ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
42
ɉɪɢɦɟɧɢɜ ɬɟɨɪɟɦɭ ɨ ɫɪɟɞɧɟɦ ɡɧɚɱɟɧɢɢ ɢɧɬɟɝɪɚɥɚ, ɫ ɭɱɟɬɨɦ ɧɟ-
ɩɪɟɪɵɜɧɨɫɬɢ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɮɭɧɤɰɢɢ ɧɚɣɞɟɦ
(
)
lim
exp lim (
) ,
( )
P l
l
P
W
W
W
O W T
W
of
of
ɝɞɟ
(0, ).
l
T

Ⱦɚɥɟɟ, ɢɫɩɨɥɶɡɨɜɚɜ ɭɫɥɨɜɢɟ (12), ɢɦɟɟɦ
(
)
lim
exp .
( )
P l
Ll
P
W
W
W
of
ɉɨɞɫɬɚɜɢɜ ɩɨɥɭɱɟɧɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɜ ɜɵɪɚɠɟɧɢɟ (15), ɧɚɣɞɟɦ
ɢɫɤɨɦɨɟ ɫɨɨɬɧɨɲɟɧɢɟ (14).
Ⱦɨɤɚɡɚɧɧɚɹ ɥɟɦɦɚ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ ɫɥɟɞɭɸɳɟɟ ɭɬɜɟɪɠɞɟɧɢɟ.
Ɍɟɨɪɟɦɚ 2.
ȼ ɭɫɥɨɜɢɹɯ ɥɟɦɦɵ ɤɪɢɜɚɹ ɮɭɧɤɰɢɢ
( )
l
y
U W
ɤɚɤ ɩɟɪɟ-
ɦɟɧɧɚɹ ɜɪɟɦɟɧɢ
W
ɢɦɟɟɬ ɧɚɤɥɨɧɧɭɸ ɚɫɢɦɩɬɨɬɭ, ɭɪɚɜɧɟɧɢɟ ɤɨɬɨɪɨɣ
ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
,
y
b
W
(16)
ɝɞɟ
1 1
.
Ll
b
e
L
(17)
Ⱦ ɨ ɤ ɚ ɡ ɚ ɬ ɟ ɥ ɶ ɫ ɬ ɜ ɨ. ɋɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (3), ɢɦɟɟɦ
( )
1
lim 1
( ) ,
( )
l
l
P t dt
P
W
W
W
U W
W
W
W
of
³
ɨɬɤɭɞɚ ɫ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɹ (14) ɧɚɣɞɟɦ
( )
lim 1.
l
W
U W
W
of
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ
k
ɧɚɤɥɨɧɧɨɣ ɚɫɢɦɩɬɨɬɵ
y k b
W
ɪɚɜɟɧ ɟɞɢɧɢɰɟ, ɬ. ɟ.
,
y
b
W
ɝɞɟ ɡɧɚɱɟɧɢɟ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɵ ɬɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɢɡ ɭɫɥɨɜɢɹ
lim ( )
.
l
b
W
U W
W
of