ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
65
Ɋɚɫɱɟɬ ɝɚɡɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɛɭɞɟɦ
ɩɪɨɜɨɞɢɬɶ ɞɥɹ ɨɛɥɚɫɬɟɣ
*
[0; ],
V
V

*
[ ; 90 ],
V
V
 q
ɝɞɟ
V
ɭɝɨɥ ɦɟɠ-
ɞɭ ɨɫɶɸ ɬɟɥɚ ɢ ɜɟɤɬɨɪɨɦ ɫɤɨɪɨɫɬɢ ɜ ɩɪɨɢɡɜɨɥɶɧɨɣ ɬɨɱɤɟ ɧɚ ɟɝɨ ɩɨ-
ɜɟɪɯɧɨɫɬɢ;
*
V
ɨɩɪɟɞɟɥɹɟɬ ɩɨɥɨɠɟɧɢɟ ɡɜɭɤɨɜɨɣ ɬɨɱɤɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ
ɬɟɥɚ [1].
Ɋɚɫɱɟɬ ɞɚɜɥɟɧɢɹ ɩɪɢ

*
[ ; 90
°]
ı ı
.
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɥɨɠɟɧɢɹ
ɡɜɭɤɨɜɨɣ ɬɨɱɤɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɫɧɚɱɚɥɚ ɧɚɣɞɟɦ ɟɟ ɧɚ ɩɨɜɟɪɯɧɨ-
ɫɬɢ ɫɮɟɪɵ, ɢɫɩɨɥɶɡɭɹ ɚɩɩɪɨɤɫɢɦɚɰɢɨɧɧɵɟ ɮɨɪɦɭɥɵ ɞɥɹ ɞɚɜɥɟɧɢɹ ɧɚ
ɫɮɟɪɟ [2]:
3
2
2
1
ln ,
p
E T
E T
(1)
ɝɞɟ
T
ɰɟɧɬɪɚɥɶɧɵɣ ɭɝɨɥ.
Ʉɪɨɦɟ ɬɨɝɨ, ɭɱɬɟɦ, ɱɬɨ ɞɚɜɥɟɧɢɟ ɜ ɡɜɭɤɨɜɨɣ ɬɨɱɤɟ, ɨɬɧɟɫɟɧɧɨɟ ɤ
ɞɚɜɥɟɧɢɸ ɜ ɬɨɱɤɟ ɬɨɪɦɨɠɟɧɢɹ,
1
*
2 .
1
p
J
J
J
§
·
¨
¸
©
¹
Ɍɨɝɞɚ ɢɡ ɪɚɜɟɧɫɬɜɚ (1)
ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ
3
2
2
1
2
ln
0,
1
1
J
E T
E T
J
J
§
·
¨
¸
©
¹
ɪɟɲɢɜ ɤɨɬɨɪɨɟ, ɧɚɣɞɟɦ ɩɨɥɨɠɟɧɢɟ ɡɜɭɤɨɜɨɣ ɬɨɱɤɢ ɧɚ ɫɮɟɪɟ:
**
**
.
2
S
V
T
ȼɵɱɢɫɥɢɦ ɞɥɹ ɫɮɟɪɵ ɜ ɡɜɭɤɨɜɨɣ ɬɨɱɤɟ ɨɬɧɨɲɟɧɢɟ
2
2
**
d f d
f
V
,
ɝɞɟ
f
ɤɨɧɬɭɪɧɚɹ ɮɭɧɤɰɢɹ, ɤɨɬɨɪɚɹ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
1 ,
f
r v
U
(2)
) (
V
r
ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɪɚɞɢɭɫ, ɨɩɢɫɵɜɚɸɳɢɣ ɝɟɨɦɟɬɪɢɸ ɬɟɥɚ;
) (
V
U
ɩɥɨɬɧɨɫɬɶ ɱɚɫɬɢɰ ɝɚɡɚ;
( )
v
V
ɦɨɞɭɥɶ ɫɤɨɪɨɫɬɢ.
ȼɫɟ ɩɪɨɢɡɜɨɞɧɵɟ ɜɵɱɢɫɥɹɸɬ ɩɨ ɚɪɝɭɦɟɧɬɚɦ, ɢɡɦɟɧɹɸɳɢɦɫɹ
ɜɞɨɥɶ ɬɟɥɚ, ɬ. ɟ. ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɷɧɬɪɨɩɢɢ. ȼ ɤɚɱɟɫɬɜɟ ɚɪɝɭɦɟɧɬɨɜ ɩɪɢ
ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɢ ɜɞɨɥɶ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɚɜɥɟɧɢɟ
ɪ
ɢɥɢ ɭɝɨɥ
.
V
ɍɱɢɬɵɜɚɹ, ɱɬɨ
1 ,
dv
dp
v
U
ɩɟɪɟɩɢɲɟɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ
ɤɨɧɬɭɪɧɨɣ ɮɭɧɤɰɢɢ (2) ɜ ɜɢɞɟ
1 ;
dv
f
r dp
(3)