ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
124
ɝɞɟ
( ),
y
O
( )
T y
c
— ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɬɪɟɬɶɟɝɨ ɬɟɥɚ;
( )
f y
— ɢɫɬɨɱɧɢɤɢ ɬɟɩɥɨɬɵ, ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɜ ɬɪɟɬɶɟɦ ɬɟɥɟ.
ɉɨɫɬɚɜɢɦ ɧɚ ɝɪɚɧɢɰɚɯ ɬɪɟɬɶɟɝɨ ɬɟɥɚ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ:
2
2 2
, 0
ɩɪɢ
0;
T T
T T
y
O
O
c
c
(4)
1
1 2
,
ɩɪɢ
,
T T
T T
y
O G
O
G
c
c
(5)
ɝɞɟ
1
T
ɢ
2
T
— ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɩɨɤɪɵɬɢɹɯ 1 ɢ 2;
1 2
,
O O
— ɬɟɩɥɨɩɪɨ-
ɜɨɞɧɨɫɬɶ ɦɚɬɟɪɢɚɥɨɜ ɩɨɤɪɵɬɢɣ 1 ɢ 2.
ɍɫɥɨɜɢɹ (4) ɢ (5) — ɷɬɨ ɨɛɵɱɧɵɟ ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɬɟɦɩɟɪɚɬɭɪ ɢ
ɩɨɬɨɤɨɜ ɬɟɩɥɨɬɵ ɦɟɠɞɭ ɪɚɡɧɨɪɨɞɧɵɦɢ ɤɨɧɬɚɤɬɢɪɭɸɳɢɦɢ ɬɟɥɚɦɢ.
ȼɫɥɟɞɫɬɜɢɟ ɧɟɩɪɟɪɵɜɧɨɝɨ ɩɟɪɟɯɨɞɚ ɬɟɩɥɨɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɬɪɟɬɶ-
ɟɝɨ ɬɟɥɚ ɤ ɬɟɩɥɨɮɢɡɢɱɟɫɤɢɦ ɫɜɨɣɫɬɜɚɦ ɩɨɤɪɵɬɢɣ 1 ɢ 2 ɧɚ ɝɪɚɧɢɰɚɯ
y
G
ɢ
0
y
ɢɦɟɟɦ
2
0 ,
O
O
1
.
O G
O
Ɉɬɦɟɬɢɦ, ɱɬɨ
0
,
t
f
d Q
[
[
³
(6)
ɝɞɟ
Q
ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ (2).
ɉɨɫɥɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɭɪɚɜɧɟɧɢɹ (3) ɢ ɫ ɭɱɟɬɨɦ ɜɵɪɚɠɟɧɢɣ (4),
(5) ɭɫɥɨɜɢɟ ɧɟɢɞɟɚɥɶɧɨɝɨ ɤɨɧɬɚɤɬɚ [4] ɢɦɟɟɬ ɜɢɞ
2 2 1 1
.
T T Q
O
O
c
c
(7)
ɉɪɢɫɬɭɩɢɦ ɬɟɩɟɪɶ ɤ ɪɟɲɟɧɢɸ ɡɚɞɚɱɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɞɥɹ ɬɟɥ ɫ
ɩɨɤɪɵɬɢɹɦɢ. ɉɪɢ
0
y
ɛɭɞɟɦ ɫɬɚɜɢɬɶ ɭɫɥɨɜɢɹ (7). Ȼɭɞɟɦ ɫɱɢɬɚɬɶ,
ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɚ ɬɟɥ
0
T
ɩɨɫɬɨɹɧɧɚ ɢ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɨɤɪɭɠɚɸɳɟɣ
ɫɪɟɞɵ, ɩɨɷɬɨɦɭ ɟɟ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɡɚ ɧɚɱɚɥɨ ɨɬɫɱɟɬɚ ɬɟɦɩɟɪɚɬɭɪ, ɬ. ɟ
0
0;
T
ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
1
1 2
2
0 ɩɪɢ
ɢ
0 ɩɪɢ
.
T
y h T
y h
Ɍɨɝɞɚ ɢɡ
ɭɪɚɜɧɟɧɢɣ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɞɥɹ ɩɨɤɪɵɬɢɣ
1
2
0;
0.
T T
cc
cc
ɇɚɣɞɟɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɬɟɦɩɟɪɚɬɭɪ ɜ ɩɨɤɪɵɬɢɹɯ:
*
*
1
2
1
2
1 ;
1 .
y
y
T T
T T
h
h
§
·
§
·
¨
¸
¨
¸
©
¹
©
¹
(8)
C ɩɨɦɨɳɶɸ (8) ɭɞɨɜɥɟɬɜɨɪɢɦ ɩɟɪɜɨɦɭ ɭɪɚɜɧɟɧɢɸ (7) ɩɪɢ
0.
y
ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɥɹ ɤɨɧɬɚɤɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ
*
T
ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ
