ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
43
ɂɫɩɨɥɶɡɨɜɚɜ ɮɨɪɦɭɥɭ (3), ɢɦɟɟɦ
1
lim
( ) ,
( )
l
b
P t dt
P
W
W
W
W
of
³
ɨɬɤɭɞɚ, ɫɨɝɥɚɫɧɨ (14), ɧɚɯɨɞɢɦ (17), ɱɬɨ ɢ ɞɨɤɚɡɵɜɚɟɬ ɬɟɨɪɟɦɭ.
ȼ ɱɚɫɬɧɨɫɬɢ, ɟɫɥɢ
,
L
f
ɬɨ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (17) ɢɦɟɟɦ
0.
b
Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɟ ɧɚɤɥɨɧɧɨɣ ɚɫɢɦɩɬɨɬɵ ɩɪɢɧɢɦɚɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
.
y
W
Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɩɪɢ
L
f
ɛɢɫɫɟɤɬɪɢɫɚ ɩɟɪɜɨɝɨ ɤɨɨɪɞɢɧɚɬ-
ɧɨɝɨ ɭɝɥɚ ɫɥɭɠɢɬ ɧɚɤɥɨɧɧɨɣ ɚɫɢɦɩɬɨɬɨɣ ɞɥɹ ɩɨɤɚɡɚɬɟɥɹ
( )
l
U W
ɤɚɤ
ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ
.
W
Ɉɬɦɟɬɢɦ, ɱɬɨ ɞɥɹ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɡɚɤɨɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɧɚɪɚɛɨɬɨɤ ɞɨ ɨɬɤɚɡɚ ( ( )
,
0
const
t
P t
e
O
O
!
),
ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (3),
1
( )
1
.
l
l
e
O
U W
W
O
(18)
ȼ ɬɨ ɠɟ ɜɪɟɦɹ, ɫɨɝɥɚɫɧɨ ɪɚɜɟɧɫɬɜɚɦ (16) ɢ (17), ɢɦɟɟɦ ɜ ɤɚɱɟɫɬɜɟ
ɧɚɤɥɨɧɧɨɣ ɚɫɢɦɩɬɨɬɵ ɞɥɹ ɤɪɢɜɨɣ ( )
l
U W
ɫɥɟɞɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ:
1 1
.
l
y
e
O
W
O
(19)
ȼɢɞɧɨ, ɱɬɨ ɩɪɚɜɵɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɣ (18) ɢ (19) ɪɚɜɧɵ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɡɚɤɨɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɧɚɪɚɛɨɬɨɤ ɞɨ ɨɬɤɚɡɚ ɭɪɚɜɧɟɧɢɟ ɤɪɢɜɨɣ ( )
l
U W
ɤɚɤ ɮɭɧɤɰɢɹ ɜɪɟɦɟɧɢ
W
ɢ ɭɪɚɜɧɟɧɢɟ ɟɟ ɧɚɤɥɨɧɧɨɣ ɚɫɢɦɩɬɨɬɵ ɫɨɜɩɚɞɚɸɬ.
ɑɬɨɛɵ ɩɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤ ɮɭɧɤɰɢɢ
( )
l
y
U W
ɞɥɹ ɞɪɭɝɢɯ ɤɥɚɫɫɨɜ
ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɧɚɪɚɛɨɬɨɤ ɞɨ ɨɬɤɚɡɚ, ɢɡɦɟɧɢɦ ɮɨɪɦɭɥɭ (3), ɩɪɢɧɹɜ ɜ
ɧɟɣ
0
( )
exp ( ) .
t
P t
u du
O
§
·
¨
¸
¨
¸
©
¹
³
Ɍɨɝɞɚ ɩɨɥɭɱɢɦ
0
( )
exp
( )
,
l
t
l
u du dt
W
W
U W
W
O
§
·
§
·
¨
¸
¨
¸
¨
¸
¨
¸
©
¹
©
¹
³
³
ɨɬɤɭɞɚ ɧɚɣɞɟɦ
0
( ) 1
exp
( )
( ) (
) .
l
t
l
u du
t dt
W
W
U W
O
O W
O W
W
§
·
w
¨
¸
¨
¸
w
©
¹
³
³
(20)