ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
69
ɋ ɭɱɟɬɨɦ
2
2
2
2
2
2
M 1
1 1
1 1
M
v p
p
p
p
v
v
p v
p
U
J
J
J
J
U
U
J U
J
ɜɵɪɚɠɟɧɢɟ (10) ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɧɟɥɢɧɟɣɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶ-
ɧɨ
.
V
Ɋɟɲɢɜ ɟɝɨ, ɩɨɥɭɱɢɦ ɢɫɤɨɦɵɣ ɭɝɨɥ
0
0 *
[ ; ]
V
V V
.
ɉɨɫɤɨɥɶɤɭ
0
0
V
V
d
df
,
ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɮɭɧɤɰɢɹ
) (
V
f
ɢɡɦɟɧɹ-
ɟɬɫɹ ɩɨ ɩɚɪɚɛɨɥɢɱɟɫɤɨɦɭ ɡɚɤɨɧɭ ɫ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ
Ⱥ
ɢ
ȼ
ɧɚ ɢɧɬɟɪ-
ɜɚɥɟ
*
[0; ] :
V
2
0
(
)
.
f A
B
V V
(12)
ɉɪɢ
0
V
V
0
0
( )
,
f
f
b
V
ɩɪɢ
*
V
V
2
*
*
* 0
( )
(
)
.
f
f
a
b
V
V
V
Ɍɨɝɞɚ
2
0
*
0
*
)
(
V
V
f
f
a
ɢ ɭɪɚɜɧɟɧɢɟ (12) ɩɪɢɦɟɬ ɜɢɞ
2
* 0
0
0
2
* 0
(
)
.
(
)
f
f
f
f
V V
V
V
(13)
Ɂɞɟɫɶ
*
*
*
*
1
.
( ) ( ( )) ( ( ))
f
r
p v p
V U
V
V
ɑɬɨɛɵ ɨɩɪɟɞɟɥɢɬɶ
0
f
,
ɜɵɱɢɫɥɢɦ
2
0
0
*
2
*
sin
( ) (
)
.
sin
p
p p
p
V
V
V
f
f
Ɍɨɝɞɚ
0
0
0
0
1
.
( )
( )
( )
f
r
p v p
V U
V
V
ɉɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (13) ɜ ɭɪɚɜɧɟɧɢɟ (1), ɩɨɥɭɱɢɦ
2
* 0
0
0
2
* 0
1
(
)
,
( ) ( ) ( ) (
)
f
f
f
r
p v p
V V
V U
V
V