ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
98
ɧɢɟ ɧɟɜɨɡɦɭɳɟɧɧɨɝɨ ɝɚɡɚ;
2
0
e e
p v
c
U
—
ɫɤɨɪɨɫɬɧɨɣ ɧɚɩɨɪ ɧɚɛɟɝɚɸɳɟ-
ɝɨ ɩɨɬɨɤɚ ɝɨɪɹɱɟɝɨ ɝɚɡɚ;
e
q
—
ɬɟɩɥɨɜɨɣ ɩɨɬɨɤ ɤ ɝɨɪɹɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ. Ɂɞɟɫɶ
e
U
—
ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ;
e
v
—
ɤɨɦɩɨɧɟɧɬɚ ɫɤɨ-
ɪɨɫɬɢ ɩɨɬɨɤɚ, ɤɚɫɚɬɟɥɶɧɚɹ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ. ɋ ɭɱɟɬɨɦ ɷɬɨɝɨ
0
0
0
(
);
(
);
(
)
f
f
w i
i
w e
e
w
D D p
D D p
D D p
c
T
T
T
(3)
ɝɞɟ
w
T
—
ɬɟɦɩɟɪɚɬɭɪɚ ɩɨɜɟɪɯɧɨɫɬɢ, ɹɜɥɹɸɳɚɹɫɹ ɮɭɧɤɰɢɟɣ ɬɟɩɥɨɜɨ-
ɝɨ ɩɨɬɨɤɚ
e
q
ɢ ɫɤɨɪɨɫɬɢ
:
D
(
)
w w e
q D
T
T
(3
ɚ)
ɉɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (3ɚ) ɜ (3), ɩɨɥɭɱɢɦ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɟɣ
,
f
D
i
D
ɢ
e
D
ɨɬ
0
,
p
0
p
c
ɢ .
e
q
3.
Ɍɭɪɛɭɥɟɧɬɧɨɟ ɝɨɪɟɧɢɟ ɬɚɤɠɟ ɨɩɢɫɵɜɚɟɬɫɹ ɷɬɨɣ ɦɨɞɟɥɶɸ, ɩɨ-
ɫɤɨɥɶɤɭ ɩɨɹɜɥɟɧɢɟ ɬɭɪɛɭɥɟɧɬɧɨɫɬɢ ɜ ɧɚɛɟɝɚɸɳɟɦ ɩɨɬɨɤɟ ɨɡɧɚɱɚɟɬ,
ɱɬɨ ɢɡɦɟɧɹɸɬɫɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɬɨɤɚ
e
q
ɢ
0
p
c
.
ɉɪɨɜɟɪɢɦ ɞɨɩɭɫɬɢɦɨɫɬɶ ɩɪɟɞɩɨɥɨɠɟɧɢɹ (1). ȼɨɨɛɳɟ ɝɨɜɨɪɹ, ɜɫɟ
ɷɬɢ ɬɪɢ ɩɪɨɰɟɫɫɚ ɝɨɪɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɫɜɹɡɚɧɧɵɦɢ. Ɉɞɧɚɤɨ ɩɪɢ ɮɢɤ-
ɫɢɪɨɜɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɩɨɜɟɪɯɧɨɫɬɢ
w
T
ɢ ɞɚɜɥɟɧɢɢ
0
p
ɜɥɢɹɧɢɟ
ɮɢɥɶɬɪɚɰɢɨɧɧɨɝɨ ɢ ɜɧɟɲɧɟɝɨ ɷɪɨɡɢɨɧɧɨɝɨ ɝɨɪɟɧɢɹ ɧɚ ɫɤɨɪɨɫɬɶ ɫɜɨ-
ɛɨɞɧɨɝɨ ɝɨɪɟɧɢɹ
f
D
ɧɟ ɹɜɥɹɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɦ, ɩɨɫɤɨɥɶɤɭ
f
D
ɨɩɪɟ-
ɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɫɜɨɣɫɬɜɚɦɢ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ. ȼ ɬɨ ɠɟ
ɜɪɟɦɹ ɨɛɪɚɬɧɨɟ ɜɥɢɹɧɢɟ
f
D
ɧɚ
i
D
ɢ
e
D
ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɟɟ ɡɧɚɱɢ-
ɬɟɥɶɧɵɦ ɞɚɠɟ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɵɯ
w
T
ɢ
0
p
,
ɩɨɫɤɨɥɶɤɭ ɱɟɦ ɜɵɲɟ
ɫɤɨɪɨɫɬɶ ɫɜɨɛɨɞɧɨɝɨ ɝɨɪɟɧɢɹ, ɬɟɦ ɦɟɧɶɲɟ ɧɚɝɪɟɜ ɜɧɭɬɪɟɧɧɟɣ ɡɨɧɵ
ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ ɜɫɥɟɞɫɬɜɢɟ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ, ɚ ɡɧɚɱɢɬ, ɬɟɦ ɧɢɠɟ
ɜɧɭɬɪɟɧɧɟɟ ɩɨɪɨɜɨɟ ɝɚɡɨɜɨɟ ɞɚɜɥɟɧɢɟ ,
p
ɜɵɲɟ ɩɪɨɱɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ
ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɦɟɧɶɲɟ ɡɧɚɱɟɧɢɹ
i
D
ɢ
e
D
.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɟɞɩɨɥɨɠɟɧɢɟ (1) ɫɜɨɞɢɬɫɹ ɤ ɭɫɥɨɜɢɸ, ɱɬɨ ɫɤɨ-
ɪɨɫɬɶ ɫɜɨɛɨɞɧɨɝɨ ɝɨɪɟɧɢɹ
f
D
ɧɟ ɞɨɥɠɧɚ ɩɪɟɜɵɲɚɬɶ ɫɤɨɪɨɫɬɶ ɪɚɫ-
ɩɪɨɫɬɪɚɧɟɧɢɹ ɮɪɨɧɬɚ ɧɚɝɪɟɜɚ
0
(
)
h
D k cl
U
:
,
f
h
D D
d
ɝɞɟ ,
k
U
,
ɫ
—
ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ, ɩɥɨɬɧɨɫɬɶ ɢ ɬɟɩɥɨɟɦɤɨɫɬɶ ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ;
0
l
—
ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɩɨɪ.
ȿɫɥɢ
,
f
h
D D
ɬɨ ɩɪɨɝɪɟɬɚɹ ɡɨɧɚ ɩɟɪɟɞ ɮɪɨɧɬɨɦ ɫɜɨɛɨɞɧɨɝɨ ɝɨ-
ɪɟɧɢɹ ɦɚɥɚ ɢ ɫɤɨɪɨɫɬɢ ɷɪɨɡɢɨɧɧɨɝɨ ɢ ɮɢɥɶɬɪɚɰɢɨɧɧɨɝɨ ɝɨɪɟɧɢɹ ɫɭ-
ɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɹɬ ɨɬ
f
D
.
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨ
ɩɪɨɜɟɪɢɬɶ ɞɨɩɭɫɬɢɦɨɫɬɶ ɩɪɟɞɩɨɥɨɠɟɧɢɹ (1). Ɋɟɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɫɤɨ-
ɪɨɫɬɟɣ
f
D
ɢ
h
D
ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɵ ɞɥɹ ɪɚɫɫɦɨɬɪɟɧɧɨɝɨ ɡɞɟɫɶ