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ɋɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɦɟɬɚɥɥɟɤɤɨɧɰɭɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɨɩɪɟɞɟ
μ
ɥɹɟɦɩɨɮɨɪɦɭɥɟ
@2> =
=
⋅+
ȼɤɨɧɰɟɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɫɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɦɟɬɚɥɥɟɛɵɥɨ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɧɟɨɛɯɨɞɢɦɨ ɩɨɜɵɫɢɬɶ ɟɝɨ ɫɨɞɟɪɠɚɧɢɟ ɧɚ ɢɥɢ
P ɤɝ
=⋅ =
>2@
Ʉɨɥɢɱɟɫɬɜɨɤɢɫɥɨɪɨɞɚɧɟɨɛɯɨɞɢɦɨɝɨɜɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞ
2
=++=
ɤɝP
8.5.2. ɒɥɚɤɨɨɛɪɚɡɨɜɚɧɢɟ
ɉɪɢɧɢɦɚɟɦɨɤɢɫɥɟɧɧɨɫɬɶɲɥɚɤɚɩɟɪɢɨɞɚɨɤɢɫɥɟɧɢɹɜȼɟɥɢɱɢɧɚɨɬɧɨ
ɲɟɧɢɹɤɨɥɢɱɟɫɬɜɚɠɟɥɟɡɚɫɨɞɟɪɠɚɳɟɝɨɫɹɜɤɨɦɩɨɧɟɧɬɚɯɲɥɚɤɚ)H2ɢ)ɟɈ
ɪɚɜɧɚ
Ɍɨɝɞɚɩɪɨɰɟɧɬɧɨɟɫɨɞɟɪɠɚɧɢɟɠɟɥɟɡɚɜɲɥɚɤɟɨɬ)H2
μ
)H
=
)H2
μ
)H2
ɚɩɪɨɰɟɧɬɧɨɟɫɨɞɟɪɠɚɧɢɟɠɟɥɟɡɚɜɲɥɚɤɟɨɬ)ɟɈ
)H
ɋɥɟɞɨɜɚɬɟɥɶɧɨɜɲɥɚɤɟɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɫɨɞɟɪɠɢɬɫɹ
)H
2)H
2)H
)H2
=
)H
2)H
⋅
μ⋅
)H
=⋅=⋅
===
)H
2)H
ɝɞɟ)ɟɈ±ɫɨɞɟɪɠɚɧɢɟɨɤɫɢɞɚɜɲɥɚɤɟ
Ɍɨɝɞɚɩɨɮɨɪɦɭɥɟɫɨɞɟɪɠɚɧɢɟ)ɟɈɜɲɥɚɤɟ
2)H
=
⋅
=⋅
Ɇɚɫɫɭɨɤɫɢɞɨɜɠɟɥɟɡɚɜɲɥɚɤɟɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɦɨɠɧɨɧɚɣɬɢɩɨɮɨ
ɪɦɭɥɚɦ
P
P
P
2)H
)H2
⋅=
ɲɥ)H2
2)H
P
⋅=
ɲɥ
ɝɞɟ)H2)ɟɈ±ɫɨɞɟɪɠɚɧɢɟɨɤɫɢɞɨɜɜɲɥɚɤɟ
ɉɨɫɥɟɫɤɚɱɢɜɚɧɢɹɲɥɚɤɚɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɜɜɚɧɧɟɟɝɨɨɫɬɚɥɨɫɶɢɥɢ
ɤɝɌɨɝɞɚɲɥɚɤɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɜɧɟɫɟɬ
&D2±
0J2± ⋅
6L2± ⋅
ȺOɈ± ⋅
)H2± ⋅
)H2± ⋅
32± ⋅
ɆQɈ± ⋅
ɋUɈ± ⋅
6± ⋅
ɉɨɫɬɭɩɢɬɜɲɥɚɤɢɡɦɟɬɚɥɥɚɫɦɜɵɲɟ
⋅
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɂɬɨɝɨɤɝ
ɆQɈ±ɤɝ
6L2±ɤɝ
ɊɈ±ɤɝ
ɋUɈ±ɤɝ
ɂɬɨɝɨɤɝ
ɇɨɜɵɣɲɥɚɤ ɧɚɜɨɞɢɬɫɹɩɪɢɫɚɞɤɨɣ ɢɡɜɟɫɬɢȾɥɹ ɭɞɚɥɟɧɢɹɮɨɫɮɨɪɚ ɢɡɦɟ
ɬɚɥɥɚɧɟɨɛɯɨɞɢɦɚɨɫɧɨɜɧɨɫɬɶɲɥɚɤɚȼ ɉɪɢɧɢɦɚɹȼ ɩɨɥɭɱɢɦ
PP
+
ɢɡɜ&D2ɲɥɩ&D2
=
ɢɡɜ6L2ɲɥɩ6L2
ɝɞɟ
P
ɲɥɩ&D2
P
P ±ɫɨɞɟɪɠɚɧɢɟɋɚɈɢ6L2ɜɢɡɜɟɫɬɢɤɝ
ɢɡɜ&D2
%
=
P ±ɫɨɞɟɪɠɚɧɢɟɋɚɈɢ6L2ɜɩɟɪɜɨɦɲɥɚɤɟɤɝ
ɲɥɩ6L2
ɢɡɜ6L2
PP
+
Ɉɬɫɸɞɚɫɥɟɞɭɟɬɱɬɨɦɚɫɫɚɢɡɜɟɫɬɢ
ɝɞɟɋɚɈ
6L2
ɢɡɜ
Ɍɨɝɞɚɦɚɫɫɚɢɡɜɟɫɬɢɩɨɮɨɪɦɭɥɟ
±ɫɨɞɟɪɠɚɧɢɟɋɚɈɢ6L2ɜɢɡɜɟɫɬɢ
ɢɡɜ
P
ɢɡɜ
P P
⋅−
6L2 ɩɲɥ &D2 ɩɲɥ
P
=
ɢɡɜ
=
&D2
ɢɡɜ
−⋅
−⋅
⋅−
6L2
ɉɪɢɧɢɦɚɟɦɤɨɥɢɱɟɫɬɜɨɢɡɜɟɫɬɢɤɝ
ɂɡɜɟɫɬɶɜɧɟɫɟɬɜɲɥɚɤ
&D2± ɤɝ
0J2± ɤɝ
6L2± ɤɝ
$O2± ɤɝ
)H2± ɤɝ
32± ɤɝ
ɉɪɢɷɬɨɦɨɛɪɚɡɭɟɬɫɹɋɈ± ⋅
Ɉɛɳɚɹɦɚɫɫɚɲɥɚɤɚɛɟɡɨɤɫɢɞɨɜɠɟɥɟɡɚ
ɋɭɦɦɚɪɧɨɟɤɨɥɢɱɟɫɬɜɨɲɥɚɤɚɧɚɣɞɟɦɩɨɮɨɪɦɭɥɟ
ɝɞɟ
P
±ɦɚɫɫɚɲɥɚɤɚɛɟɡɨɤɫɢɞɨɜɠɟɥɟɡɚɤɝ
ɲɥ
P
6± ɤɝ
ɂɬɨɝɨɤɝ
=
ɲɥ
ɤɝ
P
)H 2 )H2
−
=⋅
=⋅
=⋅
=⋅
=⋅
=⋅
=⋅
ɲɥ
)ɟɈ)H2±ɫɨɞɟɪɠɚɧɢɟɨɤɫɢɞɨɜɜɲɥɚɤɟ
ɤɝ
ɢɡɜ
=
ɤɝ
ɤɝ =++
ɤɝ
Ɍɨɝɞɚɦɚɫɫɚɲɥɚɤɚɩɨɮɨɪɦɭɥɟ
−
=
+
=⋅=
=⋅=
P
=
ɲɥ
Ɇɚɫɫɵɨɤɫɢɞɨɜɠɟɥɟɡɚɩɨɮɨɪɦɭɥɚɦ
P
)H2
P
2)H
ɤɝ
ɤɝ
ɤɝ
ɋɨɩɨɫɬɚɜɢɦɷɬɢɞɚɧɧɵɟɫɩɨɫɬɭɩɥɟɧɢɟɦɠɟɥɟɡɚɜɲɥɚɤɜɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟ
ɪɢɨɞ
ɂɡɲɥɚɤɚɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɩɨɫɬɭɩɚɟɬ
)H2±ɤɝ)H2±ɤɝ
ɂɡɢɡɜɟɫɬɢɩɨɫɬɭɩɚɟɬ)ɟɈ±ɤɝ
ɂɬɨɝɨ)H2±ɤɝ)ɟɈ±ɤɝɋɥɟɞɨɜɚɬɟɥɶɧɨɧɟɨɛɯɨɞɢɦɨ
ɞɨɛɚɜɢɬɶɨɤɫɢɞɨɜɠɟɥɟɡɚɜɤɨɥɢɱɟɫɬɜɟ
)H2±ɤɝ)H2±ɤɝ
Ⱦɥɹɷɬɨɝɨɩɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɛɪɚɡɨɜɚɧɢɟ)ɟɈ
ɩɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɛɪɚɡɨɜɚɧɢɟ)H2
ɉɨɬɪɟɛɭɟɬɫɹɠɟɥɟɡɚɧɚɨɛɪɚɡɨɜɚɧɢɟ)ɟɈ
ɩɨɬɪɟɛɭɟɬɫɹɠɟɥɟɡɚɧɚɨɛɪɚɡɨɜɚɧɢɟ)H2
P
P
=
2
μ
P
=
2
P
P
=
@)H>
μ
P
2)H
2)H
P
μ
)H2
2)H
P
=
@)H>
2
)H2
2)H
)H2
μ
)H2
2
)H
)H
=⋅⋅=μ⋅⋅
=⋅⋅=μ⋅⋅
=⋅⋅=μ⋅⋅
=⋅=μ⋅
ɤɝ
ɤɝ
ɤɝ
ɤɝ
Ʉɨɥɢɱɟɫɬɜɨ ɢ ɫɨɫɬɚɜ ɲɥɚɤɚ ɨɤɢɫɥɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɩɪɟɞɫɬɚɜɥɟɧ ɜ
ɬɚɛɥ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ɚ
U
ɬ
ɬ
Ʉɨɥɢɱɟɫɬɜɨɢɫɨɫɬɚɜɲɥɚɤɚɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɤɝ
Ʉɨɦɩɨɧɟɧɬ
ɋɚɈ ±
0J2 ±
6L2
ȺɈ ±
)H2 ±
)H2
ɊɈ
0Q2 ±
&
±
2
6 ±
ɂɬɨɝɨ
ɒɥɚɤɩɟɪɢɨɞɚ
ɩɥɚɜɥɟɧɢɹ
ɉɨɫɬɭɩɢɬ
ɢɡɦɟɬɚɥɥ
ɉɨɫɬɭɩɢɬ
ɢɡɢɡɜɟɫɬɢ
ɂɬɨɝɨ ɂɬɨɝɨ
8.5.3. Ɉɩɪɟɞɟɥɟɧɢɟ ɫɨɫɬɚɜɚ ɦɟɬɚɥɥɚ ɨɤɢɫɥɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ
Ʉɨɥɢɱɟɫɬɜɨɠɟɥɟɡɚɩɨɲɟɞɲɟɝɨɧɚɨɛɪɚɡɨɜɚɧɢɟɨɤɫɢɞɨɜɠɟɥɟɡɚ±ɤɝ
Ɍɨɝɞɚɠɟɥɟɡɚɜɦɟɬɚɥɥɟɨɫɬɚɧɟɬɫɹ
ɤɝ =−
ɋɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚ ɪɚɫɬɜɨɪɟɧɧɨɝɨɜ ɦɟɬɚɥɥɟɜ ɤɨɧɰɟɨɤɢɫɥɢɬɟɥɶɧɨɝɨ
ɩɟɪɢɨɞɚ
P ɤɝ
=⋅ =
>2@
Ʉɨɥɢɱɟɫɬɜɨɢɫɨɫɬɚɜɦɟɬɚɥɥɚɜɤɨɧɰɟɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɩɪɟɞɫɬɚɜɥɟɧɵ
ɜɬɚɛɥ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
Ʉɨɥɢɱɟɫɬɜɨɢɫɨɫɬɚɜɦɟɬɚɥɥɚɜɤɨɧɰɟɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚ
ɋɨɞɟɪɠɚɧɢɟ
ɜɦɟɬɚɥɥɟ
ɤɝ
ɋɨɞɟɪɠɚɧɢɟ
ɜɦɟɬɚɥɥɟ
ɤɝ
ɋ 6L 0Q Ɋ 6 Ɉ
ɗɥɟɦɟɧ
ɋU 1L ɋX )H
ɗɥɟɦɟɧ
ɂɬɨɝɨ
Ɉɩɪɟɞɟɥɟɧɢɟɤɨɥɢɱɟɫɬɜɚɢɫɨɫɬɚɜɚɝɚɡɨɜɜɩɟɪɢɨɞɵɩɥɚɜɥɟɧɢɹ
ɢɨɤɢɫɥɟɧɢɹ
Ɉɛɳɟɟɤɨɥɢɱɟɫɬɜɨ^ɋɈ`ɫɨɫɬɚɜɥɹɟɬɤɝ
Ɂɚɜɪɟɦɹɩɥɚɜɤɢɪɚɫɯɨɞɭɟɬɫɹɤɝɬɷɥɟɤɬɪɨɞɨɜȼɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹɪɚɫɯɨɞ
ɭɝɥɟɪɨɞɚɫɨɫɬɚɜɢɬɚɜɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞȼɷɥɟɤɬɪɨɞɟɫɨɞɟɪɠɚ
ɧɢɟɭɝɥɟɪɨɞɚɫɨɫɬɚɜɥɹɟɬɬɨɝɞɚɨɤɢɫɥɹɟɬɫɹɭɝɥɟɪɨɞɚ
P
⋅
=
&
=⋅
ɤɝ
ɉɪɢɧɢɦɚɟɦɱɬɨ ɭɝɥɟɪɨɞɚ ɨɤɢɫɥɹɟɬɫɹ ɞɨ^ɋɈ` ɚ − ɞɨ ^ɋɈ`
Ɍɨɝɞɚɨɛɪɚɡɭɟɬɫɹ
P
⋅
P
=
{}
&2
P
=
{}
&2
Ʉɨɥɢɱɟɫɬɜɨɤɢɫɥɨɪɨɞɚɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɭɝɥɟɪɨɞɚɫɨɫɬɚɜɢɬ
&
=μ⋅
μ
⋅
μ
&2
&
P
&
&
=μ⋅
&2
&&22
&&22
⋅
⋅
=⋅
=⋅
=⋅−=−=
=⋅−=−=
ɤɝ
ɤɝ
ɤɝPPP
ɤɝPPP
ɂɬɨɝɨɦɚɫɫɚɤɢɫɥɨɪɨɞɚɧɚɨɤɢɫɥɟɧɢɟɭɝɥɟɪɨɞɚɪɚɜɧɚɤɝ
Ɉɛɳɟɟ ɤɨɥɢɱɟɫɬɜɨ ɬɪɟɛɭɟɦɨɝɨ ɤɢɫɥɨɪɨɞɚ ɡɚ ɞɜɚ ɩɟɪɢɨɞɚ ɫɨɫɬɚɜɢɬ
ɤɝ
ɉɪɢɧɢɦɚɟɦɱɬɨɢɥɢɤɝɤɢɫɥɨɪɨɞɚɩɪɢɯɨɞɢɬɫɹɧɚɤɢɫɥɨɪɨɞɜɨɡ
ɞɭɯɚɈɛɴɟɦɤɢɫɥɨɪɨɞɚɜɜɨɡɞɭɯɟ
=
9
2
P
μ
2
2
=⋅=⋅
ɦ
Ʉɨɥɢɱɟɫɬɜɨɫɨɩɭɬɫɬɜɭɸɳɟɝɨɚɡɨɬɚɧɚɯɨɞɢɦɢɡɭɫɥɨɜɢɹɱɬɨɨɛɴɟɦɧɨɟɫɨɞɟ
ɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɜɨɡɞɭɯɟɪɚɜɧɨɬɨɝɞɚ
9
Ɇɚɫɫɨɜɨɟɫɨɞɟɪɠɚɧɢɟɤɢɫɥɨɪɨɞɚɜɜɨɡɞɭɯɟɬɨɝɞɚ
P
Ɉɛɴɟɦɢɦɚɫɫɚɜɨɡɞɭɯɚ
−
=
−
=
12ȼ
12ȼ
=⋅
21
=⋅
21
ɦ9
ɤɝP
=+=+=
=+=+=
ɦ999
ɤɝPPP
Ʉɨɥɢɱɟɫɬɜɨɧɟɨɛɯɨɞɢɦɨɝɨɝɚɡɨɨɛɪɚɡɧɨɝɨɤɢɫɥɨɪɨɞɚɨɩɪɟɞɟɥɹɟɬɫɹɩɪɢɭɫɥɨ
ɜɢɢɱɬɨɤɨɷɮɮɢɰɢɟɧɬɟɝɨɢɫɩɨɥɶɡɨɜɚɧɢɹN
ɢɫɩ
ρ
−
=
P
2
=⋅
N
ɢɫɩ
ɤɝ
Ʉɨɥɢɱɟɫɬɜɨɬɟɯɧɢɱɟɫɤɨɝɨɤɢɫɥɨɪɨɞɚɨɩɪɟɞɟɥɹɟɦ ɢɡɭɫɥɨɜɢɹ ɱɬɨɫɨɞɟɪɠɚ
ɧɢɟɤɢɫɥɨɪɨɞɚɜɧɟɦ
P
2
ɬɟɯ
9
2
ɬɟɯ
=
μ
2
=⋅=
=⋅
2
ɬɟɯ
ɤɝ
ɦP
ɋɤɢɫɥɨɪɨɞɨɦɜɧɨɫɢɬɫɹɚɡɨɬɚ− ɤɝ
ɉɪɢɧɚɝɪɟɜɟɢɡɜɟɫɬɢɜɵɞɟɥɹɟɬɫɹ^ɋɈ`ɤɝ
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W% ɋɪȼ ɦɦɪɬɫɬI ȿ ɦɦɪɬɫɬ
ȼɥɚɠɧɨɫɬɶɚɬɦɨɫɮɟɪɧɨɝɨɜɨɡɞɭɯɚ
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Ʉɨɥɢɱɟɫɬɜɨɜɨɞɹɧɨɝɨɩɚɪɚɜɦɚɬɦɨɫɮɟɪɧɨɝɨɜɨɡɞɭɯɚ
Ɇɚɫɫɚɜɥɚɝɢ
ȼɨɞɹɧɨɣɩɚɪɪɟɚɝɢɪɭɟɬɫɨɤɢɫɶɸɭɝɥɟɪɨɞɚɩɨɪɟɚɤɰɢɢ
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ɩɚɪɚɜ
P
P
S
W
ɜɜ
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I(S
ɜ
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P
P
{}
+
{}
ɋɈ
{}
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P
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P
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μ
+
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ɦɤɝ
ɤɝ9P
ɤɝ
ɤɝ
ɤɝ
ɉɪɢɧɢɦɚɟɦɱɬɨɝɚɡɨɨɛɪɚɡɧɨɝɨɤɢɫɥɨɪɨɞɚɢɡɪɚɫɯɨɞɨɜɚɧɧɨɝɨɜɩɟɪɢ
ɨɞɵɩɥɚɜɥɟɧɢɹɢɨɤɢɫɥɟɧɢɹɭɲɥɨɜɚɬɦɨɫɮɟɪɭɩɟɱɢɬɟ
P
2
=⋅=
ɤɝ
ɦ
ɗɬɨɬɤɢɫɥɨɪɨɞɜɫɬɭɩɢɬɜɪɟɚɤɰɢɸɫɋɈɜɪɟɡɭɥɶɬɚɬɟɨɛɪɚɡɭɟɬɫɹɭɝɥɟɤɢɫɥɵɣ
ɭɝɭ
ɭ
U
ɭ
ɝɚɡɜɤɨɥɢɱɟɫɬɜɟ
P
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{}
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Ⱦɥɹɷɬɨɝɨɩɨɬɪɟɛɭɟɬɫɹ^ɋɈ`ɜɤɨɥɢɱɟɫɬɜɟ
=
&2
μ⋅
2
− ɤɝ
=μ⋅
⋅
=⋅
ɤɝ
Ɇɚɫɫɨɜɵɣɢɩɪɨɰɟɧɬɧɵɣɫɨɫɬɚɜɝɚɡɨɜɡɚɞɜɚɩɟɪɢɨɞɚɩɪɟɞɫɬɚɜɥɟɧɜɬɚɛɥ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ɋɨɫɬɚɜɝɚɡɨɜɡɚɞɜɚɩɟɪɢɨɞɚ
ɋɨɞɟɪɠɚɧɢɟ
ɝɚɡɨɜ
ɤɝ
ɦ
ɋɈ ɋɈ + 1 ɂɬɨɝɨ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɪɢɯɨɞɧɵɟ ɢ ɪɚɫɯɨɞɧɵɟ ɫɬɚɬɶɢ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ
ɢɦɟɸɬɫɥɟɞɭɸɳɢɣɜɢɞ
ɂɡɪɚɫɯɨɞɨɜɚɧɨɤɝ ɉɨɥɭɱɟɧɨɤɝ
± ɦɟɬɚɥɥɚ±
Ⱥ
ɠɢɞɤɨɝɨɱ
ɦɟɬɚɥɥɚɩɪɟɞɵɞ
ɧ± ɲɥɚɤɚ±
ɳɟɣɩɥɚɜɤɢ± ɝɚɡɨɜ±
ɢɡɜɟɫɬɢ± ɩɵɥɢ±
ɞɨɥɨɦɢɬɚ± ɜɬɨɦɱɢɫɥɟ
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±
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ɝɚɡɨɨɛɪɚɡɧɨɝɨɤɢɫɥɨɪɨɞɚ± &
ɲɥɚɤɚɩɪɟɞɵɞ
ɳɟɣɩɥɚɜɤɢ±
2
±
ȼɫɟɝɨ ȼɫɟɝɨ
ɇɟɜɹɡɤɚ
ȼɵɯɨɞɠɢɞɤɨɣɫɬɚɥɢ
\ ==
ɤɝ =−
=⋅
ɗɇȿɊȽȿɌɂɑȿɋɄɂɃȻȺɅȺɇɋȼɕɉɅȺȼɄɂɋɌȺɅɂɆȺɊɄɂ
ȼɒȺɏɌɇɈɃȾɍȽɈȼɈɃɉȿɑɂ
ɋɬɚɬɶɢɩɪɢɯɨɞɚɬɟɩɥɨɬɵ
Ʉɨɥɢɱɟɫɬɜɨɬɟɩɥɚɜɧɨɫɢɦɨɟɷɥɟɤɬɪɢɱɟɫɤɨɣɷɧɟɪɝɢɟɣ:ɢɡɦɟɪɹɸɬɫɞɨɫ
ɬɚɬɨɱɧɨɜɵɫɨɤɨɣɬɨɱɧɨɫɬɶɸɫɱɟɬɱɢɤɚɦɢɚɤɬɢɜɧɨɣɷɧɟɪɝɢɢɤɨɬɨɪɵɟɭɫɬɚɧɚɜɥɢ
ɜɚɸɬɧɚɩɟɱɢɄɨɥɢɱɟɫɬɜɨɬɟɩɥɚȽȾɠɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɚɦ
τ
ɩɥ
⋅⋅=
3.:
ɩɥɷɥ
τ
ɨɤ
⋅⋅=
3.:
ɨɤɷɥ
ɝɞɟɄ±ɤɨɷɮɮɢɰɢɟɧɬɢɫɩɨɥɶɡɨɜɚɧɢɹɦɨɳɧɨɫɬɢ
IJɩɥ±ɜɪɟɦɹɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɦɢɧ
3
±ɦɨɳɧɨɫɬɶɜɜɨɞɢɦɚɹɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹɆȼɬ
ɷɥɩɥ
Ɋ
±ɦɨɳɧɨɫɬɶɜɜɨɞɢɦɚɹɜɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞɆȼɬ
ɷɤɨɤ
IJɨɤ±ɜɪɟɦɹɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɦɢɧ
Ɍɨɝɞɚɤɨɥɢɱɟɫɬɜɨɬɟɩɥɚɨɩɪɟɞɟɥɹɟɦɨɟɩɨɮɨɪɦɭɥɚɦ
: : : Ɇȼɬ ɱ ȽȾɠ=+= + = ⋅
Ʉɨɥɢɱɟɫɬɜɨɬɟɩɥɚɜɧɨɫɢɦɨɟɠɢɞɤɢɦɱɭɝɭɧɨɦɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɟ
P
ɝɞɟ
±ɦɚɫɫɚɠɢɞɤɨɝɨɱɭɝɭɧɚɤɝ
ɱɠ
ɠ
ɋ
±ɫɪɟɞɧɹɹɭɞɟɥɶɧɚɹɬɟɩɥɨɟɦɤɨɫɬɶɠɢɞɤɨɝɨɱɭɝɭɧɚɜɢɧɬɟɪɜɚɥɟɬɟɦɩɟɪɚ
ɱ
:
:
ɠ
ɱɱɠ
ɬɜ
ɱɩɥɱɩɥɱ
⋅=⋅⋅=
⋅=⋅⋅=
⋅++−⋅⋅=
ɱɆȼɬ
ɱɆȼɬ
WɋT@WW>ɋP:
ɱɩɥ
ɬɭɪɋɤȾɠɤɝ⋅Ʉ
Wɱ±ɬɟɦɩɟɪɚɬɭɪɚɡɚɥɢɜɚɟɦɨɝɨɱɭɝɭɧɚɋ
W
±ɬɟɦɩɟɪɚɬɭɪɚɩɥɚɜɥɟɧɢɹɱɭɝɭɧɚɋ
ɩɥɱ
Tɩɥ±ɫɤɪɵɬɚɹɬɟɩɥɨɬɚɩɥɚɜɥɟɧɢɹɤȾɠɤɝ
ɬɜ
ɋ
±ɫɪɟɞɧɹɹɭɞɟɥɶɧɚɹɬɟɩɥɨɟɦɤɨɫɬɶɬɜɟɪɞɨɝɨɱɭɝɭɧɚɜɢɧɬɟɪɜɚɥɟɬɟɦɩɟɪɚ
ɱ
ɬɭɪɋɤȾɠɤɝ⋅Ʉ
Ɍɨɝɞɚɩɨɮɨɪɦɭɥɟɨɩɪɟɞɟɥɹɟɦɤɨɥɢɱɟɫɬɜɨɬɟɩɥɚɜɧɨɫɢɦɨɝɨɱɭɝɭɧɨɦ
()
[]
=⋅++−⋅⋅=
ȽȾɠ:
Ʉɨɥɢɱɟɫɬɜɨɬɟɩɥɚɩɨɫɬɭɩɚɸɳɟɝɨɫɲɢɯɬɨɣ
ɜɧɨɫɢɦɨɝɨɲɢɯɬɨɣɩɟɪɜɨɣɤɨɪɡɢɧɵ
ɜɧɨɫɢɦɨɟɲɢɯɬɨɣɜɬɨɪɨɣɤɨɪɡɢɧɵ
ɝɞɟ .
±ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɭɫɜɨɟɧɢɹ ɩɪɢɩɨɞɨɝɪɟɜɟ ɲɢɯɬɵ ɨɬɯɨɞɹɳɢɦɢɝɚ
ɭɫɜ
=
()
WW&P.:
−=
ɧɲɲɲɭɫɜ
W&P:
ɲɲɲ
ɡɚɦɢ
P
±ɦɚɫɫɚɲɢɯɬɵɜɩɟɪɜɨɣɜɬɨɪɨɣɤɨɪɡɢɧɟɤɝ
ɲ
ɋ
±ɭɞɟɥɶɧɚɹɬɟɩɥɨɟɦɤɨɫɬɶɫɤɪɚɩɚȾɠɤɝ⋅Ʉ
ɲ
Wɲ±ɬɟɦɩɟɪɚɬɭɪɚɩɪɢɤɨɬɨɪɨɣɲɢɯɬɚɡɚɝɪɭɠɚɟɬɫɹɜɩɟɱɶɋ
Wɧ±ɧɚɱɚɥɶɧɚɹɬɟɦɩɟɪɚɬɭɪɚɲɢɯɬɵɋ
Ɍɨɝɞɚɧɚɯɨɞɢɦɤɨɥɢɱɟɫɬɜɨɬɟɩɥɚɜɧɨɫɢɦɨɟɲɢɯɬɨɣɩɨɮɨɪɦɭɥɚɦ
Ʉɨɥɢɱɟɫɬɜɨɬɟɩɥɚɩɨɫɬɭɩɚɸɳɟɝɨɫɢɡɜɟɫɬɶɸ
()
ɝɞɟɋ
±ɭɞɟɥɶɧɚɹɬɟɩɥɨɟɦɤɨɫɬɶɢɡɜɟɫɬɢ
ɢɡɜ
ɋ W W
=+⋅ +−⋅ + =
ɢɡɜ ɢɡɜ ɢɡɜ
ɤȾɠ ɤɝ Ʉ
=+⋅⋅−⋅⋅= ⋅
Ɍɨɝɞɚ
Ʉɨɥɢɱɟɫɬɜɨɬɟɩɥɚɜɧɨɫɢɦɨɟɫɞɨɥɨɦɢɬɨɦ
−−
ɩɪɢW ɋɬɟɩɥɨɟɦɤɨɫɬɶɞɨɥɨɦɢɬɚɋ
ɩɪɢW ɋɋ
ɌɨɝɞɚɩɪɢW
Ⱦɠɤɝ⋅Ʉ
ɞɨɥ
ɬɟɩɥɨɟɦɤɨɫɬɶɞɨɥɨɦɢɬɚɧɚɯɨɞɢɦɩɨɮɨɪɦɭɥɟ
ɞɨɥ
ɋ
Δ
ɋ
+=
ɞɨɥɞɨɥ
Ɍ
Δ
()
ɲ
=
−
() ()
=⋅⋅=
=
Ⱦɠɤɝ⋅Ʉ
ɞɨɥ
W
+=
−−
W&P:
ɢɡɜɢɡɜɢɡɜ
ȽȾɠ:
W&P:
ɞɨɥɞɨɥɞɨɥ
−
−
=⋅⋅=
⋅=−⋅⋅=
=⋅+⋅=+=
ȽȾɠ:
Ⱦɠ:
ɲɲ
ȽȾɠ:::
()
()
ȾɠWWW:
⋅=⋅⋅+⋅⋅+=
−
ɄɤɝȾɠ
⋅=
Ɍɟɩɥɨ ɷɤɡɨɬɟɪɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ: Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ : ɧɟɨɛɯɨɞɢɦɨ
ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɫɨɫɬɚɜɢɬɶ ɦɚɬɟɪɢɚɥɶɧɵɣɛɚɥɚɧɫ ɫɩɨɦɨɳɶɸ ɤɨɬɨɪɨɝɨ ɭɫɬɚɧɚ
ɜɥɢɜɚɸɬɫɨɫɬɚɜɢɤɨɥɢɱɟɫɬɜɨɢɫɯɨɞɧɵɯɦɚɬɟɪɢɚɥɨɜɢɩɪɨɞɭɤɬɨɜɩɥɚɜɤɢɗɧɟɪɝɢɹ
ɷɤɡɨɬɟɪɦɢɱɟɫɤɢɯɪɟɚɤɰɢɣɨɤɢɫɥɟɧɢɹɤɨɦɩɨɧɟɧɬɨɜɦɟɬɚɥɥɨɲɢɯɬɵɜɵɞɟɥɹɟɬɫɹɜ
ɪɚɡɥɢɱɧɵɯɡɨɧɚɯɪɚɛɨɱɟɝɨɩɪɨɫɬɪɚɧɫɬɜɚȾɋɉɧɚɩɨɜɟɪɯɧɨɫɬɢɤɭɫɤɨɜɲɢɯɬɵɜ
ɠɢɞɤɨɣ ɜɚɧɧɟ ɢ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ ɱɬɨ ɩɪɟɞɨɩɪɟɞɟɥɹɟɬ ɢ ɪɚɡɥɢɱɧɭɸ ɫɬɟɩɟɧɶ
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