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Ɉɛɳɢɣ
ȼɲɥɚɤ
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ɥɟɧɢɸɲɢɯɬɵɩɪɟɞɫɬɚɜɥɟɧɜɬɚɛɥɗɥɟɦɟɧɬɵ7L:$O0R9ɢɡɡɚɦɚɥɨɝɨɢɯ
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ɂɬɨɝɨ
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ɜɪɚɫɩɥɚɜɟ
ɋɨɞɟɪɠɚɧɢɟɷɥɟɦɟɧɬɚ
ɜɪɚɫɩɥɚɜɟ
Ɉɩɪɟɞɟɥɹɟɦɤɨɥɢɱɟɫɬɜɨɤɢɫɥɨɪɨɞɚɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɷɥɟɦɟɧɬɨɜ
ɲɢɯɬɵ
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>&@^2`→^&2`
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=
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=
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ɨɛɪɚɡɭɟɬɫɹ&U2
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ɱɟɦ)H
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>)H@^2`→)H2
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ɥɟɧɢɹɲɢɯɬɵɜɩɟɪɢɨɞɩɥɚɜɥɟɧɢɹ
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ɋɨɫɬɚɜɦɟɬɚɥɥɚɩɨɪɚɫɩɥɚɜɥɟɧɢɸɲɢɯɬɵ
ɗɥɟɦɟɧɬɋ6L0Q36
ɋɨɞɟɪɠɚɧɢɟɤɝ
ɋɨɞɟɪɠɚɧɢɟ
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ɋɨɞɟɪɠɚɧɢɟɤɝ
ɋɨɞɟɪɠɚɧɢɟ
8.4.2. ɒɥɚɤɨɨɛɪɚɡɨɜɚɧɢɟ
ɉɪɢɧɢɦɚɟɦɱɬɨɩɨɫɥɟɜɵɩɭɫɤɚɩɪɟɞɵɞɭɳɟɣɩɥɚɜɤɢɜɜɚɧɧɟɨɫɬɚɟɬɫɹɩɪɢ
ɦɟɪɧɨɲɥɚɤɚɌɨɝɞɚɲɥɚɤɩɪɟɞɵɞɭɳɟɣɩɥɚɜɤɢɜɧɟɫɟɬ
&D2±ɤɝ
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±ɤɝ
3
2
±ɤɝ
&U
2
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±ɤɝ
)H
2
ɂɬɨɝɨɤɝ
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P
P
P
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ɢɡɜ
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P
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P
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P
P
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Ʉɨɥɢɱɟɫɬɜɨɢɫɨɫɬɚɜɲɥɚɤɚɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɩɪɟɞɫɬɚɜɥɟɧɵɜɬɚɛɥ
Ɉɫɧɨɜɧɨɫɬɶɲɥɚɤɚɩɨɨɤɨɧɱɚɧɢɢɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹ
P
%
&D2
P
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===
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Ʉɨɥɢɱɟɫɬɜɨɢɫɨɫɬɚɜɲɥɚɤɚɩɟɪɢɨɞɚɩɥɚɜɥɟɧɢɹɤɝ
Ʉɨɦɩɨɧɟɧɬ
ɋɚɈ ±
0J2 ±
6L2
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ɊɈ
0Q2 ± ±
&
± ± ±
2
6 ± ±
ɂɬɨɝɨ
ɒɥɚɤ
ɩɪɟɞɵɞɭɳɟɣ
ɩɥɚɜɤɢ
ɉɨɫɬɭɩɢɥɨ
ɢɡɦɟɬɚɥɥɚ
ɂɡɜɟɫɬɶ Ⱦɨɥɨɦɢɬ ɂɬɨɝɨ ɂɬɨɝɨ
Ɉɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞ
μ
8.5.1. Ɉɤɢɫɥɟɧɢɟ ɷɥɟɦɟɧɬɨɜ
ɂɡɨɩɵɬɚɢɡɜɟɫɬɧɨɱɬɨɩɪɢɦɟɪɧɨɷɥɟɦɟɧɬɨɜɨɤɢɫɥɹɸɬɫɹɤɢɫɥɨɪɨɞɨɦ
)H2ɚɨɫɬɚɥɶɧɵɟ−ɝɚɡɨɨɛɪɚɡɧɵɦɤɢɫɥɨɪɨɞɨɦɜɞɭɜɚɟɦɵɦɜɠɢɞɤɢɣɦɟ
ɬɚɥɥ
Ʉ ɤɨɧɰɭ ɨɤɢɫɥɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɜ ɦɟɬɚɥɥɟ ɞɨɥɠɧɨ ɨɫɬɚɬɶɫɹ ɭɝɥɟɪɨɞɚ
Ɍɨɝɞɚɨɫɬɚɧɟɬɫɹɜɦɟɬɚɥɥɟɭɝɥɟɪɨɞɚ
Ɂɚɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞɞɨɥɠɧɨɨɤɢɫɥɢɬɶɫɹ
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¬¼
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>&@^Ɉ`→^ɋɈ`
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ɥɹɟɦɩɨɮɨɪɦɭɥɟ
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ɨɛɪɚɡɭɟɬɫɹ^ɋɈ`
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`&2^
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>&@)H2→>)H@^&2`
Ɍɨɝɞɚɤɨɥɢɱɟɫɬɜɨɨɤɫɢɞɚɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɷɥɟɦɟɧɬɚ
)H2
⋅
⋅
=
⋅
P
LP
⋅
= ɤɝ
μ⋅ν
LL
=⋅⋅
=⋅⋅
L
μ⋅ν⋅
)H2)H2
ɤɝ
ɤɝ
ɝɞɟ±ɞɨɥɹɷɥɟɦɟɧɬɚɨɤɢɫɥɹɸɳɟɝɨɫɹɡɚɫɱɟɬ)H2
PLμL±ɦɚɫɫɚɢɦɨɥɟɤɭɥɹɪɧɚɹɦɚɫɫɚɷɥɟɦɟɧɬɚ
μ
±ɦɨɥɟɤɭɥɹɪɧɚɹɦɚɫɫɚ)H2
)H2
Ʉɨɥɢɱɟɫɬɜɨɨɤɫɢɞɚɨɛɪɚɡɭɸɳɟɝɨɫɹɜɪɟɡɭɥɶɬɚɬɟɨɤɢɫɥɟɧɢɹɧɚɯɨɞɢɦɩɨɮɨ
ɪɦɭɥɟ
ɝɞɟ
±ɦɨɥɟɤɭɥɹɪɧɚɹɦɚɫɫɚɨɤɫɢɞɚ
ML
\[
P
ML
P
⋅
= ɤɝ
L
μ⋅ν
LL
μ⋅ν⋅
MLML
\[\[\[
Ɍɨɝɞɚɤɨɥɢɱɟɫɬɜɨ)H2ɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɭɝɥɟɪɨɞɚ
ɨɛɪɚɡɭɟɬɫɹ^ɋɈ`
⋅
&P
=
)H2
P
=
`&2^
⋅
⋅
⋅
=⋅⋅
=⋅⋅
ɤɝ
ɤɝ
ɄɤɨɧɰɭɩɟɪɢɨɞɚɞɨɥɠɧɨɨɫɬɚɬɶɫɹɦɚɪɝɚɧɰɚɢɥɢɤɝɌɨɝɞɚ
ɨɤɢɫɥɹɟɬɫɹɦɚɪɝɚɧɰɚɡɚɩɟɪɢɨɞ− ɤɝ
Ɉɤɢɫɥɟɧɢɟɦɚɪɝɚɧɰɚɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>ɆQ@^2`→ɆQ2
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɤɢɫɥɟɧɢɟɦɚɪɝɚɧɰɚ
⋅
0QP
2
ɨɛɪɚɡɭɟɬɫɹɆQɈ
P
Ɉɤɢɫɥɟɧɢɟɦɚɪɝɚɧɰɚɨɤɫɢɞɨɦɠɟɥɟɡɚ)H2ɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
=
⋅
=
0Q2
⋅
>ɆQ@)H2→>)H@ɆQɈ
Ʉɨɥɢɱɟɫɬɜɨ)H2ɧɟɨɛɯɨɞɢɦɨɟɞɥɹɨɤɢɫɥɟɧɢɹɦɚɪɝɚɧɰɚ
0QP
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ɨɛɪɚɡɭɟɬɫɹɆQɈ
P
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⋅
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ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɄɤɨɧɰɭɩɟɪɢɨɞɚɞɨɥɠɧɨɨɫɬɚɬɶɫɹɤɪɟɦɧɢɹɢɥɢɤɝɌɨɝɞɚɨɤɢ
ɫɥɢɬɫɹɤɪɟɦɧɢɹɡɚɩɟɪɢɨɞ− ɤɝ
Ɉɤɢɫɥɟɧɢɟɤɪɟɦɧɢɹɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>6L@^2`→6L2
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɤɢɫɥɟɧɢɟɤɪɟɦɧɢɹ
⋅
6LP
=
2
⋅
=⋅⋅
ɤɝ
ɨɛɪɚɡɭɟɬɫɹ6L2
P
Ɉɤɢɫɥɟɧɢɟɤɪɟɦɧɢɹɨɤɫɢɞɨɦɠɟɥɟɡɚ)H2ɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>6L@)H2→>)H@6L2
Ʉɨɥɢɱɟɫɬɜɨ)H2ɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɤɪɟɦɧɢɹ
)H2
ɨɛɪɚɡɭɟɬɫɹ6L2
P
⋅
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6L2
6LP
=
6L2
⋅
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ɤɝ
ɤɝ
ɤɝ
ɄɤɨɧɰɭɩɟɪɢɨɞɚɮɨɫɮɨɪɚɨɫɬɚɧɟɬɫɹɢɥɢɤɝɌɨɝɞɚɨɤɢɫɥɢɬɫɹ
ɮɨɫɮɨɪɚɡɚɩɟɪɢɨɞ ɤɝ =−
Ɉɤɢɫɥɟɧɢɟɮɨɫɮɨɪɚɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>Ɋ@^Ɉ`→ɊɈ
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɤɢɫɥɟɧɢɟɮɨɫɮɨɪɚ
⋅
3P
=
2
ɨɛɪɚɡɭɟɬɫɹɊɈ
P
23
Ɉɤɢɫɥɟɧɢɟɮɨɫɮɨɪɚɨɤɫɢɞɨɦɠɟɥɟɡɚ)H2ɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
⋅
⋅
=
⋅
>Ɋ@)H2→ɊɈ>)H@
Ʉɨɥɢɱɟɫɬɜɨ)H2ɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɮɨɫɮɨɪɚ
⋅
3P
=
)H2
ɨɛɪɚɡɭɟɬɫɹɊɈ
P
⋅
=
23
⋅
⋅
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=⋅⋅
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ɤɝ
ɤɝ
ɤɝ
ɤɝ
Ʉ ɤɨɧɰɭ ɩɟɪɢɨɞɚ ɨɫɬɚɧɟɬɫɹ ɯɪɨɦɚ ɢɥɢ ɤɝ Ɍɨɝɞɚ ɨɤɢɫɥɢɬɫɹ
ɯɪɨɦɚɡɚɩɟɪɢɨɞ ɤɝ =−
Ɉɤɢɫɥɟɧɢɟɯɪɨɦɚɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
>ɋU@^Ɉ`→ɋUɈ
ɉɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚɧɚɨɤɢɫɥɟɧɢɟɯɪɨɦɚ
2
ɨɛɪɚɡɭɟɬɫɹɋUɈ
P
2&U
Ɉɤɢɫɥɟɧɢɟɯɪɨɦɚɨɤɫɢɞɨɦɠɟɥɟɡɚ)H2ɩɪɨɢɫɯɨɞɢɬɩɨɪɟɚɤɰɢɢ
⋅
ɋUP
=
⋅
⋅
=
⋅
>&U@)H2 &U2>)H@
Ʉɨɥɢɱɟɫɬɜɨ)H2ɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɯɪɨɦɚ
&UP
=
)H2
ɨɛɪɚɡɭɟɬɫɹɋUɈ
P
⋅
=
2&U
⋅
⋅
⋅
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=⋅⋅
=⋅⋅
=⋅⋅
ɤɝ
ɤɝ
ɤɝ
ɤɝ
ɉɪɢɧɢɦɚɟɦɱɬɨɧɢɤɟɥɶɢɦɟɞɶɜɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞɢɡɦɟɬɚɥɥɚɧɟɭɞɚ
ɥɹɸɬɫɹ
Ɍɨɝɞɚɫɭɦɦɚɪɧɨɟɤɨɥɢɱɟɫɬɜɨɤɢɫɥɨɪɨɞɚɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɨɤɢɫɥɟɧɢɹɷɥɟ
ɦɟɧɬɨɜ
Ɉɛɳɟɟɤɨɥɢɱɟɫɬɜɨɡɚɤɢɫɢɠɟɥɟɡɚɞɥɹɨɤɢɫɥɟɧɢɹɷɥɟɦɟɧɬɨɜ
Ⱦɥɹɩɨɥɭɱɟɧɢɹɬɚɤɨɝɨɤɨɥɢɱɟɫɬɜɚ)H2ɩɨɬɪɟɛɭɟɬɫɹɤɢɫɥɨɪɨɞɚ
¦
¦
Q
=
L
Q
L
=
==
22
==
)H2)H2
ɤɝLP0
ɤɝLP0
>)H@^2`→)H2
0
P
2
ɉɪɢɷɬɨɦɩɨɬɪɟɛɭɟɬɫɹɠɟɥɟɡɚ
P
)H2
=
μ
)H2
0
=
@)H>
μ
)H2
2
)H2
)H
=⋅⋅=μ⋅
=⋅=μ⋅
ɤɝ
ɤɝ
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