ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
48
Ɋɚɜɟɧɫɬɜɚ (2) — ɤɪɚɟɜɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɤɨɦɩɨɧɟɧɬɵ
E
z
= u
ɷɥɟɤɬɪɢɱɟ-
ɫɤɨɝɨ ɩɨɥɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɰɢɥɢɧɞɪɚ ɢ ɜɧɟɲɧɟɣ ɝɪɚɧɢɰɟ ɞɢɷɥɟɤɬɪɢ-
ɱɟɫɤɨɝɨ ɫɥɨɹ.
Ɉɩɭɫɤɚɹ ɫɭɛɢɧɞɟɤɫɵ ɫɭɦɦɢɪɨɜɚɧɢɹ, ɩɪɨɟɤɰɢɨɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚ-
ɞɚɱɢ (1), (2) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ ɪɹɞɚ
ˆ ( , )
( ) ( ),
u r
r
A
Q
Q
Q
M
M \
¦
(3)
ɝɞɟ
( )
A
Q
M
—
ɧɟɩɟɪɢɨɞɢɱɟɫɤɢɟ ɩɨ ɭɝɥɭ
M
ɮɭɧɤɰɢɢ, ɷɤɫɩɨɧɟɧɰɢɚɥɶ-
ɧɨ ɭɛɵɜɚɸɳɢɟ ɩɪɢ
|
M
|
o f
.
ɉɪɨɟɤɰɢɨɧɧɵɟ ɪɚɜɟɧɫɬɜɚ, ɷɤɜɢɜɚɥɟɧɬɧɵɟ ɡɚɞɚɱɟ (1), (2),
ˆ ( , ) ( )
( ),
a
L u r
r rd r f
P
P
M
M
\
f
˜
³
(4)
ɝɞɟ
L =
2
,
,
;
r
k r
M
M
'
0
0
( )
( ) (
);
f
r
P
P
M \
G M M
( )
r
Q
\
=
( )
k
r
Q
\
=
(1)
0
( ),
k
k
C H k r
Q
Q
k
C
Q
—
ɧɨɪɦɢɪɨɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ,
k =
1,
...
,
f
.
Ʉɨɦɩɥɟɤɫɧɵɟ ɱɢɫɥɚ
Q
k
ɹɜɥɹɸɬɫɹ ɤɨɪɧɹɦɢ ɞɢɫɩɟɪɫɢɨɧɧɨɝɨ ɭɪɚɜ-
ɧɟɧɢɹ
(1)
0
( ) 0.
k
H k r
Q
(5)
Ⱥɫɢɦɩɬɨɬɢɱɟɫɤɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɞɥɹ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ (5) [1]
Q
k
|
k
0
a
+
V
k
/ 3;
i
e
S
V
k
=
1/ 3
0
,
6
k
k a q
§ ·
¨ ¸ © ¹
ɝɞɟ
q
k
—
ɤɨɪɧɢ ɮɭɧɤɰɢɢ ɗɣɪɢ
.
Ɇɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɫɢɫɬɟɦɚ ɮɭɧɤɰɢɣ
^ `
(
)
k
r
\
Q
ɹɜɥɹɟɬɫɹ ɨɪɬɨ-
ɧɨɪɦɢɪɨɜɚɧɧɵɦ ɛɚɡɢɫɨɦ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ
L
2
[
a
,
f
]
ɮɭɧɤɰɢɣ
v
(
r
,
M
)
ɩɪɢ
ɤɚɠɞɨɦ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ ɭɝɥɚ
M
.
Ʉɪɨɦɟ ɬɨɝɨ, ɛɟɫɤɨɧɟɱɧɚɹ ɫɢɫɬɟɦɚ ɨɛɵɤɧɨɜɟɧɧɵɯ ɞɢɮɮɟɪɟɧɰɢ-
ɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (ɈȾɍ) ɤɚɤ ɪɚɡɜɟɪɧɭɬɚɹ ɮɨɪɦɚ ɩɪɨɟɤɰɢɨɧɧɵɯ ɪɚ-
ɜɟɧɫɬɜ (4) ɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɩɨɩɪɚ-
ɜɨɤ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɯ ɧɟɤɨɬɨɪɨɣ ɫɬɟɩɟɧɢ ɨɛɪɚɬɧɨɣ ɜɟɥɢɱɢɧɵ
ɛɨɥɶɲɨɝɨ ɩɚɪɚɦɟɬɪɚ
k
0
a
,
ɡɚɦɟɧɹɟɬɫɹ ɫɢɫɬɟɦɨɣ ɫ ɞɢɚɝɨɧɚɥɶɧɨɣ ɦɚɬɪɢ-
ɰɟɣ, ɩɪɢɛɥɢɠɟɧɧɨɟ ɪɟɲɟɧɢɟ ɤɚɠɞɨɝɨ ɧɟɡɚɜɢɫɢɦɨɝɨ ɈȾɍ ɤɨɬɨɪɨɣ
ɫɬɪɨɢɬɫɹ ɜ ɹɜɧɨɦ ɜɢɞɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢ-
ɠɟɧɢɹ ȼɟɧɬɰɟɥɹ—Ʉɪɚɦɟɪɫɚ—Ȼɪɢɥɥɸɷɧɚ.