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U
U
ɭ
Ɍɚɛɥɢɰɚ
1L : 0R 9 &X $O )H
ɥɟɝɢɪɭɸɳɢɯɢɪɚɫɤɢɫɥɢɬɟɥɟɣɤɨɬɨɪɵɟɩɪɟɞɩɨɥɚɝɚɟɬɫɹ
ɢɫɩɨɥɶɡɨɜɚɬɶɜɩɪɨɰɟɫɫɟɜɵɩɥɚɜɤɢ
Ɍɚɛɥɢɰɚ
1L 7L : $O 0R &X 9 )H
ɍɝɚɪɵɷɥɟɦɟɧɬɨɜɩɪɢɜɵɩɥɚɜɤɟɫɬɚɥɢɜȾɋɉɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹ
ɏɢɦɢɱɟɫɤɢɣɫɨɫɬɚɜ
ɇ ± ± ± ± ± ± ± ± ± ± ±
Ⱥ ± ± ± ± ± ± ± ± ± ±
Ɏɋ ± ± ± ± ± ±
Ɏɏ ± ± ± ± ± ± ±
ɎɆɧ ± ± ± ± ± ± ±
Ɇɚɬɟɪɢɚɥ & 6L 0Q 3 6 &
ɍɝɚɪ & 6L 0Q 3 6 &
Ɉɛɳɢɣ ¨Ɋ
ȼɲɥɚɤ
ɥɟɬ
ȼ
Ɉɤɢɫɥɟɧɢɟɷɥɟɦɟɧɬɨɜɢɨɠɢɞɚɟɦɵɣɯɢɦɢɱɟɫɤɢɣɫɨɫɬɚɜɦɟɬɚɥɥɚɩɨɪɚɫɩɥɚɜ
μ
μ
ɥɟɧɢɸɲɢɯɬɵɩɪɟɞɫɬɚɜɥɟɧɜɬɚɛɥ
Ɍɚɛɥɢɰɚ
ɏɢɦɢɱɟɫɤɢɣɫɨɫɬɚɜɦɟɬɚɥɥɚɩɨɪɚɫɩɥɚɜɥɟɧɢɸɲɢɯɬɵɤɝ
ɗɥɟɦɟɧɬ
&
6L
0Q
3
6
&U
1L
7L
:
0R
9
&X
$O
)H
ȼɫɟɝɨ
ɂɫɯɨɞɧɨɟ
ɫɨɞɟɪɠɚɧɢɟ
ɍɝɚɪɷɥɟɦɟɧɬɚ
Ɇɚɫɫɚɷɥɟɦɟɧɬɚ
ɜɪɚɫɩɥɚɜɟ
ɋɨɞɟɪɠɚɧɢɟɷɥɟɦɟɧɬɚ
ɜɪɚɫɩɥɚɜɟ
Ɋɚɫɱɟɬɜɟɥɢɱɢɧɩɪɢɜɟɞɟɧɧɵɯɜɬɚɛɥɢɰɟɧɚɩɪɢɦɟɪɟɭɝɥɟɪɨɞɚ
ɂɫɯɨɞɧɨɟɫɨɞɟɪɠɚɧɢɟ±ɤɝɫɦɬɚɛɥ
ɍɝɚɪɷɥɟɦɟɧɬɚ±
=⋅
ɤɝ
ɝɞɟ±ɢɫɯɨɞɧɨɟɫɨɞɟɪɠɚɧɢɟ
±ɨɛɳɢɣɭɝɚɪɷɥɟɦɟɧɬɚɫɦɬɚɛɥ
Ɇɚɫɫɚɷɥɟɦɟɧɬɚɜɪɚɫɩɥɚɜɟ± ɤɝ
ɋɨɞɟɪɠɚɧɢɟɷɥɟɦɟɧɬɚɜɪɚɫɩɥɚɜɟ±
=⋅
=−
ɝɞɟ±ɦɚɫɫɚɷɥɟɦɟɧɬɚɜɪɚɫɩɥɚɜɟɤɝ
±ɫɭɦɦɚɪɧɚɹɦɚɫɫɚɪɚɫɩɥɚɜɚɤɝ
Ɋɚɫɱɟɬɞɟɮɨɫɮɨɪɚɰɢɢɩɪɢɜɟɞɟɧɞɚɥɟɟ
Ɋɚɫɱɟɬɤɨɥɢɱɟɫɬɜɚɨɛɪɚɡɭɸɳɟɝɨɫɹɨɤɫɢɞɚ
P
Y
P
RL
L
=
Y
L
P
ɤɝɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɟ
RL
\[
μ××
RLRL
μ×
\[\[\[
ɝɞɟPL±ɦɚɫɫɚɨɤɢɫɥɹɸɳɟɝɨɫɹɷɥɟɦɟɧɬɚLɫɦɬɚɛɥ±ɭɝɚɪɷɥɟɦɟɧɬɚɤɝ
Y
Y
íɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɟɤɨɷɮɮɢɰɢɟɧɬɵɷɥɟɦɟɧɬɚLɢɨɤɫɢɞɚ\[RL ɫɨɨɬ
RL
L
\[
ɜɟɬɫɬɜɟɧɧɨ
±ɦɨɥɟɤɭɥɹɪɧɵɟɦɚɫɫɵɷɥɟɦɟɧɬɚLɢɨɤɫɢɞɚ\[RL ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
L
RL
\[
Ɋɚɫɱɟɬɤɨɥɢɱɟɫɬɜɚ ɤɢɫɥɨɪɨɞɚɤɝ ɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹ ɨɤɢɫɥɟɧɢɹɷɥɟɦɟɧɬɨɜ
ɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɟɤɝ
PPLP
ɍɝɥɟɪɨɞɈɤɢɫɥɟɧɢɟɭɝɥɟɪɨɞɚɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>&@ò^2` ^&2`
ɈɛɪɚɡɭɟɬɫɹɋɈ±
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɤɢɫɥɟɧɢɟɭɝɥɟɪɨɞɚ
=⋅
−=
LRL2
\[
ɤɝ
ɤɝ
=−
Ʉɪɟɦɧɢɣɉɪɢɨɤɢɫɥɟɧɢɢɤɪɟɦɧɢɹɩɨɪɟɚɤɰɢɢ>6L@>2@→6L2
ɟɬɫɹɤɪɟɦɧɟɡɟɦɚ
=⋅
ɤɝ
ɇɚɨɤɢɫɥɟɧɢɟɤɪɟɦɧɢɹɩɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚ±ɤɝ
ɆɚɪɝɚɧɟɰɈɤɢɫɥɟɧɢɟɦɚɪɝɚɧɰɚɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
Ɉɛɪɚɡɭɟɬɫɹ0Q2±
>0Q@ò^2` 0Q2
=⋅
ɤɝɂɡɷɬɨɝɨɤɨɥɢɱɟɫɬɜɚɬɟ
ɪɹɟɬɫɹɫɝɚɡɚɦɢɚɩɟɪɟɯɨɞɢɬɜɲɥɚɤɫɦɬɚɛɥ
ɋɝɚɡɚɦɢɬɟɪɹɟɬɫɹ
ɢɡɧɢɯ
ȼɲɥɚɤɩɟɪɟɯɨɞɢɬ
ɢɡɧɢɯ
=
=
=
=
ɤɝ0Q2
ɤɝ0Q2
ɤɝ0Q
ɤɝ0Q
ɢ±ɤɨɥɢɱɟɫɬɜɨ0Q2ɢɥɢ0Qɤɨɬɨɪɨɟɬɟɪɹɟɬɫɹɫɝɚɡɚɦɢɢɩɟɪɟɯɨɞɢɬɜ
ɲɥɚɤɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɞɥɹɨɤɢɫɥɟɧɢɹɜɫɟɝɨɦɚɪɝɚɧɰɚ±ɤɝ
ɋɟɪɚɉɪɢɧɢɦɚɟɦɱɬɨɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹɫɟɪɚɢɡɲɢɯɬɵɧɟɭɞɚɥɹɟɬɫɹ
ɏɪɨɦɈɤɢɫɥɟɧɢɟɯɪɨɦɚɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>&U@^2` &U2
Ɉɛɪɚɡɭɟɬɫɹɨɤɫɢɞɚɯɪɨɦɚ&U2±
ɍɧɨɫɢɬɫɹɩɟɱɧɵɦɢɝɚɡɚɦɢ
ɢɡɧɢɯ
ɉɟɪɟɯɨɞɢɬɜɲɥɚɤ
=
=
=
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ɤɝ&U2
ɤɝ&U
ɤɝ&U2
ɤɝ
ɨɛɪɚɡɭ
ɢɡɧɢɯ
=
ɤɝ&U
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɞɥɹɨɤɢɫɥɟɧɢɹɜɫɟɝɨɯɪɨɦɚ±ɤɝ
ɇɢɤɟɥɶɋɱɢɬɚɟɦɱɬɨɜɨɜɪɟɦɹɩɥɚɜɥɟɧɢɹɜɡɨɧɟɷɥɟɤɬɪɢɱɟɫɤɢɯɞɭɝɢɫɩɚɪɹ
ɟɬɫɹɧɢɤɟɥɹɢɦɟɜɲɟɝɨɫɹɜɲɢɯɬɟɫɦɬɚɛɥɂɫɩɚɪɢɜɲɢɣɫɹɧɢɤɟɥɶɭɧɨ
ɫɢɬɫɹɩɟɱɧɵɦɢɝɚɡɚɦɢɜɤɨɥɢɱɟɫɬɜɟɤɝɫɦɬɚɛɥ
ɌɢɬɚɧɈɤɫɢɞɬɢɬɚɧɚɩɨɥɧɨɫɬɶɸɩɟɪɟɯɨɞɢɬɜɲɥɚɤɫɦɬɚɛɥ
Ɉɛɪɚɡɭɟɬɫɹ7L2
±
=⋅
ɤɝ
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɞɥɹɨɤɢɫɥɟɧɢɹɬɢɬɚɧɚ±ɤɝ
ȼɨɥɶɮɪɚɦ.ɉɪɢɧɢɦɚɟɦɱɬɨɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹɜɨɥɶɮɪɚɦɢɡɲɢɯɬɵɧɟɭɞɚ
ɥɹɟɬɫɹ
Ⱥɥɸɦɢɧɢɣ.ɉɪɢɨɤɢɫɥɟɧɢɢɚɥɸɦɢɧɢɹɨɛɪɚɡɭɟɬɫɹɝɥɢɧɨɡɟɦɚ
=⋅
ɤɝ
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɞɥɹɨɤɢɫɥɟɧɢɹɚɥɸɦɢɧɢɹ±ɤɝ
Ɇɨɥɢɛɞɟɧ, ɦɟɞɶ, ɜɚɧɚɞɢɣɉɪɢɧɢɦɚɟɦɱɬɨɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹɷɬɢɷɥɟɦɟɧɬɵ
ɢɡɲɢɯɬɵɧɟɭɞɚɥɹɸɬɫɹɫɦɬɚɛɥȾɨɩɭɫɤɚɟɦɱɬɨɜɚɧɚɞɢɣɧɟɨɤɢɫɥɹɟɬɫɹɩɨ
ɩɪɢɱɢɧɟɧɟɛɨɥɶɲɨɝɨɟɝɨɩɪɢɫɭɬɫɬɜɢɹɜɲɢɯɬɟ
ɀɟɥɟɡɨɋɱɢɬɚɟɦɱɬɨɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹɨɤɢɫɥɢɜɲɟɝɨɫɹɠɟɥɟɡɚɬɟɪɹ
ɟɬɫɹɫɝɚɡɚɦɢɚɩɟɪɟɯɨɞɢɬɜɲɥɚɤɫɦɬɚɛɥ
ɉɨɪɟɚɤɰɢɢ>)H@ò^2
ɍɧɨɫɢɬɫɹɩɟɱɧɵɦɢɝɚɡɚɦɢ
ɢɡɧɢɯ
ɉɟɪɟɯɨɞɢɬɜɲɥɚɤ
ɢɡɧɢɯ
` )H2ɨɛɪɚɡɭɟɬɫɹɨɤɫɢɞɨɜɠɟɥɟɡɚɜɩɟɪɟɫɱɟɬɟɧɚ
)H2±
=
=
=
=
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ɤɝ)H2
ɤɝ)H
ɤɝ)H
ɤɝ
ɤɝ)H2
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɞɥɹɨɤɢɫɥɟɧɢɹɜɫɟɝɨɠɟɥɟɡɚ±ɤɝ
Ɇɟɬɚɥɥ. ȼɤɨɧɰɟɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɜɩɟɱɢɨɫɬɚɟɬɫɹɫɥɟɞɭɸɳɟɟɤɨɥɢɱɟɫɬɜɨ
ɦɟɬɚɥɥɚɫɭɱɟɬɨɦ ɭɝɚɪɨɜɷɥɟɦɟɧɬɨɜ ɤɝɫɦɬɚɛɥ ɫɨɞɟɪɠɚɧɢɟ
ɭɝɥɟɪɨɞɚɜɦɟɬɚɥɥɟɫɨɫɬɚɜɢɬɫɦɬɚɛɥ
ɋɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɦɟɬɚɥɥɟɨɩɪɟɞɟɥɹɟɦɢɡɝɪɚɮɢɤɚɢɥɢɩɨɮɨɪɦɭɥɟ
[]
&
·
¸
¹
§
[]
2 +
−=
¨
©
ɋɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɦɟɬɚɥɥɟ
μ×μ
[]
&
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¸
¹
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[]
2 =+
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¨
©
Ɉɩɪɟɞɟɥɹɟɦɫɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɦɟɬɚɥɥɟɤɨɬɨɪɨɟɩɨɲɥɨɧɚɧɚɫɵɳɟɧɢɟ
ɦɟɬɚɥɥɚɢɫɩɨɥɶɡɭɹɩɪɨɩɨɪɰɢɸ
[
+
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=
ɝɞɟɯ±ɢɫɤɨɦɚɹɜɟɥɢɱɢɧɚɤɝ
[ +
±ɦɚɫɫɚɦɟɬɚɥɥɚɫɭɱɟɬɨɦɫɨɞɟɪɠɚɧɢɹɤɢɫɥɨɪɨɞɚɤɝ
±ɫɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɦɟɬɚɥɥɟ
ɯ ɤɝ
2.2.2. ɒɥɚɤɨɨɛɪɚɡɨɜɚɧɢɟ
ɒɥɚɤɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɨɛɪɚɡɭɟɬɫɹɢɡɢɡɜɟɫɬɢɚɝɥɨɦɟɪɚɬɚɫɨɫɬɚɜɥɹɸɳɢɯ
ɪɚɡɪɭɲɚɸɳɟɣɫɹɮɭɬɟɪɨɜɤɢɜɚɧɧɵɫɬɟɧɢɫɜɨɞɚɨɤɫɢɞɨɜɩɨɥɭɱɟɧɧɵɯɩɪɢɨɤɢɫ
ɥɟɧɢɢɤɨɦɩɨɧɟɧɬɨɜɦɟɬɚɥɥɢɱɟɫɤɨɣɲɢɯɬɵ
Ɋɚɫɱɟɬɤɨɥɢɱɟɫɬɜɚɤɨɦɩɨɧɟɧɬɨɜɜɧɨɫɢɦɵɯɜɲɥɚɤɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɟ
⋅
MP
M
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ɝɞɟ
±ɦɚɫɫɚɤɨɦɩɨɧɟɧɬɚLɜɧɨɫɢɦɨɝɨɲɥɚɤɨɨɛɪɚɡɭɸɳɢɦMɤɝ
MP
L
±ɪɚɫɯɨɞɲɥɚɤɨɨɛɪɚɡɭɸɳɟɝɨMɤɝ
P
M
L±ɫɨɞɟɪɠɚɧɢɟɤɨɦɩɨɧɟɧɬɚ
ȺɊɚɫɱɟɬɤɨɦɩɨɧɟɧɬɨɜɜɧɨɫɢɦɵɯɢɡɜɟɫɬɶɸɜɲɥɚɤɤɝ
&D2±
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ȼɞɚɧɧɨɦɪɚɫɱɟɬɟɜɟɞɟɦɩɟɪɟɫɱɟɬɧɚ)H2ɩɨɮɨɪɦɭɥɟ
ɝɞɟ
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±ɦɨɥɟɤɭɥɹɪɧɵɟɦɚɫɫɵ)H2ɢ)H2ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
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ȼɫɟɝɨ
ȼɫɟɝɨ
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