ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
67
2
2
2
*
*
2
*
sin
sin
cos .
cos
p
p
V
V
V
V
(7)
ɇɚɣɞɟɦ
2
*
*
2
*
sin
2
sin cos 2
cos sin
cos
p
dp
d
V
V
V
V
V
V
V
2
2
* *
*
2
*
cos
sin
sin 2
cos
p
V
V
V
V
§
·
¨
¸
©
¹
*
2
*
sin 2
(1 )
.
cos
p
V
V
Ɍɨɝɞɚ ɜ ɡɜɭɤɨɜɨɣ ɬɨɱɤɟ ɫɮɟɪɵ
**
*
*
**
2
**
**
sin 2
(1 )
2(1 )
tg .
cos
dp
p
p
d
V
V
V
V
(8)
Ⱦɥɹ ɬɟɥ, ɨɬɥɢɱɧɵɯ ɨɬ ɫɮɟɪɵ,
*
*
*
2(1 )
tg .
dp
p
d
V
V
Ɏɨɪɦɭɥɚ (7)
ɢɦɟɟɬ ɬɭ ɠɟ ɫɬɪɭɤɬɭɪɭ, ɱɬɨ ɢ ɤɥɚɫɫɢɱɟɫɤɚɹ ɮɨɪɦɭɥɚ ɇɶɸɬɨɧɚ, ɢ ɩɪɢ
*
[ ; 90 ]
V
V
 q
ɢɥɢ
**
[ ; 90 ]
V
V
 q
ɬɚɤɠɟ ɞɚɟɬ ɯɨɪɨɲɢɟ ɪɟɡɭɥɶɬɚɬɵ. ɉɨɞɫɬɚ-
ɜɢɦ ɜɵɪɚɠɟɧɢɹ (6) ɢ (8) ɜ ɭɪɚɜɧɟɧɢɟ (5). ɍɱɢɬɵɜɚɹ, ɱɬɨ ɞɥɹ ɫɮɟɪɵ ɫ ɪɚ-
ɞɢɭɫɨɦ ɤɪɢɜɢɡɧɵ
R
= 1 ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɪɚɞɢɭɫ
r
(
V
)
= cos
V
,
ɜɵɱɢɫɥɢɦ
ɡɧɚɱɟɧɢɟ
2
2
**
d f d
f
V
.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɨ ɨɬɧɨɲɟɧɢɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ
R
.
ɋɨɝɥɚɫɧɨ ɪɚɛɨɬɟ [1], ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɡɧɚɱɟɧɢɟ
2
2
*
d f d
f
V
ɜ ɡɜɭɤɨɜɨɣ ɬɨɱɤɟ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɬɟɥɚ ɬɚɤɨɟ ɠɟ, ɤɚɤ ɧɚ ɫɮɟɪɟ. Ɍɨɝɞɚ
ɫ ɭɱɟɬɨɦ
3
3
*
const
d v v
dp
U
ɩɪɢ
*
p p
ɩɨɥɭɱɢɦ ɧɟɥɢɧɟɣɧɨɟ ɭɪɚɜ-
ɧɟɧɢɟ
2
2
2
2
2
2
3
*
*
*
2
3
*
*
**
*
2
( )
.
( )
dr d
d r d r
d f d
d v dp
V
f
d
r
dp
V
V
V
V
U
V
V
§
·
¨
¸
©
¹
Ɋɟɲɢɜ ɟɝɨ, ɧɚɣɞɟɦ
*
V
.
Ɍɟɩɟɪɶ ɧɚ ɢɧɬɟɪɜɚɥɟ
*
[ ; 90 ]
V
q
ɜɵɱɢɫɥɢɦ
ɩɨ ɭɬɨɱɧɟɧɧɨɣ ɮɨɪɦɭɥɟ (7) ɞɚɜɥɟɧɢɟ ɧɚ ɩɪɨɢɡɜɨɥɶɧɨɦ ɝɥɚɞɤɨɦ ɡɚ-
ɬɭɩɥɟɧɧɨɦ ɬɟɥɟ.
Ɋɚɫɱɟɬ ɞɚɜɥɟɧɢɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɩɪɢ
*
[0; ].
ı ı

ɇɚɣɞɟɦ
ɬɚɤɭɸ ɬɨɱɤɭ
0
V
,
ɜ ɤɨɬɨɪɨɣ
0.
df
d
V