ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
49
ɉɟɪɢɨɞɢɱɟɫɤɨɟ ɩɨ ɭɝɥɭ
M
ɪɟɲɟɧɢɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɭɦɦɢɪɨɜɚ-
ɧɢɟɦ ɜɫɟɯ ɜɟɬɜɟɣ ɧɟɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɪɟɲɟɧɢɹ (3) ɜ ɜɢɞɟ
ˆ
( , )
( ,
2 ).
u r
u r
n
M
M
S
f
f
¦
ɋ ɭɱɟɬɨɦ ɫɞɟɥɚɧɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ ɨɛɨɛɳɟɧɧɵɣ ɪɹɞ ȼɚɬɫɨɧɚ ɤɚɤ
ɪɟɡɭɥɶɬɚɬ ɷɬɨɝɨ ɫɭɦɦɢɪɨɜɚɧɢɹ ɢɦɟɟɬ ɜɢɞ
( , )
u r
M
> @
1/3 / 3
8
i
ka e
S
S
0
0 0
(1)
(1)
( )
( )
m
m
m
m
C H k r H k r
Q
Q
¦
0
1
cos ( , )
2 .
sin
2
m
m
m
p
S
S
M M
§
·
¨
¸
©
¹
(6)
Ɂɞɟɫɶ
0
( , )
m
p
M M
sgn(
M
M
0
)
0
1/ 2
( ) ;
m
g t dt
M
M
³
S
m
=
0
1/ 2
( ) ;
m
g t dt
M
M
³
m
C
=
3/ 2
2
3
,
3 6 ( )
m
A q
S
c
ɝɞɟ ( )
m
A g
c
—
ɡɧɚɱɟɧɢɹ ɩɪɨɢɡɜɨɞɧɨɣ ɮɭɧɤɰɢɢ ɗɣ-
ɪɢ ( )
;
m
A q q
g
m
(
t
)
=
2
m
Q
(
k
2
2
0
k
)
2
2
( )
.
a
U M
ª
º
¬
¼
ɉɪɢ
k = k
0
(
ɨɬɫɭɬɫɬɜɢɟ ɩɨɤɪɵɬɢɹ) ɩɨɫɥɟɞɧɢɣ ɫɨɦɧɨɠɢɬɟɥɶ ɨɛɳɟ-
ɝɨ ɱɥɟɧɚ ɪɹɞɚ (6) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɛɵɱɧɨɦɭ ɪɹɞɭ ȼɚɬɫɨɧɚ [1] ɞɥɹ ɤɪɭ-
ɝɨɜɨɝɨ ɰɢɥɢɧɞɪɚ ɛɟɡ ɩɨɤɪɵɬɢɹ:
0
cos |
|
.
sin
m
m
Q
M M
S
SQ
Ʌɭɱɟɜɚɹ ɤɚɪɬɢɧɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɨɥɹ ɜ ɨɫɜɟɳɟɧɧɨɣ ɨɛɥɚɫɬɢ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ ɞɥɹ ɫɬɚɰɢɨɧɚɪɧɵɯ ɬɨɱɟɤ ɨɩɬɢɱɟɫɤɨɝɨ ɢɧ-
ɬɟɝɪɚɥɚ:
(2)
(1)
(1)
0
0
(1)
1
cos ( , )
( )
( )
( )
1
2
,
8
( )
sin
2
C
p
S
H ka H kr H kr
d
S
H ka
Q
Q
Q
Q
Q
Q
Q
M M
Q
§
·
¨
¸
©
¹
³
ɝɞɟ ɤɨɧɬɭɪ
ɋ
ɢɦɟɟɬ ɜɢɞ, ɢɡɨɛɪɚɠɟɧɧɵɣ ɧɚ ɪɢɫ. 1,
2
arccos
a
p
+ k
0
p
0
sgn
M M
0
sgn
M M
0
0
1/ 2
( )
k p
g t dt
M
M
³
=