ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
90
ɋɩɨɫɨɛ ɪɚɫɱɟɬɚ ɩɥɨɳɚɞɢ ɩɨɜɟɪɯɧɨɫɬɢ ɝɨɪɟɧɢɹ ɜ ɫɥɭɱɚɟ ɡɚɪɹ-
ɞɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ.
ɉɪɟɞɩɨɥɚɝɚɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ
ɦɟɬɨɞɚ Ɇɨɧɬɟ-Ʉɚɪɥɨ, ɩɟɪɟɣɞɟɦ ɨɬ ɩɥɨɳɚɞɢ ɩɨɜɟɪɯɧɨɫɬɢ ɝɨɪɟɧɢɹ
b
S e
ɤɚɤ ɮɭɧɤɰɢɢ ɬɨɥɳɢɧɵ ɜɵɝɨɪɟɜɲɟɝɨ ɫɜɨɞɚ
e
ɤ ɨɛɴɟɦɭ ɜɵɝɨ-
ɪɟɜɲɟɣ ɱɚɫɬɢ ɡɚɪɹɞɚ
0
e
b
b
e S e de
:
³
ɢ ɤ ɬɟɤɭɳɟɦɭ ɨɛɴɟɦɭ ɡɚɪɹɞɚ
ɡ
ɡ0
,
b
e
e
: : :
(1)
ɝɞɟ
ɡ0
:
—
ɧɚɱɚɥɶɧɵɣ ɨɛɴɟɦ, ɡɚɧɢɦɚɟɦɵɣ ɡɚɪɹɞɨɦ. Ȼɭɞɟɦ ɢɫɤɚɬɶ ɜ
ɪɚɫɱɟɬɟ ɜɟɥɢɱɢɧɭ (1). Ɂɚɬɟɦ ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚɪɹɞɚ ɦɨɠɧɨ ɪɚɫ-
ɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ
ɡ
,
b
d
S e
de
:
(2)
ɢɫɩɨɥɶɡɭɹ ɱɢɫɥɟɧɧɨɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ.
ɉɭɫɬɶ ɝɟɨɦɟɬɪɢɹ ɡɚɪɹɞɚ ɡɚɞɚɧɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɤɨɬɨɪɨɣ ɫɢɫɬɟɦɵ
ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɤɨɨɪɞɢɧɚɬ
Oxyz
.
Ⱦɚɥɟɟ ɧɟɨɛɯɨɞɢɦɨ ɪɟɚɥɢɡɨɜɚɬɶ ɚɥ-
ɝɨɪɢɬɦ, ɤɨɬɨɪɵɣ ɩɨɡɜɨɥɢɬ ɭɫɬɚɧɨɜɢɬɶ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨ ɜɵɛɪɚɧɧɨɣ
ɬɨɱɤɢ ɩɪɨɫɬɪɚɧɫɬɜɚ
, ,
x y z
ɟɟ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɤ ɧɚɱɚɥɶɧɨɦɭ ɨɛɴɟ-
ɦɭ ɡɚɪɹɞɚ ɢ ɜɵɱɢɫɥɢɬɶ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɧɟɟ
, ,
x y z
U
ɞɨ ɧɚɱɚɥɶɧɨɣ ɩɨ-
ɜɟɪɯɧɨɫɬɢ ɝɨɪɟɧɢɹ ɡɚɪɹɞɚ (ɩɨ ɤɪɚɬɱɚɣɲɟɦɭ ɩɭɬɢ, ɩɪɨɯɨɞɹɳɟɦɭ ɩɨ
ɬɨɱɤɚɦ ɡɚɪɹɞɚ ɢ ɧɟ ɩɟɪɟɫɟɤɚɸɳɟɦɭ ɟɝɨ ɝɪɚɧɢɰ). Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɬɨɱɤɚɦ,
ɧɟ ɩɪɢɧɚɞɥɟɠɚɳɢɦ ɡɚɪɹɞɭ, ɦɨɠɧɨ ɩɪɢɩɢɫɚɬɶ ɡɧɚɱɟɧɢɹ
, ,
0.
x y z
U
Ɂɚɤɥɸɱɢɦ ɨɛɥɚɫɬɶ, ɡɚɧɢɦɚɟɦɭɸ ɡɚɪɹɞɨɦ, ɜ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞ ɫ
ɪɚɡɦɟɪɚɦɢ
,
b
e
x x x
d d
b
e
y y y
d d
ɢ
.
b
e
z z z
d d
ɋɮɨɪɦɢɪɭɟɦ ɞɨɫɬɚ-
ɬɨɱɧɨ ɩɪɟɞɫɬɚɜɢɬɟɥɶɧɭɸ ɜɵɛɨɪɤɭ 3
N
ɩɫɟɜɞɨɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɞɥɹ
ɩɪɟɞɫɬɚɜɥɟɧɢɹ
N
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɬɨɱɟɤ
, ,
,
i
i
i
x y z
ɩɪɢɧɚɞɥɟɠɚ-
ɳɢɯ ɞɚɧɧɨɦɭ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞɭ:
,
b i
e
x x x
d d
,
b i
e
y y y
d d
.
b i
e
z z z
d d
Ⱦɚɥɟɟ ɡɚɞɚɞɢɦɫɹ ɧɚɛɨɪɨɦ ɡɧɚɱɟɧɢɣ
1
2
max
0, , ...,
,
e e e
ɞɥɹ ɤɨɬɨɪɵɯ ɜɵ-
ɱɢɫɥɢɦ ɡɧɚɱɟɧɢɹ
ɡ
.
e
:
ɉɨɞɫɱɢɬɚɜ ɤɨɥɢɱɟɫɬɜɨ
k
N
ɬɨɱɟɤ
, ,
,
i
i
i
x y z
ɞɥɹ ɤɨɬɨɪɵɯ
, ,
,
i
i i
k
x y z e
U
t
ɨɩɪɟɞɟɥɢɦ
ɡ
.
k
k
e b e
b e b
N e
x x y y z z
N
:
|
(3)