞɟɮɨɪɦɢɪɭɟɦɨɫɬɢ ɝɪɭɧɬɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ,
ɯɚɪɚɤɬɟɪɢɡɭɟɦɨɝɨ ɫɨɨɬɧɨɲɟɧɢɟɦ
E
ɨɫ
/E
ɫɬ
ɦɨɞɭɥɹ ɭɩɪɭɝɨɫɬɢ E
ɫɬ
ɦɚɬɟɪɢɚɥɚ ɫɬɟɧɤɢ
ɢ ɦɨɞɭɥɹ ɞɟɮɨɪɦɚɰɢɢ
E
ɨɫ
ɝɪɭɧɬɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ, ɧɚ ɤɨɬɨɪɨɟ ɨɩɢɪɚɟɬɫɹ ɫɬɟɧɤɚ.
ɉɪɢ ɷɬɨɦ ɞɟɦɨɧɫɬɪɢɪɭɸɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɡɞɟɥɟɧɢɹ ɬɟɦɚɬɢɤɢ ɇɂɊɋ, ɩɨ
ɧɚɩɪɚɜɥɟɧɢɹɦ, ɧɚɩɪɢɦɟɪ: 1. ɂɫɫɥɟɞɨɜɚɧɢɟ ɢɡɦɟɧɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɩɨ ɥɢɧɢɢ
ɤɨɧɬɚɤɬɚ ɫɬɟɧɤɢ ɫ ɝɪɭɧɬɨɜɵɦ ɨɫɧɨɜɚɧɢɟɦ; 2. ɂɡɭɱɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɇȾɋ ɫɬɟɧɤɢ
ɩɨ ɟɟ ɜɵɫɨɬɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɟɮɨɪɦɚɰɢɢ ɨɫɧɨɜɚɧɢɹ ɫɬɟɧɤɢ; 3.ɂɡɭɱɟɧɢɟ
ɤɨɧɰɟɧɬɪɚɰɢɢ ɧɚɩɪɹɠɟɧɢɣ ɜ ɡɨɧɟ ɭɝɥɨɜɵɯ ɬɨɱɟɤ ɩɨɞɨɲɜɵ; ɢɬ.ɞ.
126
ɋȺɇɄɌ-ɉȿɌȿɊȻɍɊȽɋɄɂɃ
ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɉɈɅɂɌȿɏɇɂɑȿɋɄɂɃ
ɍɇɂȼȿɊɋɂɌȿɌ
ɂɇɀȿɇȿɊɇɈ ɋɌɊɈɂɌȿɅɖɇɕɃ ɎȺɄɍɅɖɌȿɌ
Ʉɚɮɟɞɪɚ ɝɪɚɠɞɚɧɫɤɨɝɨ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɢ ɩɪɢɤɥɚɞɧɨɣ ɷɤɨɥɨɝɢɢ
ɂɇɎɈɊɆȺɐɂɈɇɇɈ-ɄɈɆɉɖɘɌȿɊɇɕȿ
ɌȿɏɇɈɅɈȽɂɂ ȼ ɋɌɊɈɂɌȿɅɖɋɌȼȿ
ɈɌɑȿɌ
ɨ ɜɵɩɨɥɧɟɧɢɢ ɇɂɊɋ
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɩɪɨɝɪɚɦɦɵ SCAD ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɥɢɹɧɢɹ
ɞɟɮɨɪɦɚɰɢɢ ɨɫɧɨɜɚɧɢɹ ɤɨɧɫɨɥɶɧɨɣ ɛɚɥɤɢ-ɫɬɟɧɤɢ ɧɚ ɟɟ ɇȾɋ
ȼɵɩɨɥɧɢɥ ɫɬɭɞɟɧɬ ɝɪɭɩɩɵ
Ɉɰɟɧɤɚ ɪɚɛɨɬɵ ɩɪɟɩɨɞɚɜɚɬɟɥɟɦ
ɋ.-ɉɟɬɟɪɛɭɪɝ
2009
127
1. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ
Ɋɚɫɫɦɨɬɪɢɦ ɛɟɬɨɧɧɭɸ ɩɨɞɩɨɪɧɭɸ ɫɬɟɧɤɭ ɫ ɩɨɩɟɪɟɱɧɵɦ ɫɟɱɟɧɢɟɦ
ɬɪɟɭɝɨɥɶɧɨɝɨ ɜɢɞɚ (ɪɢɫ. 1).
Ɋɢɫ. 1
Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɫɬɟɧɤɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɢ
ɭɤɚɡɚɧɧɨɝɨ ɧɚ ɪɢɫ. 1 ɞɚɜɥɟɧɢɹ ɧɚ ɟɟ ɝɪɚɧɶ ɜ ɭɫɥɨɜɢɹɯ ɩɥɨɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ. ȼ
ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɇȾɋ ɫɬɟɧɤɢ ɢɡ ɧɟɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ Y
ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɩɥɨɫɤɨɫɬɢ XZ (ɫɦ. ɪɢɫ.1) ɜɵɞɟɥɹɟɬɫɹ ɫɥɨɣ ɬɨɥɳɢɧɨɣ b = 1 ɦ,
ɚ ɜɫɟ ɧɚɝɪɭɡɤɢ ɢ ɢɫɤɨɦɵɟ ɜɟɥɢɱɢɧɵ ɇȾɋ ɨɬɧɨɫɹɬɫɹ ɤ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ
ɫɥɨɹ, ɥɟɠɚɳɟɣ ɜ ɩɥɨɫɤɨɫɬɢ XZ.
Ɍɪɟɭɝɨɥɶɧɵɣ ɩɪɨɮɢɥɶ ɫɬɟɧɤɢ ɜɵɛɪɚɧ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ
ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɨɝɨ ɜ ɡɚɝɥɚɜɢɢ ɪɚɛɨɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɧɚɱɚɥɚ ɢɫɩɨɥɶɡɨɜɚɬɶ
ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ, ɩɨɥɭɱɟɧɧɨɟ ɮɪɚɧɰɭɡɫɤɢɦ ɭɱɟɧɵɦ
Ɇ.Ʌɟɜɢ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ ɧɚɩɪɹɠɟɧɢɣ ɞɥɹ ɫɬɟɧɤɢ ɬɪɟɭɝɨɥɶɧɨɝɨ ɩɪɨɮɢɥɹ
ɛɟɫɤɨɧɟɱɧɨɣ ɜɵɫɨɬɵ (ɫɦ. ɪɢɫ. 1 ɩɪɢ H =
f ).
Ⱦɥɹ ɬɚɤɨɝɨ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɜɚɪɢɚɧɬɚ ɜɵɞɟɥɟɧɧɨɝɨ ɫɥɨɹ ɫɬɟɧɤɢ ɟɞɢɧɢɱɧɨɣ
ɬɨɥɳɢɧɵ ɩɨɥɭɱɚɟɬɫɹ ɇȾɋ ɫɬɟɧɤɢ ɜ ɭɫɥɨɜɢɹɯ ɩɥɨɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɛɟɡ ɭɱɟɬɚ
ɜɥɢɹɧɢɹ ɤɨɧɬɚɤɬɚ ɫɬɟɧɤɢ ɩɨ ɟɟ ɩɨɞɨɲɜɟ ɫ ɝɪɭɧɬɨɜɵɦ ɨɫɧɨɜɚɧɢɟɦ.
ȼ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ (ɩɪɢ ɤɨɧɟɱɧɨɦ ɡɧɚɱɟɧɢɢ ɜɵɫɨɬɵ H ɫɬɟɧɤɢ ɢ ɭɱɟɬɟ ɟɟ
ɤɨɧɬɚɤɬɚ ɫ ɨɫɧɨɜɚɧɢɟɦ) ɇȾɋ ɫɬɟɧɤɢ ɢɡɦɟɧɢɬɫɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɇȾɋ ɫɬɟɧɤɢ,
ɩɨɥɭɱɟɧɧɨɦ
ɜ ɬɟɨɪɟɬɢɱɟɫɤɨɦ ɜɚɪɢɚɧɬɟ. ɉɪɢ ɷɬɨɦ, ɤɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɜ ɨɬɱɟɬɟ
ɩɨ ɪɚɛɨɬɟ 1 ɍɆɄ, ɧɚ ɷɬɨ ɢɡɦɟɧɟɧɢɟ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɢ ɤɚɱɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ
ɢɡɦɟɧɟɧɢɟ ɠɟɫɬɤɨɫɬɢ ɝɪɭɧɬɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ.
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɜɵɩɨɥɧɟɧɨ ɢɫɫɥɟɞɨɜɚɧɢɟ ɢɡɦɟɧɟɧɢɹ ɇȾɋ ɫɬɟɧɤɢ
ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɡɦɟɧɟɧɢɹ ɦɨɞɭɥɹ ɞɟɮɨɪɦɚɰɢɢ E
oɫ
– ɩɚɪɚɦɟɬɪɚ,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɝɨ ɠɟɫɬɤɨɫɬɶ ɝɪɭɧɬɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ.
H
3
H
G
h/3
2h/3
1
2
E
h = H Etg
Z
Y
h = H Etg
R
H
Hq
H 1
J
X
128
ɑɬɨɛɵ ɜɵɩɨɥɧɢɬɶ ɬɚɤɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ
ɫɬɟɧɤɢ (ɫɦ. ɪɢɫ. 1 ɞɚɧɧɨɝɨ ɨɬɱɟɬɚ) ɜɟɥɢɱɢɧɭ h = Htg
E ɩɨɫɬɨɹɧɧɨɣ ɩɪɢ ɡɚɞɚɧɧɵɯ
ɩɨɫɬɨɹɧɧɵɯ ɡɧɚɱɟɧɢɹɯ H ɢ
E . Ɇɨɞɭɥɶ E
ɫɬ
ɭɩɪɭɝɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɫɬɟɧɤɢ ɬɚɤɠɟ
ɛɭɞɟɦ ɩɨɥɚɝɚɬɶ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɹ ɛɟɬɨɧɚ ɤɥɚɫɫɚ ȼ25.
Ƚɪɭɧɬɨɜɨɟ ɨɫɧɨɜɚɧɢɟ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ ɥɢɧɟɣɧɨ –
ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɫ ɦɨɞɭɥɟɦ ɭɩɪɭɝɨɫɬɢ ɪɚɜɧɨɦ ɦɨɞɭɥɸ
ɞɟɮɨɪɦɚɰɢɢ ɝɪɭɧɬɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ, ɩɪɢɧɹɜ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɪɹɞ ɤɨɧɤɪɟɬɧɵɯ
ɡɧɚɱɟɧɢɣ E
oɫ
= k·ȿ
ɫɬ
, ɝɞɟ k = 1000; 100; 10; 4; 2; 1; 0.5; 0.25; 0,1; 0.01; 0.001.
Ⱦɥɹ ɭɱɟɬɚ ɜɥɢɹɧɢɹ ɞɟɮɨɪɦɚɰɢɢ ɭɩɪɭɝɨɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ, ɦɨɞɟɥɢɪɭɸɳɟɣ
ɝɪɭɧɬɨɜɨɟ ɨɫɧɨɜɚɧɢɟ, ɧɚ ɇȾɋ ɫɬɟɧɤɢ ɩɪɢɦɟɦ ɟɳɟ ɧɟɤɨɬɨɪɵɟ ɞɨɩɭɳɟɧɢɹ.
ɉɪɢ ɫɨɫɬɚɜɥɟɧɢɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɛɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ
ɨɧɚ ɧɟɜɟɫɨɦɚ ɢ ɟɟ ɞɟɮɨɪɦɚɰɢɢ ɛɭɞɭɬ ɜɵɡɵɜɚɬɶɫɹ ɬɨɥɶɤɨ ɧɚɩɪɹɠɟɧɢɹɦɢ,
ɩɟɪɟɞɚɸɳɢɦɢɫɹ ɨɬ ɫɬɟɧɤɢ ɩɨ ɟɟ ɩɨɞɨɲɜɟ, ɤɨɬɨɪɭɸ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɧɟɪɚɡɪɵɜɧɨ
ɫɜɹɡɚɧɧɨɣ ɫ ɩɨɥɭɩɥɨɫɤɨɫɬɶɸ ɜɨ ɜɫɟɯ
ɬɨɱɤɚɯ ɤɨɧɬɚɤɬɚ.
ɂɡɜɟɫɬɧɨ (ɫɦ. ɧɚɩɪɢɦɟɪ,[11]), ɱɬɨ ɞɟɮɨɪɦɚɰɢɢ ɨɫɧɨɜɚɧɢɣ ɫɨɨɪɭɠɟɧɢɣ
ɞɨɫɬɚɬɨɱɧɨ ɛɵɫɬɪɨ ɭɦɟɧɶɲɚɸɬɫɹ ɫ ɭɞɚɥɟɧɢɟɦ ɨɬ ɩɨɞɨɲɜɵ ɫɨɨɪɭɠɟɧɢɹ.
ɉɨɷɬɨɦɭ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɞɟɥɚɟɦ ɞɨɩɭɳɟɧɢɟ ɨɛ ɨɬɫɭɬɫɬɜɢɢ
ɩɟɪɟɦɟɳɟɧɢɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɩɨ ɤɨɧɬɭɪɭ ɧɚ ɞɨɫɬɚɬɨɱɧɨɦ ɭɞɚɥɟɧɢɢ ɨɬ ɩɨɞɨɲɜɵ
ɫɬɟɧɤɢ. ɍɩɪɨɳɚɹ ɡɚɞɚɱɭ, ɩɪɢɦɟɦ ɬɚɤɢɦ ɤɨɧɬɭɪ 3-4-5-6 ɩɨɥɭɩɥɨɫɤɨɫɬɢ (ɪɢɫ. 2).
Ɋɢɫ.2
Hq
H
1
J
2
h =H Etg
0.5h
1
E
o
H
C
E
h
3h
3
4
5
6
0.5
h
E
ɛ
129
ɉɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ ɜɵɩɨɥɧɢɦ ɧɚ ɉɄ ɦɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɫ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD.
2. Ʉɨɦɩɨɧɟɧɬɵ ɧɚɩɪɹɠɟɧɢɣ ɜ ɫɬɟɧɤɟ ɬɪɟɭɝɨɥɶɧɨɝɨ ɩɪɨɮɢɥɹ
ɛɟɡ ɭɱɟɬɚ ɜɥɢɹɧɢɹ ɟɟ ɤɨɧɬɚɤɬɚ ɫ ɝɪɭɧɬɨɜɵɦ ɨɫɧɨɜɚɧɢɟɦ
ȼɵɪɚɠɟɧɢɹ ɞɥɹ ɤɨɦɩɨɧɟɧɬɨɜ ɧɚɩɪɹɠɟɧɢɣ ɜ ɩɨɩɟɪɟɱɧɨɦ ɫɟɱɟɧɢɢ ɫɬɟɧɤɢ,
ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɭɫɥɨɜɢɹɯ ɩɥɨɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ, ɩɨɥɭɱɟɧɵ Ɇ.Ʌɟɜɢ ɫ ɩɨɦɨɳɶɸ
ɮɭɧɤɰɢɢ ɧɚɩɪɹɠɟɧɢɣ [7, 9]. Ⱦɥɹ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ, ɭɤɚɡɚɧɧɨɣ ɧɚ ɪɢɫ. 1, ɷɬɢ
ɜɵɪɚɠɟɧɢɹ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
z
x 1
J V ;
)zctg()ctg2ctg(
2
1ɫɬ
3
1ɫɬ
EJJEJEJ V x
z
;
x
xz
EJ W
2
1
ctg .
(1)
Ɂɞɟɫɶ
J
ɫɬ
– ɨɛɴɟɦɧɵɣ ɜɟɫ ɛɟɬɨɧɚ ɫɬɟɧɤɢ;
1
J
= q
H
/H – ɩɨɫɬɨɹɧɧɚɹ ɜɟɥɢɱɢɧɚ,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɧɚɝɪɭɡɤɢɧɚ
ɜɟɪɬɢɤɚɥɶɧɭɸ ɫɬɨɪɨɧɭ ɬɪɟɭɝɨɥɶɧɨɝɨ ɩɪɨɮɢɥɹ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫɬɟɧɤɢ.
ɉɪɢ ɷɬɨɦ ɭɞɨɜɥɟɬɜɨɪɹɸɬɫɹ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ
z
x 1
J V ; 0 W
xz
(2)
ɧɚ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɨɪɨɧɟ ɫɬɟɧɤɢ (
x = 0) ɢ ɧɚ ɟɟ ɧɚɤɥɨɧɧɨɣ ɫɬɨɪɨɧɟ (x =z tgE ):
0sincos
EWEV
zxx
;
0sincos EVEW
zxz
.
(3)
ɉɪɢɜɟɞɟɦ ɷɩɸɪɵ ɭɤɚɡɚɧɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ ɧɚɩɪɹɠɟɧɢɣ ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ
ɞɥɹ ɱɚɫɬɧɨɝɨ ɫɥɭɱɚɹ (ɩɪɢ
z= H ɢ tg E = 0.75) ɩɪɢ ɡɚɝɪɭɠɟɧɢɹɯ:
x ɬɨɥɶɤɨ ɫɨɛɫɬɜɟɧɧɵɦ ɜɟɫɨɦ ɫɬɟɧɤɢ (ɪɢɫ. 3, ɚ);
x ɬɨɥɶɤɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɧɚɝɪɭɡɤɨɣ ɧɚ ɜɟɪɬɢɤɚɥɶɧɭɸ ɛɨɤɨɜɭɸ ɝɪɚɧɶ
ɫɬɟɧɤɢ (ɪɢɫ. 3,
ɛ;
x ɤɨɦɛɢɧɚɰɢɟɣ ɞɜɭɯ ɩɪɟɞɵɞɭɳɢɯ ɡɚɝɪɭɠɟɧɢɣ (ɪɢɫ. 3, ɜ).
ɂɡ ɪɢɫ. 3,
ɚ, ɛ, ɜ ɜɢɞɧɨ, ɱɬɨ ɷɩɸɪɵ ɩɪɢ ɤɨɦɛɢɧɚɰɢɢ ɡɚɝɪɭɠɟɧɢɣ
ɩɨɥɭɱɚɸɬɫɹ ɩɪɨɫɬɵɦ ɫɥɨɠɟɧɢɟɦ ɨɪɞɢɧɚɬ ɜ ɬɨɱɤɚɯ 1 ɢ 2 ɩɨɞɨɲɜɵ ɫɬɟɧɤɢ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɩɸɪ ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ ɢ ɨɬ ɞɚɜɥɟɧɢɹ ɧɚ ɟɟ
ɛɨɤɨɜɭɸ ɝɪɚɧɶ. ɉɪɢ ɷɬɨɦ ɜɢɞɧɨ, ɱɬɨ ɨɪɞɢɧɚɬɚ
EJJ V
2
1ɫɬ1,
ctgHH
z
ɷɩɸɪɵ
Z
V ɜ ɬɨɱɤɟ 1 ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨ ɡɚɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɚɯ, ɜɯɨɞɹɳɢɯ ɜ ɩɪɢɜɟɞɟɧɧɨɟ
ɨɛɳɟɟ ɜɵɪɚɠɟɧɢɟ, ɦɨɠɟɬ ɩɨɥɭɱɢɬɶɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɣ, ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɢ ɪɚɜɧɨɣ
ɧɭɥɸ. ȼɢɞɧɨ ɬɚɤɠɟ, ɱɬɨ ɦɨɠɧɨ, ɧɚɡɧɚɱɢɜ ɜɵɫɨɬɭ ɫɬɟɧɤɢ
H, ɪɟɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ
ɜɟɥɢɱɢɧ
1
J
ɢ
J
cɬ
ɢ ɧɟɨɛɯɨɞɢɦɨɟ ɪɚɫɱɟɬɱɢɤɭ ɡɧɚɱɟɧɢɟ ɢ ɡɧɚɤ ɧɚɩɪɹɠɟɧɢɹV
z,1
,
ɩɨɥɭɱɢɬɶ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ
E ɫɬɟɧɤɢ (ɭɝɥɚ ɧɚɤɥɨɧɚ ɟɟ ɧɢɡɨɜɨɣ ɝɪɚɧɢ).