ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
52
0
0
0
2
0
0
0
2
0
0
( , , )
.
cos
1
1
sin
1
r
r q
r
a
a
q
M M
H
G
H
G
M M
M M
H
H
c
­
½
­
½
§
·
§
·
°
°
°
°
®
¾
®
¾
¨
¸
¨
¸
°
°
°
°
©
¹
©
¹
¯
¿
¯
¿
ɉɨɫɥɟɞɧɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɨɡɧɚɱɚɸɬ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɡɚɜɢɫɹɳɢɣ
ɨɬ ɭɝɥɨɜ
M
,
M
0
ɫɞɜɢɝ (ɩɚɪɚɥɥɚɤɫ)
'
r
0
= r
0
–
0
r
c
ɦɟɠɞɭ ɢɫɬɢɧɧɵɦ ɩɨ-
ɥɨɠɟɧɢɟɦ ɬɨɱɟɱɧɨɝɨ ɢɫɬɨɱɧɢɤɚ (
r
0
,
M
0
)
ɢ ɧɚɛɥɸɞɚɟɦɵɦ (
0
r
c
,
M
0
),
ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɜɥɢɹɧɢɟɦ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɥɨɹ ɧɚ ɪɚɫɫɟɹɧɧɨɟ ɩɨ-
ɥɟ (ɪɢɫ. 3).
Ɋɢɫ. 3. Ɇɚɥɵɣ ɫɞɜɢɝ (ɩɚɪɚɥɥɚɤɫ) ɧɚɛɥɸɞɚɟɦɨɝɨ ɩɨɥɨɠɟɧɢɹ ɢɫɬɨɱɧɢɤɚ ɞɥɹ ɰɢ-
ɥɢɧɞɪɚ ɫ ɩɨɤɪɵɬɢɟɦ
Ɉɬɦɟɬɢɦ ɬɚɤɠɟ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɫɪɟɞɵ ɫɥɨɹ ɫ Re
H
0 (
ɫɥɭɱɚɣ ɯɨ-
ɥɨɞɧɨɣ ɩɥɚɡɦɵ) ɜɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɜ ɡɧɚɦɟɧɚɬɟɥɟ ɷɬɨɝɨ ɜɵɪɚɠɟɧɢɹ ɨɬ-
ɪɢɰɚɬɟɥɶɧɨ
0
(
r
c
!
r
0
),
ɬ. ɟ. ɩɚɪɚɥɥɚɤɫ
'
r
0
ɢɦɟɟɬ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɣ
ɡɧɚɤ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɨɠɧɨ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɜɟɥɢɱɢɧɚ ɢ ɡɧɚɤ ɩɚɪɚɥ-
ɥɚɤɫɚ
'
r
0
ɦɨɝɭɬ ɫɥɭɠɢɬɶ ɨɫɧɨɜɨɣ ɞɥɹ ɞɢɚɝɧɨɫɬɢɤɢ ɫɜɨɣɫɬɜ ɫɪɟɞɵ ɧɟ-
ɨɞɧɨɪɨɞɧɨɝɨ ɫɥɨɹ, ɤɚɤ, ɧɚɩɪɢɦɟɪ, ɜ ɬɟɯɧɨɥɨɝɢɹɯ ɧɟɪɚɡɪɭɲɚɸɳɟɝɨ
ɤɨɧɬɪɨɥɹ ɩɚɪɚɦɟɬɪɨɜ ɬɨɧɤɢɯ ɩɨɥɢɦɟɪɧɵɯ ɩɥɟɧɨɤ.
ɗɮɮɟɤɬɢɜɧɵɣ ɭɝɨɥ.
Ⱦɪɭɝɨɣ ɫɩɨɫɨɛ ɩɪɢɜɟɫɬɢ ɭɪɚɜɧɟɧɢɟ (8) ɤ
ɩɪɨɫɬɟɣɲɟɦɭ ɜɢɞɭ (9) — ɜɜɟɞɟɧɢɟ ɷɮɮɟɤɬɢɜɧɨɝɨ ɭɝɥɚ
0
M
c
ɩɨɥɨɠɟɧɢɹ
ɬɨɱɟɱɧɨɝɨ ɢɫɬɨɱɧɢɤɚ ɩɨ ɮɨɪɦɭɥɟ
k
0
q
0
sgn
M M
1/ 2
0
0
( )
k q
g t dt
M
M
³
= |
M
0
M
c
|.
(11)
ɗɬɨ ɬɚɤɠɟ ɩɪɢɜɨɞɢɬ ɭɪɚɜɧɟɧɢɟ ɫɬɚɰɢɨɧɚɪɧɨɣ ɬɨɱɤɢ ɤ ɜɢɞɭ (9) ɫ
0
M
c
ɜɦɟɫɬɨ
M
0
: