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6. ɇȿɂɇȿɊɐɂȺɅɖɇɕȿ ɋɂɋɌȿɆɕ ɈɌɋɑȿɌȺ
Z
6.1. Ʉɪɚɬɤɢɟ ɫɜɟɞɟɧɢɹ ɢɡ ɬɟɨɪɢɢ
Ɋɟɲɟɧɢɟ ɡɚɞɚɱ ɜ ɦɟɯɚɧɢɤɟ ɧɚɱɢɧɚɟɬɫɹ ɫ ɜɵɛɨɪɚ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɦɟɯɚɧɢɱɟɫɤɢɟ ɹɜɥɟɧɢɹ ɨɤɚɡɵɜɚɟɬɫɹ ɭɞɨɛɧɨ ɨɩɢɫɵɜɚɬɶ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ,
ɤɨɬɨɪɭɸ ɧɚɡɜɚɥɢ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɨɣ – ɷɬɨ «ɚɛɫɨɥɸɬɧɚɹ» ɧɟɩɨɞɜɢɠɧɚɹ ɫɢɫɬɟɦɚ. Ⱦɪɭɝɢɟ ɫɢɫɬɟɦɵ, ɞɜɢɠɭɳɢɟɫɹ ɪɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ
«ɚɛɫɨɥɸɬɧɨɣ», ɬɚɤɠɟ ɹɜɥɹɟɬɫɹ ɢɧɟɪɰɢɚɥɶɧɵɦɢ. ɋɥɟɞɭɟɬ ɨɫɨɛɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ
ɬɚɤɚɹ «ɚɛɫɨɥɸɬɧɚɹ» ɫɢɫɬɟɦɚ ɨɬɫɱɟɬɚ ɹɜɥɹɟɬɫɹ
ɥɟɧɧɵɯ ɭɫɥɨɜɢɹɯ, ɫ ɯɨɪɨɲɟɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ, ɬɚɤɢɦɢ ɫɢɫɬɟɦɚɦɢ ɦɨɝɭɬ ɫɥɭɠɢɬɶ ɝɟɥɢɨ- ɢ ɝɟɨɰɟɧɬɪɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ, ɚ ɬɚɤɠɟ ɫɢɫɬɟɦɚ, ɫɜɹɡɚɧɧɚɹ ɫ ɰɟɧɬɪɨɦ
ɦɚɫɫ ɧɚɲɟɣ Ƚɚɥɚɤɬɢɤɢ ɢ ȼɫɟɥɟɧɧɨɣ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɜ ɩɨɜɫɟɞɧɟɜɧɨɣ ɩɪɚɤɬɢɤɟ ɧɚɦ
ɱɚɫɬɨ ɩɪɢɯɨɞɢɬɫɹ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɞɜɢɠɟɧɢɟ ɬɟɥ ɜ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ, ɞɜɢɠɭɳɢɯɫɹ
ɫ ɭɫɤɨɪɟɧɢɟɦ.
ɉɪɟɞɫɬɚɜɢɦ ɫɟɛɟ
ɞɢɬɫɹ ɧɚɛɥɸɞɚɬɟɥɶ, ɠɟɫɬɤɨ ɫɜɹɡɚɧɧɵɣ ɫ ɥɟɜɨɣ ɫɬɟɧɤɨɣ (ɪɢɫ. 6.1). ɇɚ ɢɞɟɚɥɶɧɨ
ɝɥɚɞɤɨɦ ɩɨɥɭ ɧɚɯɨɞɢɬɫɹ ɲɚɪ, ɚ ɤ ɩɨɬɨɥɤɭ ɜɚɝɨɧɚ ɧɚ ɧɢɬɢ ɩɨɞɜɟɲɟɧ ɞɪɭɝɨɣ ɲɚɪ.
ȼɬɨɪɨɣ ɧɚɛɥɸɞɚɬɟɥɶ ɧɚɯɨɞɢɬɫɹ ɧɚ Ɂɟɦɥɟ. ȼɚɝɨɧ ɧɚɱɢɧɚɟɬ ɞɜɢɠɟɧɢɟ ɫ ɭɫɤɨɪɟ-
G
ɧɢɟɦ
a
ɨɬɧɨɫɢɬɟɥɶɧɨ Ɂɟɦɥɢ. ɑɟɦɭ ɪɚɜɧɵ ɭɫɤɨɪɟɧɢɹ ɬɟɥ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɷɬɢɯ
ɧɚɛɥɸɞɚɬɟɥɟɣ?
ɜɚɝɨɧ ɩɨɟɡɞɚ, ɤɨɬɨɪɵɣ ɧɚɯɨɞɢɬɫɹ ɜ ɩɨɤɨɟ. ȼ ɜɚɝɨɧɟ ɧɚɯɨ-
ȼɜɟɞɟɧɢɟ
ɢɞɟɚɥɢɡɚɰɢɟɣ. Ʌɢɲɶ ɩɪɢ ɨɩɪɟɞɟ-
Ɋɢɫ. 6.1
ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ
ɩɨɞɜɟɲɟɧɧɵɣ ɧɚ ɧɢɬɢ, ɩɪɢɯɨɞɢɬ ɜ ɞɜɢɠɟɧɢɟ, ɩɪɢ ɷɬɨɦ ɧɢɬɶ ɨɬɤɥɨɧɹɟɬɫɹ ɜɩɪɚɜɨ
ɨɬ ɜɟɪɬɢɤɚɥɢ ɢ ɫɩɭɫɬɹ ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɫɬɚɧɟɬ ɧɟɢɡɦɟɧɧɵɦ.
ɍɫɤɨɪɟɧɢɟ ɷɬɨɝɨ ɲɚɪɚ, ɤɚɤ ɢ ɩɨɟɡɞɚ, ɪɚɜɧɨ
ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ
ɧɨ
aG ɢ ɲɚɪ ɛɭɞɟɬ ɞɜɢɝɚɬɶɫɹ ɤ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɣ ɫɬɟɧɤɟ. ɒɚɪ, ɩɨɞɜɟɲɟɧɧɵɣ
ɧɚ ɧɢɬɢ, ɧɚɱɢɧɚɟɬ ɞɜɢɝɚɬɶɫɹ ɫ ɭɫɤɨɪɟɧɢɟɦ
ɭɫɤɨɪɟɧɢɟ ɫɬɚɧɟɬ ɪɚɜɧɵɦ ɧɭɥɸ.
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɩɥɚɬɮɨɪɦɭ, ɪɚɜɧɨɦɟɪɧɨ ɜɪɚɳɚɸɳɭɸɫɹ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ
ɤɨɬɨɪɨɝɨ ɩɪɢɜɹɡɚɧɚ ɧɢɬɶ ɫ ɲɚɪɨɦ. ɑɟɦɭ ɪɚɜɧɨ ɭɫɤɨɪɟɧɢɟ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɞɜɭɯ
ɧɚɛɥɸɞɚɬɟɥɟɣ (ɪɢɫ. 6.2)?
71
G
. ɇɚ ɩɥɚɬɮɨɪɦɟ ɩɨɦɟɳɟɧ ɜɟɪɬɢɤɚɥɶɧɵɣ ɫɬɟɪɠɟɧɶ, ɤ ɜɟɪɯɧɟɦɭ ɤɨɧɰɭ
ɧɚɛɥɸɞɚɬɟɥɹ ɧɚ Ɂɟɦɥɟ ɲɚɪ ɧɚ ɩɨɥɭ ɨɫɬɚɟɬɫɹ ɧɚ ɦɟɫɬɟ. ɒɚɪ,
G
a
.
ɧɚɛɥɸɞɚɬɟɥɹ ɜ ɜɚɝɨɧɟ ɭɫɤɨɪɟɧɢɟ ɲɚɪɚ ɧɚ ɩɨɥɭ ɛɭɞɟɬ ɪɚɜ-
aG . ɋɩɭɫɬɹ ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɟɝɨ
Ɋɢɫ. 6.2
r
ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ
ɧɚɛɥɸɞɚɬɟɥɹ ɧɚ Ɂɟɦɥɟ ɲɚɪ ɨɬɤɥɨɧɹɟɬɫɹ ɨɬ ɜɟɪɬɢɤɚɥɢ ɢ ɫɨ-
ɜɟɪɲɚɟɬ ɪɚɜɧɨɦɟɪɧɨɟ ɜɪɚɳɟɧɢɟ ɩɨ ɨɤɪɭɠɧɨɫɬɢ. ɉɨɷɬɨɦɭ ɭɫɤɨɪɟɧɢɟ ɧɚɩɪɚɜɥɟɧɨ
ɤ ɰɟɧɬɪɭ ɨɤɪɭɠɧɨɫɬɢ ɢ ɪɚɜɧɨ
ɰ
.2Rma
Z
ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɧɚɛɥɸɞɚɬɟɥɹ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɧɚ ɩɥɚɬɮɨɪɦɟ, ɲɚɪ ɧɚɯɨɞɢɬɫɹ
ɜ ɩɨɤɨɟ, ɚ ɧɢɬɶ ɨɬɤɥɨɧɟɧɚ ɧɚ ɧɟɤɨɬɨɪɵɣ ɭɝɨɥ ɨɬ ɜɟɪɬɢɤɚɥɢ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ,
ɫ ɟɝɨ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɫɤɨɪɟɧɢɟ ɪɚɜɧɨ ɧɭɥɸ.
ɉɨɷɬɨɦɭ ɜ ɤɥɚɫɫɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ ɜɨɡɧɢɤɚɟɬ ɫɥɟɞɭɸɳɚɹ ɡɚɞɚɱɚ: ɧɚɦ ɢɡɜɟɫɬɧɨ ɭɫɤɨɪɟɧɢɟ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɜ ɨɞɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ; ɬɪɟɛɭɟɬɫɹ
ɧɚɣɬɢ ɭɫɤɨɪɟɧɢɟ ɷɬɨɣ ɬɨɱɤɢ ɩɨ
ɨɬɧɨɲɟɧɢɸ ɤ ɞɪɭɝɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ.
ɋɢɫɬɟɦɚ ɨɬɫɱɟɬɚ, ɞɜɢɠɭɳɚɹɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ «ɧɟɩɨɞɜɢɠɧɨɣ» ɫ ɭɫɤɨɪɟɧɢ-
ɟɦ, ɧɚɡɵɜɚɟɬɫɹ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɨɣ ɨɬɫɱɟɬɚ. ɉɨɞ «ɧɟɩɨɞɜɢɠɧɨɣ» ɫɢɫɬɟ-
ɦɨɣ ɦɵ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɢɧɟɪɰɢɚɥɶɧɭɸ ɫɢɫɬɟɦɭ.
Ʉɢɧɟɦɚɬɢɤɚ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ
ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ
ɉɭɫɬɶ ɢɦɟɸɬɫɹ ɞɜɟ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ (ɪɢɫ. 6.3). ɋɢɫɬɟɦɚ OXYZ – «ɧɟɩɨ-
ɞɜɢɠɧɚɹ» ɫɢɫɬɟɦɚ, ɤɨɬɨɪɭɸ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɫɢɫɬɟɦɨɣ O, ɢ ɫɢɫɬɟɦɚ O
cXcYcZc
ɞɜɢɠɭɳɚɹɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɟɪɜɨɣ, ɤɨɬɨɪɭɸ ɧɚɡɨɜɟɦ ɫɢɫɬɟɦɨɣ O'. Ⱦɜɢɠɟɧɢɟ ɩɨɫɥɟɞɧɟɣ ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɭɩɚɬɟɥɶɧɵɦ, ɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɨɧɚ ɦɨɠɟɬ ɜɪɚɳɚɬɶɫɹ
ɜɨɤɪɭɝ ɧɟɤɨɬɨɪɨɣ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɬɨɱɤɭ O'. Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɧɚɥɨɠɢɦ ɨɞɧɨ
ɨɝɪɚɧɢɱɟɧɢɟ – ɩɭɫɬɶ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ
G
ɩɨɫɬɨɹɧɧɚ.
Z
Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɧɟɤɨɬɨɪɨɣ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ Ɇ. ɉɨɥɨɠɟɧɢɟ ɷɬɨɣ
ɬɨɱɤɢ ɜ ɫɢɫɬɟɦɟ O ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɨɦ
o
U
ɳɟɣɫɹ ɫɢɫɬɟɦɵ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɨɦ
.
, ɩɪɢɱɟɦ:
ooo
Urr (6.1)
0
o
, ɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɜɢɠɭ-
72
/
Ɋɢɫ. 6.3
X
ɋɤɨɪɨɫɬɶ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ Ɇ ɜ ɫɢɫɬɟɦɟ O ɪɚɜɧɚ:
G
rd
X
ɢ
dt
dt
ooo
U
d
rd
0
.
dt
ɗɬɨ ɜɵɪɚɠɟɧɢɟ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ:
ooo
XXX
,
o
ɝɞɟ
X
– ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ Ɇ ɜ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ (O);
ɢ
o
X
– ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ Ɇ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ (O
ɧɢ
c
xd
k
o
X
– ɫɤɨɪɨɫɬɶ ɬɨɣ ɬɨɱɤɢ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɜ ɤɨɬɨɪɨɣ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟ-
e
X
ɧɢ
ɧɢ ɧɚɯɨɞɢɬɫɹ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ Ɇ. ɉɨɫɤɨɥɶɤɭ ɫɢɫɬɟɦɚ O
ɥɨɠɟɧɢɟ ɟɞɢɧɢɱɧɵɯ ɜɟɤɬɨɪɨɜ (
i
dt
GG
,,
kji
ɧɢɟɢ
c
):
c
yd
c
dt
G
ccc
) ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ
oooo
c
zd
c
j
c
;
(6.2)
dt
c
ɜɪɚɳɚɟɬɫɹ, ɬɨ ɩɨ-
ɜɵɪɚɠɟɧɢɸ:
oooo
º
ª
UZXX
,,
o
ɝɞɟ
X
– ɫɤɨɪɨɫɬɶ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɨɱɤɢ Oc ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ
0
ɨɬɫɱɟɬɚ. ɋɤɨɪɨɫɬɶ
o
X
ɢɧɚɱɟ ɧɚɡɵɜɚɸɬ ɩɟɪɟɧɨɫɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɗɬɨ ɧɚɡɜɚɧɢɟ
e
0
e
(6.3)
»
«
¼
¬
ɩɪɨɢɫɯɨɞɢɬ ɨɬ ɩɟɪɟɧɨɫɧɨɝɨ ɞɜɢɠɟɧɢɹ ɢɥɢ ɞɜɢɠɟɧɢɹ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟ-
ɬɚ ɢ ɜɫɟɯ ɩɨɫɬɨɹɧɧɨ ɫɜɹɡɚɧɧɵɯ ɫ ɧɟɸ ɬɨɱɟɤ ɩɪɨɫɬɪɚɧɫɬɜɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɩɨɞɜɢɠɧɨɣ (ɛɚɡɨɜɨɣ) ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ. ȼɚɠɧɨ ɨɬɦɟɬɢɬɶ, ɫɨɝɥɚɫɧɨ (6.3), ɱɬɨ ɩɟɪɟɧɨɫɧɚɹ ɫɤɨɪɨɫɬɶ ɪɚɜɧɚ ɫɤɨɪɨɫɬɢ
G
ɜ ɬɨɦ ɢ ɬɨɥɶɤɨ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɩɨɞɜɢɠ-
ɢ
ɧɚɹ ɫɢɫɬɟɦɚ ɨɬɫɱɟɬɚ ɞɜɢɠɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɩɨɫɬɭɩɚɬɟɥɶɧɨ.
73
ȼɵɱɢɫɥɢɦ ɭɫɤɨɪɟɧɢɟ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ Ɇ ɜ ɷɬɢɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ. ɉɨ
ɨɩɪɟɞɟɥɟɧɢɸ ɢɦɟɟɦ:
o
a
ɢ
d
d
dt
dt
ooo
XXX
d
ɧɢe
.
dt
Ɉɩɭɫɤɚɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɩɪɢɜɟɞɟɦ ɨɤɨɧɱɚɬɟɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ. ɍɫɤɨɪɟɧɢɟ
ɜ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɪɚɜɧɨ:
oooo
.
aaaa
Ɂɞɟɫɶ
o
a
– ɭɫɤɨɪɟɧɢɟ ɬɨɣ ɬɨɱɤɢ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɜ ɤɨɬɨɪɨɣ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ
e
(6.4)
keɧɢɢ
ɜɪɟɦɟɧɢ ɧɚɯɨɞɢɬɫɹ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ Ɇ. Ɉɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
ooooo
ª
aa
e
0
«
¬
ɉɟɪɜɵɣ ɱɥɟɧ ɜ ɷɬɨɦ ɜɵɪɚɠɟɧɢɢ ɨɩɪɟɞɟɥɹɟɬ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ O
º
º
ª
.,,
UZZ
(6.5)
»
»
«
¬
¼
¼
c
, ɱɬɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɩɟɪɟɧɨɫɧɨɟ ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɞɜɢɠɭɳɟɣɫɹ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɩɨɞɜɢɠɧɨɣ. ȼɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɨɩɪɟɞɟɥɟɧɨ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɶɸ ɜɪɚɳɟɧɢɹ ɞɜɢɠɭɳɟɣɫɹ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɢ ɧɚɡɵɜɚɟɬɫɹ ɩɟɪɟɧɨɫɧɨɟ ɜɪɚɳɚɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ. ɇɚɤɨɧɟɰ, ɩɨɫɥɟɞɧɟɟ ɬɪɟɬɶɟ ɫɥɚɝɚɟɦɨɟ ɜɵɪɚɠɟɧɢɹ ɬɚɤɠɟ ɨɛɭɫɥɨɜɥɟɧɨ ɜɪɚɳɟɧɢɟɦ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɜɟɤɬɨɪ,
ɤɨɬɨɪɵɣ ɫɨɜɩɚɞɚɟɬ ɫ ɧɨɪɦɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɩɟɪɟɧɨɫɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɬɨɣ
ɬɨɱɤɢ ɜɪɚɳɚɸɳɟɣɫɹ ɫɢɫɬɟɦɵ, ɫ ɤɨɬɨɪɨɣ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɫɨɜɩɚɞɚɟɬ ɞɜɢɠɭɳɚɹɫɹ ɬɨɱɤɚ.
ɍɫɤɨɪɟɧɢɟ
.,2
o
a
ɧɚɡɵɜɚɟɬɫɹ ɤɨɪɢɨɥɢɫɨɜɵɦ ɭɫɤɨɪɟɧɢɟɦ. Ɉɧɨ ɪɚɜɧɨ
k
a
ooo
º
ª
XZ
«
¬
(6.6)
ɧɢk
»
¼
ɗɬɨ ɭɫɤɨɪɟɧɢɟ ɪɚɜɧɨ ɧɭɥɸ ɜ ɞɜɭɯ ɫɥɭɱɚɹɯ: ɥɢɛɨ ɟɫɥɢ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ
ɜɪɚɳɟɧɢɹ ɪɚɜɧɚ ɧɭɥɸ, ɥɢɛɨ ɟɫɥɢ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ Ɇ ɠɟɫɬɤɨ ɫɜɹɡɚɧɚ ɫ ɩɪɨɫɬɪɚɧɫɬɜɨɦ ɜ ɫɢɫɬɟɦɟ O
c
, ɬɨ ɟɫɬɶ ɨɧɚ ɧɚɯɨɞɢɬɫɹ ɜ ɩɨɤɨɟ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɱɚɫɬɧɵɟ ɫɥɭɱɚɢ.
ɋɥɭɱɚɣ ɩɟɪɜɵɣ. ɋɢɫɬɟɦɚ O
oo
ɞɚ
ɢ ɢɦɟɟɦ .
0,0
Z
a
0
c
ɞɜɢɠɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ. Ɍɨɝ-
aaoo ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɛɟ ɫɢɫɬɟɦɵ ɹɜɥɹɸɬɫɹ
ɧɢɢ
ɢɧɟɪɰɢɚɥɶɧɵɦɢ.
ɋɥɭɱɚɣ ɜɬɨɪɨɣ. .0,0
ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɪɚɜɧɨ
Z
z ooa
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɫɤɨɪɟɧɢɟ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ
0
ooo
.
aaa
0
ɢɧɢ
Ɍɟɩɟɪɶ ɥɟɝɤɨ ɨɛɴɹɫɧɢɬɶ ɪɟɡɭɥɶɬɚɬɵ ɧɚɛɥɸɞɟɧɢɣ ɞɜɭɯ ɧɚɛɥɸɞɚɬɟɥɟɣ ɜ ɩɟɪɜɨɦ ɩɪɢɦɟɪɟ ɫ ɞɜɢɠɭɳɢɦɫɹ ɜɚɝɨɧɨɦ. ȼ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɧɚɛɥɸ-
ɞɚɬɟɥɶ ɜɢɞɢɬ, ɱɬɨ ɭɫɤɨɪɟɧɢɟ
o
.0
a ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɧɚɛɥɸɞɚɬɟɥɹ ɜ ɜɚɝɨɧɟ
ɢ
74
oo
X
ɭɫɤɨɪɟɧɢɟ ɲɚɪɚ ɪɚɜɧɨ
ɧɢ
ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɫ ɭɫɤɨɪɟɧɢɟɦ
ɋɥɭɱɚɣ ɬɪɟɬɢɣ.
0
ɒɚɪ, ɩɨɞɜɟɲɟɧɧɵɣ ɧɚ ɧɢɬɢ, ɞɜɢɠɟɬɫɹ ɜ
.
aa
0
ɧɢ
consta
aa
oo
Ⱦɥɹ ɧɚɛɥɸɞɚɬɟɥɹ ɜ ɜɚɝɨɧɟ:
.
aa
0
ɢ
ooo
.000
aaa
ooo
.0,,0
XZ
ª
ª
ɧɢɢ
«
«
¬
¬
Ɂɞɟɫɶ ɢɦɟɟɦ:
ɧɢ
ooooo
º
º
.,,
UZZ
»
»
¼
¼
ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɩɪɚɜɢɥɨɦ ɜɵɱɢɫɥɟɧɢɹ ɞɜɨɣɧɨɝɨ ɜɟɤɬɨɪɧɨɝɨ ɩɪɨɢɡɜɟɞɟɧɢɹ, ɩɨɥɭɱɢɦ:
ª
«
¬
º
º
ª
UZZ
»
»
«
¼
¬
¼
·
§
UZZ
¸
¨
¹
©
Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɨɫɢ ɤɨɨɪɞɢɧɚɬ ɞɜɭɯ ɫɢɫɬɟɦ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɚɪɚɥɥɟɥɶɧɵ. ɉɭɫɬɶ ɨɫɶ ɜɪɚɳɟɧɢɹ ɧɚɩɪɚɜɥɟɧɚ ɜɞɨɥɶ ɨɫɢ O
Ɍɨɝɞɚ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ Ɇ ɜɪɚɳɚɟɬɫɹ ɜ ɩɥɨɫɤɨɫɬɢ O
ɥɹɪɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ ɜɟɤɬɨɪɨɜ
o
Z ɢ
o
U ɪɚɜɧɨ ɧɭɥɸ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ,
ooooooooo
·
§
.,,
ZZU
¸
¨
¹
©
/Z/
/X/Y/
. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɤɚ-
ɭɫɤɨɪɟɧɢɟ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɪɚɜɧɨ
ooo
2
.
aa
UZ
ɢɧɢ
ȼɟɪɧɟɦɫɹ ɤ ɩɪɢɦɟɪɭ ɫ ɜɪɚɳɚɸɳɟɣɫɹ ɩɥɚɬɮɨɪɦɨɣ. ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɧɚɛɥɸɞɚɬɟɥɹ ɧɚ Ɂɟɦɥɟ ɲɚɪ ɧɚ ɧɢɬɢ ɫɨɜɟɪɲɚɟɬ ɪɚɜɧɨɦɟɪɧɨɟ ɜɪɚɳɟɧɢɟ ɩɨ ɨɤɪɭɠɧɨɫɬɢ
ɪɚɞɢɭɫɨɦ ȡ. ɉɨɷɬɨɦɭ ɫ ɟɝɨ ɬɨɱɤɢ ɡɪɟɧɢɹ, ɭɫɤɨɪɟɧɢɟ ɧɚɩɪɚɜɥɟɧɨ ɤ ɰɟɧɬɪɭ
o
ɨɤɪɭɠɧɨɫɬɢ ɢ ɪɚɜɧɨ .
§
¨
©
·
2
UZ
ɉɨɷɬɨɦɭ ɭɫɤɨɪɟɧɢɟ ɲɚɪɚ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢ-
¸
¹
ɫɬɟɦɟ ɪɚɜɧɨ ɧɭɥɸ, ɬ. ɟ. ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɧɚɛɥɸɞɚɬɟɥɹ ɲɚɪ ɩɨɤɨɢɬɫɹ.
Ʉɨɪɢɨɥɢɫɨɜɨ ɭɫɤɨɪɟɧɢɟ. ɗɬɨ ɭɫɤɨɪɟɧɢɟ ɜɨɡɧɢɤɚɟɬ ɜɨ ɜɪɚɳɚɸɳɟɣɫɹ ɫɢ-
ɫɬɟɦɟ ɨɬɫɱɟɬɚ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ ɞɜɢɠɟɬɫɹ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ
ɩɨɫɬɭɩɚɬɟɥɶɧɨ. ɉɨɫɤɨɥɶɤɭ ɷɬɨ ɭɫɤɨɪɟɧɢɟ ɟɫɬɶ ɪɟɡɭɥɶɬɚɬ ɜɟɤɬɨɪɧɨɝɨ ɩɪɨɢɡɜɟɞɟ-
o
ɧɢɹ ɜɟɤɬɨɪɨɜ
o
Z ɢ
, ɬɨ ɨɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ, ɜ ɤɨɬɨɪɨɣ ɥɟɠɚɬ ɷɬɢ
ɞɜɚ ɜɟɤɬɨɪɚ. Ɇɵ ɩɨɥɭɱɢɥɢ ɷɬɨ ɭɫɤɨɪɟɧɢɹ ɮɨɪɦɚɥɶɧɵɦ ɫɩɨɫɨɛɨɦ, ɢɫɩɨɥɶɡɭɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ.
ɋɢɥɵ ɢɧɟɪɰɢɢ
ȼ ɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ ɡɚɤɨɧɵ ɞɢɧɚɦɢɤɢ ɜɵɝɥɹɞɹɬ ɨɞɢɧɚɤɨɜɨ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɵɱɢɫɥɢɜ ɭɫɤɨɪɟɧɢɟ ɜ ɨɞɧɨɣ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ, ɦɵ ɡɧɚɟɦ
ɟɝɨ ɜɟɥɢɱɢɧɭ ɢ ɜ ɞɪɭɝɢɯ ɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɨɫɧɨɜɧɵɟ
ɩɨɥɨɠɟɧɢɹ ɦɟɯɚɧɢɤɢ ɇɶɸɬɨɧɚ ɢ ɜɫɟ ɜɵɬɟɤɚɸɳɢɟ ɢɡ ɧɢɯ ɫɥɟɞɫɬɜɢɹ ɫɩɪɚɜɟɞɥɢɜɵ ɜɨ ɜɫɟɯ ɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ. ɉɨɜɬɨɪɢɦ ɟɳɟ ɪɚɡ ɧɟɤɨɬɨɪɵɟ ɩɨɥɨɠɟɧɢɹ,
ɤɨɬɨɪɵɟ ɜɚɠɧɵ ɞɥɹ
1)
ɭɫɤɨɪɟɧɢɟ ɬɟɥ ɜɵɡɵɜɚɸɬɫɹ ɫɢɥɚɦɢ;
ɜɫɹɤɚɹ ɫɢɥɚ ɟɫɬɶ ɪɟɡɭɥɶɬɚɬ ɞɟɣɫɬɜɢɹ ɬɟɥ ɞɪɭɝ ɧɚ ɞɪɭɝɚ ɢ ɨɞɧɨɡɧɚɱɧɨ
2)
ɩɨɫɥɟɞɭɸɳɢɯ ɪɚɫɫɭɠɞɟɧɢɣ:
ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɧɮɢɝɭɪɚɰɢɟɣ ɬɟɥ ɢɥɢ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ.
75
.
ȼɟɪɧɟɦɫɹ ɤ ɩɪɢɦɟɪɭ ɫ ɞɜɢɠɭɳɢɦɫɹ ɜɚɝɨɧɨɦ (ɪɢɫ. 6.1). ɉɭɫɬɶ ɨɤɧɚ ɜɚɝɨɧɚ
ɡɚɤɪɵɬɵ. Ɋɟɥɶɫɵ ɢɞɟɚɥɶɧɨ ɝɥɚɞɤɢɟ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɭ ɧɚɛɥɸɞɚɬɟɥɹ ɜ ɜɚɝɨɧɟ ɧɟɬ
ɧɢɤɚɤɢɯ ɜɨɡɦɨɠɧɨɫɬɟɣ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɫɜɨɟɝɨ ɩɨɥɨɠɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɚɤɢɯ-ɥɢɛɨ ɬɟɥ ɜɧɟ ɜɚɝɨɧɚ ɢ ɨɧ ɫ ɩɨɥɧɵɦ ɨɫɧɨɜɚɧɢɟɦ ɫɱɢɬɚɟɬ ɜɚɝɨɧ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɨɣ ɨɬɫɱɟɬɚ. ɇɚɛɥɸɞɚɹ ɡɚ ɢɡɦɟɧɟɧɢɟɦ ɞɜɢɠɟɧɢɹ ɬɟɥ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɜɚɝɨɧɟ, ɨɧ ɧɟ ɦɨɠɟɬ ɭɤɚɡɚɬɶ ɞɪɭɝɢɯ ɬɟɥ, ɤɨɬɨɪɵɟ ɡɚɫɬɚɜɢɥɢ ɲɚɪɵ ɞɜɢɝɚɬɶɫɹ ɢɥɢ ɨɬɤɥɨɧɢɬɶɫɹ ɨɬ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ. ɉɨɷɬɨɦɭ ɨɧ ɦɨɠɟɬ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɨɞɧɨ ɢɡ ɩɨɥɨɠɟɧɢɣ ɦɟɯɚɧɢɤɢ ɇɶɸɬɨɧɚ ɧɟɫɩɪɚɜɟɞɥɢɜɨ ɢ ɨɬ ɨɞɧɨɝɨ ɢɡ ɧɢɯ ɫɥɟɞɭɟɬ ɨɬɤɚɡɚɬɶɫɹ. Ɉɬɤɚɡ ɨɬ ɩɟɪɜɨɝɨ ɩɨɥɨɠɟɧɢɹ ɛɵɥ ɛɵ
ɩɪɨɫɬɨ ɤɚɬɚɫɬɪɨɮɨɣ, ɩɨɫɤɨɥɶɤɭ
ɥɢɲɚɥ ɛɵ ɧɚɫ ɜɨɡɦɨɠɧɨɫɬɢ ɜɵɩɨɥɧɹɬɶ ɤɚɤɢɟ-
ɥɢɛɨ ɪɚɫɱɟɬɵ. ɉɨɷɬɨɦɭ ɜ ɦɟɯɚɧɢɤɟ ɨɬɤɚɡɚɥɢɫɶ ɨɬ ɜɬɨɪɨɝɨ ɩɨɥɨɠɟɧɢɹ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɦɟɯɚɧɢɤɟ ɧɟɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦ ɨɬɫɱɟɬɚ ɭɫɤɨɪɟɧɢɹ
ɜɵɡɵɜɚɸɬɫɹ ɫɢɥɚɦɢ, ɧɨ ɷɬɢ ɫɢɥɵ ɧɟɨɛɹɡɚɬɟɥɶɧɨ ɨɛɭɫɥɨɜɥɟɧɵ ɞɟɣɫɬɜɢɟɦ ɬɟɥ
ɞɪɭɝ ɧɚ ɞɪɭɝɚ. ȼ ɧɟɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ ɩɨɹɜɥɹɸɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶ-
ɧɵɟ ɫɢɥɵ, ɢɧɨɝɞɚ ɧɚɡɵɜɚɟɦɵɟ «ɮɢɤɬɢɜɧɵɦɢ», ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɤɨɬɨɪɵɯ ɭɠɟ
ɧɟɥɶɡɹ ɨɛɴɹɫɧɢɬɶ
ɞɟɣɫɬɜɢɟɦ ɧɚ ɞɚɧɧɨɟ ɬɟɥɨ ɤɚɤɢɯ-ɥɢɛɨ ɞɪɭɝɢɯ ɬɟɥ. ɂɯ ɩɨɹɜɥɟɧɢɟ ɨɛɭɫɥɨɜɥɟɧɨ ɭɫɤɨɪɟɧɢɟɦ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ «ɧɟɩɨɞɜɢɠɧɨɣ»
ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ. ɗɬɢ ɫɢɥɵ ɢ ɧɚɡɵɜɚɸɬ ɫɢɥɚɦɢ ɢɧɟɪɰɢɢ. ɗɬɢ ɫɢɥɵ ɦɨɠɧɨ ɢɡɦɟɪɢɬɶ, ɧɨ ɧɟɜɨɡɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɯ ɢɫɬɨɱɧɢɤ. Ɋɚɜɧɨɞɟɣɫɬɜɭɸɳɚɹ ɜɫɟɯ ɫɢɥ
ɢɧɟɪɰɢɢ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɞɚɧɧɨɟ ɮɢɡɢɱɟɫɤɨɟ ɬɟɥɚ, ɩɪɢɤɥɚɞɵɜɚɟɬɫɹ ɤ ɬɨɱɤɟ,
ɧɚɡɵɜɚɟɦɨɣ
ɰɟɧɬɪ ɢɧɟɪɰɢɢ ɬɟɥɚ. Ɉɫɨɛɨ ɩɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɰɟɧɬɪɨɦ ɢɧɟɪɰɢɢ ɜ
ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟ ɫɨɜɩɚɞɚɟɬ ɧɢ ɫ ɰɟɧɬɪɨɦ ɬɹɠɟɫɬɢ ɬɟɥɚ, ɧɢ ɫ ɰɟɧɬɪɨɦ ɟɝɨ ɦɚɫɫ.
ɋɨɯɪɚɧɢɜ ɩɟɪɜɨɟ ɩɨɥɨɠɟɧɢɟ ɦɟɯɚɧɢɤɢ ɇɶɸɬɨɧɚ, ɦɵ ɬɟɩɟɪɶ ɦɨɠɟɦ ɧɚɩɢ-
ɫɚɬɶ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɜ ɪɚɡɧɵɯ ɫɢɫɬɟɦɚɯ.
ȼ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɛɭɞɟɬ ɢɦɟɬɶ ɢɡɜɟɫɬ-
ɧɵɣ ɜɢɞ:
ɝɞɟ
¦
o
– ɫɭɦɦɚ ɜɫɟɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɞɚɧɧɨɟ ɬɟɥɨ ɫɨ ɫɬɨɪɨɧɵ ɞɪɭɝɢɯ
F
i
,
ɢ
¦
oo
Fam
i
ɬɟɥ. ɗɬɢ ɫɢɥɵ ɧɨɫɹɬ ɯɚɪɚɤɬɟɪ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɢ ɞɥɹ ɧɢɯ ɫɩɪɚɜɟɞɥɢɜ ɬɪɟɬɢɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ.
ȼ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɬɨɝɨ ɠɟ ɬɟɥɚ ɢɦɟ-
ɟɬ ɜɢɞ:
ooo
ma F F
ɧɢ
i ɢɧɟɪɰɢɢ
¦¦
.
Ɂɞɟɫɶ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɫɥɚɝɚɟɦɵɦ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɹɜɥɹɟɬɫɹ ɫɭɦɦɚ ɜɫɟɯ ɫɢɥ
ɢɧɟɪɰɢɢ
¦
o
F
ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɞɚɧɧɨɟ ɬɟɥɨ ɜɫɥɟɞɫɬɜɢɟ ɞɜɢɠɟɧɢɹ ɫ ɭɫɤɨ-
,
ɢɧɟɪɰɢɢ
ɪɟɧɢɟɦ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ «ɧɟɩɨɞɜɢɠɧɨɣ». Ɉɞɧɚɤɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɬɨɥɶɤɨ ɬɨɝɞɚ ɢɦɟɸɬ ɫɦɵɫɥ, ɤɨɝɞɚ ɦɵ ɦɨɠɟɦ ɨɩɪɟɞɟɥɢɬɶ ɜɯɨɞɹɳɢɟ ɜ ɧɟɝɨ ɫɢɥɵ. ɋɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɬɟɥɚɦɢ ɦɵ ɦɨɠɟɦ ɢɡɦɟɪɢɬɶ. ɑɬɨɛɵ ɨɩɪɟɞɟɥɢɬɶ ɫɢɥɵ ɢɧɟɪɰɢɢ, ɦɵ ɞɨɥɠɧɵ ɧɚɣɬɢ ɪɚɡɧɨɫɬɶ ɭɫɤɨɪɟɧɢɣ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɢ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ:
ooo
§
¨
©
·
.
Faam (6.7)
¦
ɢɧɟɪɰɢɢ
¸
ɢɧɢ
¹
76
Ɍɟɩɟɪɶ ɜɟɪɧɟɦɫɹ ɤ ɩɪɟɞɵɞɭɳɢɦ ɩɪɢɦɟɪɚɦ ɢ ɧɚɣɞɟɦ ɫɢɥɵ ɢɧɟɪɰɢɢ, ɞɟɣ-
r
ɫɬɜɭɸɳɢɟ ɧɚ ɬɟɥɚ.
ɋɢɥɵ ɢɧɟɪɰɢɢ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɞɜɢɠɭɳɟɣɫɹ ɩɪɹɦɨɥɢɧɟɣɧɨ ɫ ɭɫɤɨɪɟɧɢ-
ɟɦ. ɉɪɢɦɟɪɨɦ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɜɚɝɨɧ, ɞɜɢɠɭɳɢɣɫɹ ɫ ɩɨɫɬɨɹɧɧɵɦ ɭɫɤɨ-
ɪɟɧɢɟɦ. ȼ ɬɚɤɢɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ, ɤɪɨɦɟ ɪɟɚɥɶɧɵɯ ɫɢɥ, ɧɚ ɬɟɥɚ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ
ɢɧɟɪɰɢɢ, ɪɚɜɧɚɹ:
oo
(6.8)
,
amF
0
ɝɞɟ
o
– ɭɫɤɨɪɟɧɢɟ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ;
a
0
ɢɧɟɪɰɢɢ
m – ɦɚɫɫɚ ɬɟɥɚ, ɧɚ ɤɨɬɨɪɨɟ ɷɬɚ ɫɢɥɚ ɢɧɟɪɰɢɢ ɞɟɣɫɬɜɭɟɬ. ɉɨɫɤɨɥɶɤɭ ɷɬɚ ɫɢɥɚ
ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɤɨɨɪɞɢɧɚɬ, ɬɨ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɧɚ ɬɟɥɚ
ɨɞɢɧɚɤɨɜɨɣ ɦɚɫɫɵ ɞɟɣɫɬɜɭɟɬ ɨɞɧɚ ɢ ɬɚ ɠɟ ɫɢɥɚ ɢɧɟɪɰɢɢ. ɉɨɷɬɨɦɭ ɜ ɷɬɨɦ ɫɥɭɱɚɟ, ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɬɹɠɟɫɬɢ ɰɟɧɬɪ ɦɚɫɫ, ɰɟɧɬɪ ɬɹɠɟɫɬɢ ɢ
ɰɟɧɬɪ ɢɧɟɪɰɢɢ
ɫɨɜɩɚɞɚɸɬ.
ɉɪɢɦɟɪɨɦ ɩɪɨɹɜɥɟɧɢɹ ɬɚɤɢɯ ɫɢɥ ɹɜɥɹɟɬɫɹ ɩɪɨɰɟɞɭɪɚ ɜɡɜɟɲɢɜɚɧɢɹ ɬɟɥɚ ɜ
ɤɚɛɢɧɟ ɥɢɮɬɚ, ɞɜɢɠɭɳɟɝɨɫɹ ɫ ɭɫɤɨɪɟɧɢɟɦ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
ȼɟɫɨɦ ɬɟɥɚ ɧɚɡɵɜɚɟɬɫɹ ɫɢɥɚ, ɫ ɤɨɬɨɪɨɣ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɧɚ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɨɩɨɪɭ ɢɥɢ ɜɟɪɬɢɤɚɥɶɧɵɣ ɩɨɞɜɟɫ ɜɫɥɟɞɫɬɜɢɟ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɪɢɬɹɠɟɧɢɹ
ɤ ɢɫɬɨɱɧɢɤɭ.
ȿɫɥɢ ɪɟɲɚɬɶ ɷɬɭ ɡɚɞɚɱɭ ɜ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɬɨ ɜɟɫ
ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɪɚɜɟɧ:
G
GG
.agmP
ɬɟɥɚ ɜ ɷɬɨɣ
ɉɪɟɞɫɬɚɜɢɦ ɫɟɛɟ, ɱɬɨ ɦɵ ɧɚɯɨɞɢɦɫɹ ɜ ɡɚɤɪɵɬɨɣ ɤɚɛɢɧɟ ɥɢɮɬɚ, ɤɨɬɨɪɚɹ
ɞɜɢɠɟɬɫɹ ɫ ɭɫɤɨɪɟɧɢɟɦ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɇɟ ɢɦɟɹ ɜɨɡɦɨɠɧɨɫɬɢ
«ɜɵɝɥɹɧɭɬɶ» ɢɡ ɥɢɮɬɚ, ɧɚɛɥɸɞɚɬɟɥɶ ɧɢɤɚɤɢɦɢ ɨɩɵɬɚɦɢ ɜɧɭɬɪɢ ɤɚɛɢɧɵ ɧɟ ɦɨɠɟɬ ɭɫɬɚɧɨɜɢɬɶ, ɱɟɦ ɨɛɭɫɥɨɜɥɟɧɵ ɩɨɤɚɡɚɧɢɹ ɜɟɫɨɜ – ɢɡɦɟɧɟɧɢɟɦ ɝɪɚɜɢɬɚɰɢɢ
ɢɥɢ ɭɫɤɨɪɟɧɧɵɦ ɞɜɢɠɟɧɢɟɦ ɤɚɛɢɧɵ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɷɬɨɝɨ ɝɨɜɨɪɹɬ
ɨɛ ɷɤɜɢɜɚɥɟɧɬɧɨɫɬɢ ɫɢɥ ɢɧɟɪɰɢɢ ɢ ɬɹɝɨɬɟɧɢɹ ɜ ɨɞɧɨɪɨɞɧɨɦ ɝɪɚɜɢɬɚɰɢɨɧɧɨɦ ɩɨɥɟ. ɗɬɚ
ɷɤɜɢɜɚɥɟɧɬɧɨɫɬɶ ɥɟɠɢɬ ɜ ɨɫɧɨɜɟ ɨɛɳɟɣ ɬɟɨɪɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ ɗɣɧɲɬɟɣɧɚ.
ɋɢɥɵ ɢɧɟɪɰɢɢ ɜɨ ɜɪɚɳɚɸɳɢɯɫɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɫɢɫɬɟɦɚɯ
ɨɬɫɱɟɬɚ. ȼɪɚɳɚɸɳɚɹɫɹ ɩɥɚɬɮɨɪɦɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɢɦɟɪ ɬɚɤɨɣ ɫɢɫɬɟɦɵ
(ɪɢɫ. 6.2). ɋɢɥɚ ɢɧɟɪɰɢɢ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɩɨɤɨɹɳɟɟɫɹ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ ɬɟɥɨ, ɪɚɜɧɚ:
oo
2
rmF
Z
,
o
ɝɞɟ
– ɪɚɞɢɭɫ-ɜɟɤɬɨɪ, ɩɪɨɜɟɞɟɧɧɵɣ ɨɬ ɰɟɧɬɪɚ ɜɪɚɳɟɧɢɹ ɜ ɬɨɱɤɭ, ɝɞɟ ɧɚɯɨ-
ɢɧɟɪɰɢɢ
(6.9)
ɞɢɬɫɹ ɬɟɥɨ. ɉɨɫɤɨɥɶɤɭ ɫɢɥɚ ɢɧɟɪɰɢɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɪɚɫɫɬɨɹɧɢɸ ɨɬ ɰɟɧɬɪɚ
ɨɤɪɭɠɧɨɫɬɢ, ɬɨ ɨɧɚ ɪɚɡɥɢɱɧɚ ɜ ɪɚɡɧɵɯ ɬɨɱɤɚɯ ɜɪɚɳɚɸɳɟɣɫɹ ɫɢɫɬɟɦɵ. ɗɬɚ ɫɢɥɚ
ɧɚɡɵɜɚɟɬɫɹ ɰɟɧɬɪɨɛɟɠɧɨɣ ɫɢɥɨɣ ɢɧɟɪɰɢɢ, ɨɧɚ ɩɪɢɥɨɠɟɧɚ ɤ ɰɟɧɬɪɭ ɢɧɟɪɰɢɢ ɬɟɥɚ ɢ ɧɚɩɪɚɜɥɟɧɚ ɨɬ ɰɟɧɬɪɚ ɜɪɚɳɟɧɢɹ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɰɟɧɬɪ
ɦɚɫɫ ɢ ɰɟɧɬɪ
ɢɧɟɪɰɢɢ ɧɟ ɛɭɞɭɬ ɫɨɜɩɚɞɚɬɶ, ɷɬɨ ɪɚɡɧɵɟ ɬɨɱɤɢ ɨɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɬɟɥɚ. ɉɪɢɦɟɪɨɦ
ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ Ɂɟɦɥɹ, ɫɨɜɟɪɲɚɸɳɚɹ ɫɭɬɨɱɧɨɟ ɜɪɚɳɟɧɢɢ ɜɨɤɪɭɝ ɨɫɢ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɫɟ ɬɨɱɤɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ Ɂɟɦɥɢ ɫɨɜɟɪɲɚɸɬ ɜɪɚɳɟɧɢɟ ɩɨ
ɨɤɪɭɠɧɨɫɬɹɦ ɪɚɡɧɵɯ ɪɚɞɢɭɫɨɜ. ɉɨɷɬɨɦɭ ɧɚ ɬɟɥɚ ɞɟɣɫɬɜɭɟɬ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ
ɢɧɟɪɰɢɢ, ɪɚɜɧɚɹ:
77
22
MZ Z
RmRmF
ɝɞɟ
– ɪɚɞɢɭɫ Ɂɟɦɥɢ,
R
ɡ
M
– ɲɢɪɨɬɚ ɦɟɫɬɧɨɫɬɢ (ɪɢɫ. 6.4). Ɂɧɚɱɟɧɢɟ ɰɟɧɬɪɨɛɟɠɧɨɣ ɫɢɥɵ ɢɧɟɪɰɢɢ
,cos
ɡɰɛ
ɦɚɤɫɢɦɚɥɶɧɨ ɧɚ ɷɤɜɚɬɨɪɟ ɢ ɪɚɜɧɨ ɧɭɥɸ ɧɚ ɩɨɥɸɫɚɯ.
Ɋɢɫ. 6.4
ɋɢɥɚ Ʉɨɪɢɨɥɢɫɚ
. ȼ ɩɪɟɞɵɞɭɳɢɯ ɩɪɢɦɟɪɚɯ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɩɨɜɟɞɟɧɢɟ
ɧɟɩɨɞɜɢɠɧɵɯ ɬɟɥ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ. Ɍɟɩɟɪɶ ɪɚɫɫɦɨɬɪɢɦ
ɞɜɢɠɟɧɢɟ ɬɟɥɚ ɜɨ ɜɪɚɳɚɸɳɟɣɫɹ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ. ɂɦɟɧɧɨ ɜ ɬɚɤɢɯ ɫɢɫɬɟɦɚɯ
ɩɪɨɹɜɥɹɟɬɫɹ ɫɢɥɚ Ʉɨɪɢɨɥɢɫɚ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɩɪɨɹɜɥɟɧɢɹ ɷɬɨɣ ɫɢɥɵ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ Ɂɟɦɥɢ.
ɉɭɫɬɶ ɬɟɥɨ ɩɚɞɚɟɬ ɧɚ Ɂɟɦɥɸ ɫ ɜɵɫɨɬɵ h . ȼ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ
ɩɚɞɟɧɢɟ ɬɟɥɚ ɩɪɨɢɫɯɨɞɢɬ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɝɪɚɜɢɬɚɰɢɨɧɧɨɣ ɫɢɥɵ. ɉɪɢ ɞɜɢɠɟɧɢɢ
ɬɟɥɚ ɜɨ ɜɪɚɳɚɸɳɟɣɫɹ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɩɨɹɜɥɹɟɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ,
ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɬɨɪɨɝɨ ɦɵ ɩɨɥɭɱɢɥɢ ɜɵɲɟ (6.6). ȿɫɥɢ ɭɦɧɨɠɢɬɶ ɟɝɨ ɡɧɚɱɟɧɢɟ
ɧɚ ɦɚɫɫɭ ɬɟɥɚ, ɬɨ ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɟ ɫɢɥɵ, ɪɚɜɧɨɟ:
ooo
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ª
mF
k
.,2
XZ
»
«
¼
¬
ɗɬɚ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɫɢɥɚ ɢ ɧɚɡɵɜɚɟɬɫɹ ɫɢɥɨɣ Ʉɨɪɢɨɥɢɫɚ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ
ɷɬɚ ɫɢɥɚ ɧɚɩɪɚɜɥɟɧɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫɤɨɪɨɫɬɢ ɬɟɥɚ. ɇɚ ɩɨɜɟɪɯɧɨɫɬɢ Ɂɟɦɥɢ ɨɧɚ ɡɚɜɢɫɢɬ ɨɬ ɲɢɪɨɬɵ. ɋɜɨɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢɨɛɪɟɬɚɟɬ
ɧɚ ɩɨɥɸɫɚɯ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ Ɂɟɦɥɟɣ, ɧɚ ɫɜɨɛɨɞɧɨ
ɩɚɞɚɸɳɟɟ ɬɟɥɨ ɞɟɣɫɬɜɭɸɬ ɬɪɢ ɫɢɥɵ: ɫɢɥɚ ɬɹɠɟɫɬɢ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɤ ɰɟɧɬɪɭ Ɂɟɦɥɢ, ɢ ɞɜɟ ɫɢɥɵ ɢɧɟɪɰɢɢ: ɫɢɥɚ ɢɧɟɪɰɢɢ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɜɪɚɳɟɧɢɟɦ Ɂɟɦɥɢ, ɢ ɫɢɥɚ
Ʉɨɪɢɨɥɢɫɚ. Ɇɚɥɨɟ ɩɨ ɜɟɥɢɱɢɧɟ, ɧɨ ɞɥɢɬɟɥɶɧɨɟ ɩɨ ɜɪɟɦɟɧɢ ɞɟɣɫɬɜɢɟ ɫɢɥɵ Ʉɨɪɢɨɥɢɫɚ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɭ ɪɟɤ, ɬɟɤɭɳɢɯ ɜ ɫɟɜɟɪɧɨɦ ɩɨɥɭɲɚɪɢɢ, ɜɫɟɝɞɚ
ɩɨɞɦɵɜɚɟɬɫɹ ɩɪɚɜɵɣ ɛɟɪɟɝ, ɜ ɸɠɧɨɦ ɩɨɥɭɲɚɪɢɢ – ɥɟɜɵɣ ɛɟɪɟɝ. Ɍɨɱɧɨ ɬɚɤ ɠɟ
ɢɡɧɚɲɢɜɚɸɬɫɹ ɢ ɪɟɥɶɫɵ ɠɟɥɟɡɧɵɯ ɞɨɪɨɝ
. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɜ ɪɚɣɨɧ ɩɨɧɢɠɟɧɧɨɝɨ
ɞɚɜɥɟɧɢɹ ɧɚɩɪɚɜɥɹɸɬɫɹ ɩɨɬɨɤɢ ɜɨɡɞɭɯɚ. Ɍɚɤɢɟ ɜɟɬɪɵ ɧɚɡɵɜɚɸɬɫɹ ɰɢɤɥɨɧɚɦɢ,
ɬ. ɟ. ɜ ɷɬɢɯ ɨɛɥɚɫɬɹɯ ɜɨɡɧɢɤɚɟɬ ɤɪɭɝɨɜɨɟ ɞɜɢɠɟɧɢɟ ɜɨɡɞɭɲɧɵɯ ɦɚɫɫ. ɉɪɢɱɢɧɚ
ɷɬɨɝɨ ɬɚɤɠɟ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɞɟɣɫɬɜɢɢ ɫɢɥɵ Ʉɨɪɢɨɥɢɫɚ.
78
Ʉɥɸɱɟɜɵɟ ɩɨɧɹɬɢɹ ɢ ɬɟɪɦɢɧɵ
ȼɟɫ ɬɟɥɚ
ɂɧɟɪɰɢɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɨɬɫɱɟɬɚ
Ʉɨɪɢɨɥɢɫɨɜɨ ɭɫɤɨɪɟɧɢɟ
ɇɟɢɧɟɪɰɢɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɨɬɫɱɟɬɚ
ɉɟɪɟɧɨɫɧɨɟ ɞɜɢɠɟɧɢɟ
ɉɟɪɟɧɨɫɧɚɹ ɫɤɨɪɨɫɬɶ
ɉɟɪɟɧɨɫɧɨɟ ɭɫɤɨɪɟɧɢɟ
ɋɢɥɵ ɢɧɟɪɰɢɢ
ɋɢɥɚ Ʉɨɪɢɨɥɢɫɚ
ɋɤɨɪɨɫɬɶ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ
ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ
ɍɫɤɨɪɟɧɢɟ ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ
ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ
ɐɟɧɬɪ ɦɚɫɫ
ɐɟɧɬɪ ɢɧɟɪɰɢɢ
ɐɟɧɬɪ ɬɹɠɟɫɬɢ
ɐɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ ɢɧɟɪɰɢɢ
ɐɟɧɬɪɨɛɟɠɧɨɟ ɭɫɤɨɪɟɧɢɟ
79
Ɏɨɪɦɭɥɵ ɢ ɟɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɹ ɛɚɡɨɜɵɯ
ɚ
ɦ
ɇ
ɇ
ɇ
ɇ
ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜ ɫɢɫɬɟɦɟ ɋɂ
ɇɚɡɜɚɧɢɟ Ɏɨɪɦɭɥɚ
1. ɋɤɨɪɨɫɬɶ ɬɨɱɤɢ
ɜ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ
ɜ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ
ɜ ɢɧɟɪɰɢɚɥɶɧɨɣ ɢ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ
ɜ ɢɧɟɪɰɢɚɥɶɧɨɣ ɢ ɧɟɢɧɟɪɰɢɚɥɶɧɨɣ
5. ɋɢɥɚ ɢɧɟɪɰɢɢ ɩɪɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɦ
2. ɋɤɨɪɨɫɬɶ ɬɨɱɤɢ
3. ɋɜɹɡɶ ɫɤɨɪɨɫɬɟɣ
ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬ
4. ɋɜɹɡɶ ɭɫɤɨɪɟɧɢɣ
ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ
ɞɜɢɠɟɧɢɢ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ 0
6. ȼɟɫ ɬɟɥɚ
7. ɋɢɥɚ ɢɧɟɪɰɢɢ ɜɨ ɜɪɚɳɚɸɳɟɣɫɹ
ɫ ɩɨɫɬɨɹɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ
ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ (ɰɟɧɬɪɨɛɟɠɧɚɹ
ɫɢɥɚ ɢɧɟɪɰɢɢ)
8. ɋɢɥɚ Ʉɨɪɢɨɥɢɫɚ
X
ɢ
oooo
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G
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Fmr
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Fm
k
k
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dt
dt
ccc
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GG
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,
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;
keɧɢɢ
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ȿɞɢɧɢɰɚ
ɢɡɦɟɪɟɧɢɹ
ɜ ɫɢɫɬɟɦɟ ɋɂ
ɦɟɬɪ ɦ
ɫɟɤɭɧɞɚ ɫ
ɦɟɬɪ ɦ
ɫɟɤɭɧɞɚ ɫ
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ɫɟɤɭɧɞɚ ɫ
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