Аристов Е.В., Динкель А.Д. К РАСЧЕТУ ХАРАКТЕРИСТИК
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ɍȾɄ
Ʌ ɋȻɌɒɀɍɎ ɐȻɋȻɅɍɀɋɃɌɍɃɅ ɃɇɊɎɆɗɌɈɉ-ɎɊɋȻȽɆɚɀɇɉȾɉ
ɘɆɀɅɍɋɉɊɋɃȽɉȿȻ ɈȻ ɉɌɈɉȽɀ ɘɆɀɅɍɋɉȿȽɃȾȻɍɀɆɚ
Ɍ ɊɉɌɆɀȿɉȽȻɍɀɆɗɈɖɇ ȽɉɂȼɎɁȿɀɈɃɀɇ
ȿ ȼ ȺɊɂɋɌɈȼ Ⱥ Ⱦ ȾɂɇɄȿɅɖ
ɉɟɪɦɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ
ȼ ɫɬɚɬɶɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɜɨɩɪɨɫɵ ɩɨɥɭɱɟɧɢɹ ɜɵɪɚɠɟɧɢɣ ɩɨɡɜɨɥɹɸɳɢɯ
ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɚɧɚɥɢɡɢɪɨɜɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɷɥɟɤɬɪɨ
ɩɪɢɜɨɞɟ ɧɚ ɨɫɧɨɜɟ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɢ ɩɪɢ
ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɟɲɚɬɶ ɜɨɩɪɨɫɵ ɫɢɧɬɟɡɚ ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟ
ɧɢɹ ɤɨɨɪɞɢɧɚɬɚɦɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ
ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɧɚ ɨɫɧɨɜɟ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɩɨɫɥɟɞɨ
ɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɢ ɲɢɪɨɬɧɨ ɢɦɩɭɥɶɫɧɵɦ ɭɩɪɚɜɥɟɧɢɟɦ ɧɚɯɨɞɢɬ ɲɢ
ɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɤɨɥɟɫɧɵɯ ɬɪɚɧɫɩɨɪɬɧɵɯ ɫɪɟɞɫɬɜɚɯ ɤɚɤ ɨɫɧɨɜɧɨɣ ɬɹɝɨɜɵɣ
ɩɪɢɜɨɞ ɍɩɪɨɳɟɧɧɚɹ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɬɚɤɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɪɢɜɟɞɟɧɚ
ɧɚ ɪɢɫ
ɉ
Ɋɢɫ ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ
ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ
ɢ ɲɢɪɨɬɧɨ ɢɦɩɭɥɶɫɧɵɦ ɭɩɪɚɜɥɟɧɢɟɦ
Ɉɫɧɨɜɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɬɚɤɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɹɜɥɹɟɬɫɹ ɧɟɥɢɧɟɣɧɨɫɬɶ
ɡɚɜɢɫɢɦɨɫɬɟɣ ɨɩɢɫɵɜɚɸɳɢɯ ɟɝɨ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɢ ɯɚɪɚɤɬɟɪɢ
ɫɬɢɤ ɗɬɨ ɨɛɭɫɥɨɜɥɟɧɨ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦ ɩɨɬɨɤɨɦ
ɢ ɬɨɤɨɦ ɜɨɡɛɭɠɞɟɧɢɹ ɤɨɬɨɪɚɹ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ ɭɧɢɜɟɪɫɚɥɶɧɨɣ ɤɪɢɜɨɣ
ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɧɟ ɢɦɟɸɳɟɣ ɬɨɱɧɨɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ȼ ɫɥɟɞɫɬɜɢɟ
ɷɬɨɝɨ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɬ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɦɟɬɨɞɨɜ ɪɚɫɱɟɬɚ ɢ ɚɧɚɥɢɡɚ ɷɥɟɤɬɪɨɦɟɯɚ
ɧɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɚ ɜɫɟ ɫɜɨɞɢɬɫɹ ɪɚɫɱɟɬɭ ɬɨɥɶɤɨ ɫɬɚɬɢɱɟ
ɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢɛɥɢɠɟɧɧɵɦɢ ɝɪɚɮɢɱɟɫɤɢɦɢ ɢ ɝɪɚɮɨ ɚɧɚɥɢɬɢɱɟɫɤɢɦɢ
ɦɟɬɨɞɚɦɢ ɤɨɬɨɪɵɟ ɩɨ ɫɭɳɟɫɬɜɭ ɧɟ ɩɪɢɟɦɥɟɦɵ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɢɦɩɭɥɶɫɧɨ
ɭɩɪɚɜɥɹɟɦɵɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚɦ
Ɋɢɫ
ɍɧɢɜɟɪɫɚɥɶɧɚɹ ɤɪɢɜɚɹ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ
ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɪɚɡɪɚɛɨɬɤɚ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɦɟɬɨɞɚ ɪɚɫɱɟɬɚ ɢ ɚɧɚɥɢɡɚ ɫɬɚ
ɬɢɱɟɫɤɢɯ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢɟɦɥɟɦɵɯ ɜ ɢɧɠɟɧɟɪɧɨɣ ɩɪɚɤɬɢɤɟ
ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢɦɩɭɥɶɫɧɨ ɭɩɪɚɜɥɹɟɦɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɧɚ ɨɫɧɨɜɟ ɷɥɟɤɬɪɨ
ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɹɜɥɹɟɬɫɹ ɚɤ
ɬɭɚɥɶɧɨɣ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɜɚɠɧɨɣ ɡɚɞɚɱɟɣ
Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɚɧɚɥɢɬɢɱɟɫɤɭɸ ɚɩɩɪɨɤɫɢɦɢ
ɪɭɸɳɭɸ ɮɭɧɤɰɢɸ ɨɩɢɫɵɜɚɸɳɭɸ ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ
ɭɧɢɮɢɰɢɪɨɜɚɧɧɭɸ ɤɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɤɨɬɨɪɚɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ
ɇɚ ɨɫɧɨɜɟ ɪɚɡɥɢɱɧɵɯ ɦɟɬɨɞɨɜ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɝɪɚɮɢɱɟɫɤɢɯ ɡɚɜɢɫɢ
ɦɨɫɬɟɣ ɭɫɬɚɧɨɜɥɟɧɨ ɱɬɨ ɭɧɢɮɢɰɢɪɨɜɚɧɧɚɹ ɤɪɢɜɚɹ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɦɨɠɟɬ
ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɫɥɟɞɭɸɳɟɣ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɚɩɩɪɨɤɫɢɦɢ
ɪɭɸɳɟɣ ɮɭɧɤɰɢɟɣ
ϕ( ) =
ɝɞɟ ϕ
(
−
−
)
ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɢ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ ɜɵɪɚɠɟɧɧɵɟ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
ɟɞɢɧɢɰɚɯ
Ⱥɧɚɥɢɡ ɫɬɚɬɢɤɢ ɢɦɩɭɥɶɫɧɨ ɭɩɪɚɜɥɹɟɦɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɤɚɤ ɢɡɜɟɫɬɧɨ
ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɬɚɤ ɧɚɡɵɜɚɟɦɨɦ ɤɜɚɡɢɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ ȼ ɷɬɨɦ
ɪɟɠɢɦɟ ɤɨɨɪɞɢɧɚɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɢɦɟɸɬ ɩɟɪɟɦɟɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ
ɤɨɥɟɛɚɧɢɹ ɤɨɬɨɪɨɣ ɫ ɨɩɪɟɞɟɥɟɧɧɨɣ ɱɚɫɬɨɬɨɣ ɢ ɚɦɩɥɢɬɭɞɨɣ ɩɪɨɯɨɞɹɬ ɨɬɧɨ
ɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ ɷɬɢɯ ɤɨɨɪɞɢɧɚɬ ɉɪɢ ɷɬɨɦ ɱɚɫɬɨɬɚ ɢ ɚɦɩɥɢɬɭɞɚ
ɤɨɥɟɛɚɧɢɣ ɜ ɱɚɫɬɧɨɫɬɢ ɬɨɤɚ ɹɤɨɪɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɞɨɩɭɫɬɢɦɵɦ ɡɧɚɱɟɧɢɟɦ
ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɭɥɶɫɚɰɢɣ
∆
−
=
=
ɝɞɟ
!
ɦɚɤɫɢɦɚɥɶɧɨɟ ɢ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɹɤɨɪɹ ɜ ɢɧɬɟɪɜɚɥɟ
!
ɩɟɪɢɨɞɚ ɤɨɦɦɭɬɚɰɢɢ
Ⱦɥɹ ɚɧɚɥɢɡɚ ɤɜɚɡɢɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɩɪɨɰɟɫɫɚ ɢ ɩɨɥɭɱɟɧɢɹ ɡɚɜɢɫɢɦɨɫɬɟɣ
ɨɩɢɫɵɜɚɸɳɢɯ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɧɟɨɛɯɨɞɢɦɨ
ɢɦɟɬɶ ɭɪɚɜɧɟɧɢɹ ɨɩɢɫɵɜɚɸɳɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɩɪɨɰɟɫɫɵ ɩɪɨɬɟɤɚɸɳɢɟ ɜ
ɹɤɨɪɧɨɣ ɰɟɩɢ ɜ ɢɧɬɟɪɜɚɥɟ ɨɞɧɨɝɨ ɩɟɪɢɨɞɚ ɤɨɦɦɭɬɚɰɢɢ ɗɬɢ ɭɪɚɜɧɟɧɢɹ ɜ ɨɬɧɨ
ɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ ɡɚɩɢɲɭɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
#
ª¬Θ + Θ
"
( )º¼
+ ρ ⋅ = − ϕ ( )ν
τ
#
$
≤τ ≤ γ
#
ª¬Θ + Θ
ɝɞɟ γ
"
( )º¼
+ ρ ⋅ = −ϕ ( )ν
#
τ
≤τ ≤ −γ
½
°°
¾
°
°¿
ɫɤɜɚɠɧɨɫɬɶ ɢɦɩɭɥɶɫɨɜ ɩɢɬɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ
ɉɪɢ ɩɟɪɟɯɨɞɟ ɤ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɟɞɢɧɢɰɚɦ ɡɚ ɛɚɡɨɜɵɟ ɩɪɢɧɹɬɵ ɧɨɦɢɧɚɥɶ
ɧɵɟ ɩɚɪɚɦɟɬɪɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɚ ɡɚ ɛɚɡɨɜɨɟ ɜɪɟɦɹ ɩɪɢɧɹɬɚ ɞɥɢɬɟɥɶɧɨɫɬɶ
ɩɟɪɢɨɞɚ ɤɨɦɦɭɬɚɰɢɢ ɩɢɬɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ ɗɬɢ ɭɪɚɜɧɟɧɢɹ ɧɟɥɢɧɟɣɧɵɟ ɢ ɢɯ
ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɥɨɠɧɭɸ ɡɚɞɚɱɭ
ȼ ɤɜɚɡɢɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ ɜ ɜɢɞɭ ɬɨɝɨ ɱɬɨ ɩɟɪɢɨɞ ɤɨɦɦɭɬɚɰɢɢ ɧɚ
ɩɨɪɹɞɨɤ ɦɟɧɶɲɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɚ ɩɟɪɢɨɞɢɱɟɫɤɢɟ ɢɡ
ɦɟɧɟɧɢɹ ɬɨɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ ɩɪɨɢɫɯɨɞɹɬ ɫ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɨɣ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɱɬɨ
Θ +Θ
%
( ) = Θ(
)
&
ɬ ɟ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɡɧɚɱɟɧɢɢ
)
'
(
=
*
+
,
-
)
'
.
(
)
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ
ɜɪɟɦɟɧɢ ɜ ɢɧɬɟɪɜɚɥɟ ɩɟɪɢɨɞɚ ɤɨɦɦɭɬɚɰɢɢ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɢ ɫɜɹɡɶ ɦɟɠɞɭ ɦɚɝ
ɧɢɬɧɵɦ ɩɨɬɨɤɨɦ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ
ϕ=
ɝɞɟ
/
( )
)
'
(
/
( )⋅
)
'
)
(
ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɨɩɪɟɞɟɥɹɟɦɵɣ ɩɨ ɤɪɢɜɨɣ
ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ
ɋ ɭɱɟɬɨɦ
ɢ
ɭɪɚɜɧɟɧɢɹ
ɡɚɩɢɲɭɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
½
°°
¾
≤τ ≤ −γ °
°¿
0
)
Θ
( )
Θ
( )
+ ªρ +
τ ¬
)
'
(
0
( )ν º¼ ⋅
/
)
'
=
)
(
≤τ ≤ γ
1
0
)
ɤɨɬɨɪɵɟ ɩɪɢ
+ ªρ +
τ ¬
)
'
2
3
(
0
=
4
5
6
7
( )ν º¼ ⋅
/
)
'
=
)
(
ɹɜɥɹɸɬɫɹ ɥɢɧɟɣɧɵɦɢ
8
ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɧɟɝɨ ɡɧɚ
ɱɟɧɢɹ ɬɨɤɚ ɜ ɢɧɬɟɪɜɚɥɟ ɩɟɪɢɨɞɚ ɤɨɦɦɭɬɚɰɢɢ ɩɨɥɭɱɟɧɨ ɭɪɚɜɧɟɧɢɟ ɷɥɟɤɬɪɨɦɟ
ɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
@
ν=
γ −ρ⋅
−
−
B
A
9
;
:
<
=
>
?
ɤɨɬɨɪɵɟ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ
ɂɫɯɨɞɹ ɢɡ ɬɨɝɨ ɱɬɨ ɦɨɦɟɧɬ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ
µ = ϕ(
E
C
D
E
C
D
)
ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɢɫ
ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɩɭɬɟɦ ɭɦɧɨɠɟɧɢɹ ɡɧɚ
ɱɟɧɢɣ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɩɨ ɨɫɢ ɚɛɫɰɢɫɫ ɡɚɜɢɫɢɦɨɫɬɢ ν =
ɧɚ ɫɨɨɬɜɟɬɫɬ
F
E
C
ɜɭɸɳɢɟ ɡɧɚɱɟɧɢɹ ϕ
ɨɩɪɟɞɟɥɹɟɦɵɟ ɩɨ
( )
E
C
D
D
ν
G
H
I
J
H
K
J
H
G
γ=
I
H
P
Q
L
S
I
R
H
T
U
S
T
V
S
T
W
S
T
X
M
O
I
I
H
M
I
H
L
J
H
G
J
H
K
G
H
I
N
Ɋɢɫ
Y
Z
µ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɦɩɭɥɶɫɧɨ ɭɩɪɚɜɥɹɟɦɨɝɨ
ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɪɢ ρ =
ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ
ɦɟɯɚɧɢɱɟɫɤɢɟ
[
\
]
]
]
^
[
[
[
ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɢ ɤɨ
ɨɪɞɢɧɚɬ ɢɦɩɭɥɶɫɧɨ ɭɩɪɚɜɥɹɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɨɩɢɫɵɜɚɸɬɫɹ ɫɥɟɞɭɸɳɟɣ
ɫɢɫɬɟɦɨɣ ɭɪɚɜɧɟɧɢɣ
d
ªΘ + Θ
¬
_
`
ν
=ρª
¬
τ
d
d
( )º¼
e
e
a
⋅ϕ
e
a
b
ªγ ⋅ − ϕ
ρ¬
e
τ
d
f
+
b
a
=
b
( )−µ
b
a
e
a
b
¾
°
°¿
º
¼
e
a
( )ν º¼ ½°°
c
ɉɪɢ ɷɬɨɦ ɡɚ ɛɚɡɨɜɨɟ ɜɪɟɦɹ ɩɪɢ ɩɟɪɟɯɨɞɟ ɤ ɨɩɬɢɦɚɥɶɧɵɦ ɟɞɢɧɢɰɚɦ ɩɪɢɧɹ
ɬɚ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɧɨɦɢɧɚɥɶɧɨɦɭ
ɬɨɤɭ ɩɨɬɨɤɭ ɜɨɡɛɭɠɞɟɧɢɹ
ɍɱɢɬɵɜɚɹ
ɢ
ɭɪɚɜɧɟɧɢɹ
ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
r
Θ
−
i
j
k
i
q
g
r
h
s
r
ν
=ρª
«¬
τ
r
ªγ ⋅ − ν
ρ ¬«
s
(− )
l
t
+
m
s
n
o
τ
(
u
n
=
o
(−
t
−
i
j
k
q
g
h
t
−
i
j
k
)º¼» ½°°
l
q
g
h
¾
°
°¿
−µ º
¼»
)
l
−
n
p
ɢɥɢ ɜ ɨɩɟɪɚɬɨɪɧɨɣ ɮɨɪɦɟ
ªΘ
«¬
|
ν
−
{
i
j
k
l
(−
i
x
) + º⋅
»¼
y
q
z
v
w
|
=ρª
¬«
E
|
n
o
|
n
o
(−
{
ªγ ⋅ − ν
ρ ¬«
=
E
|
m
−
i
j
k
}
l
x
q
y
z
v
w
)
−µ º
¼»
n
p
|
(
−
{
−
i
j
k
l
x
q
y
z
v
w
)º¼» °°½
¾
°
¿°
ɉɨɥɭɱɟɧɧɵɟ ɜɵɪɚɠɟɧɢɹ ɩɨɡɜɨɥɹɸɬ ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɚɧɚɥɢɡɢ
ɪɨɜɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɧɚ ɨɫɧɨɜɟ ɷɥɟɤɬɪɨɞɜɢɝɚ
ɬɟɥɹ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɪɢɫ
ɢ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɟ
ɲɚɬɶ ɜɨɩɪɨɫɵ ɫɢɧɬɟɡɚ ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬɚɦɢ
ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ
Ɋɢɫ
Y
~
Y
Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɧɚ ɨɫɧɨɜɟ ɞɜɢɝɚɬɟɥɹ
ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ
\
ɚ ɩɪɢ γ =
ɜ ɩɪɢ γ =
ɛ ɩɪɢ γ =
Θ =
^
ɝ ɩɪɢ γ =
Θ =
Θ =
^
Θ =
Y
^
