ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
78
ɇɚ ɩɥɨɫɤɨɫɬɢ ɫɢɦɦɟɬɪɢɢ
5
6
ɡɚɞɚɸɬɫɹ ɭɫɥɨɜɢɹ ɫɢɦɦɟɬɪɢɢ:
0,
n
U
w
w
0,
˜
v n
0,
1, 2,
I
v
I
n
W
w
w
0.
n
T
w
w
(8)
ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɤ ɫɢɫɬɟɦɟ (1)—(5) ɢɦɟɸɬ ɜɢɞ
0
0
0
0 :
,
,
,
V
t
E c
v v
U
U
T
(9)
ɝɞɟ
0 0 0
, ,
U T
v
—
ɡɚɞɚɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɥɨɬɧɨɫɬɢ, ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɜɟɤɬɨ-
ɪɚ ɫɤɨɪɨɫɬɢ ɩɪɢ
t
= 0.
ȼ ɨɫɬɚɥɶɧɨɣ ɨɛɥɚɫɬɢ
\
e
V V
ɬɟɱɟɧɢɹ ɩɨɬɨɤɚ ɛɭɞɟɦ ɩɨɥɚɝɚɬɶ ɫɩɪɚ-
ɜɟɞɥɢɜɵɦɢ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɧɟɬɟɩɥɨɩɪɨɜɨɞɧɨɝɨ ɝɚɡɚ
(
ɭɪɚɜɧɟɧɢɹ ɗɣɥɟɪɚ):
0;
0;
0;
g
g g
g g
g g
g
g
g g
g
g g
t
p
t
E
E p
t
v
v
v v
E
v
U
U
U
U
U
U
w­
’ ˜
° w°
w°
’ ˜
® w °
w°
’ ˜
° w ¯
(10)
,
g
g g
p R
U T
2
/ 2,
g g
g
E e
v
.
g V g
e c
T
(11)
ɇɚ ɜɧɟɲɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ
,
e
6
ɹɜɥɹɸɳɟɣɫɹ
ɝɪɚɧɢɰɟɣ ɪɚɡɞɟɥɚ ɞɜɢɠɟɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɢ ɜɹɡɤɨɝɨ ɩɨɬɨɤɨɜ, ɮɨɪɦɭɥɢ-
ɪɭɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ ɧɟɩɪɟɪɵɜɧɨɫɬɢ:
,
g
U
U
,
gn
v
˜
v n
0,
I
˜
v lj
0,
v I
˜ ˜
n T lj
.
g
T
T
(12)
Ɂɞɟɫɶ ,
1, 2
I
I
lj
—
ɟɞɢɧɢɱɧɵɟ ɤɚɫɚɬɟɥɶɧɵɟ ɜɟɤɬɨɪɵ ɜ ɩɥɨɫɤɨɫɬɢ ;
e
6
.
gn
g
v
˜
v n
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɹɯ
3
6
ɜɯɨɞɚ ɩɨɬɨɤɚ ɢɞɟɚɥɶɧɨɝɨ
ɝɚɡɚ, ɜɵɯɨɞɚ ɩɨɬɨɤɚ
4
6
ɢ ɧɚ ɩɥɨɫɤɨɫɬɢ ɫɢɦɦɟɬɪɢɢ
5
6
ɢɦɟɸɬ ɜɢɞ
(6)—(8),
ɧɚ ɬɜɟɪɞɨɣ ɫɬɟɧɤɟ ɫɬɚɜɢɬɫɹ ɭɫɥɨɜɢɟ ɧɟɩɪɨɬɟɤɚɧɢɹ
0.
˜
v n
ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɤ ɫɢɫɬɟɦɟ (10), (11) ɫɨɜɩɚɞɚɸɬ ɫ (9).
ɍɪɚɜɧɟɧɢɹ ɇɚɜɶɟ—ɋɬɨɤɫɚ ɢ ɗɣɥɟɪɚ ɜ ɚɞɚɩɬɢɜɧɵɯ ɤɨɨɪɞɢ-
ɧɚɬɚɯ.
ȼɜɟɞɟɦ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɞɚɤɚɪɬɨɜɵ ɤɨɨɪɞɢɧɚɬɵ
j
x
,
ɰɢɥɢɧ-
ɞɪɢɱɟɫɤɢɟ ɤɨɨɪɞɢɧɚɬɵ
{ , , }
j
X r z
M
c
ɢ ɚɞɚɩɬɢɜɧɵɟ ɤɪɢɜɨɥɢɧɟɣɧɵɟ
ɤɨɨɪɞɢɧɚɬɵ
,
j
X
ɤɨɬɨɪɵɟ ɫɨɝɥɚɫɨɜɚɧɵ ɫ ɝɪɚɧɢɰɟɣ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ