ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
137
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɢɫɬɟɦɚ ɨɫɧɨɜɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɡɚɩɢɫɚɧɧɵɯ ɞɥɹ
ɧɚɝɥɹɞɧɨɫɬɢ ɜ ɥɨɤɚɥɶɧɵɯ ɞɟɤɚɪɬɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ (
x
,
y
,
z
),
ɝɞɟ
x
,
y
—
ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ, ɚ
z
—
ɜɵɫɨɬɚ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜɜɟɪɯ, ɢɦɟ-
ɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
x
ɭɪɚɜɧɟɧɢɹ ɢɦɩɭɥɶɫɚ ɩɨ ɝɨɪɢɡɨɧɬɚɥɢ
1
1 ,
x
p
lv u
x
z
W
O
U
U
w
w
w
w
1
1 ;
y
p
lu v
y
z
W
O
U
U
w
w
w
w
x
ɭɪɚɜɧɟɧɢɟ ɧɟɪɚɡɪɵɜɧɨɫɬɢ
0;
u v w
x y y
w w w
w w w
x
ɭɪɚɜɧɟɧɢɟ ɝɢɞɪɨɫɬɚɬɢɤɢ
;
p g
z
U
w
w
x
ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɦɨɪɫɤɨɣ ɜɨɞɵ
( , );
T S
U
U
x
ɭɪɚɜɧɟɧɢɟ ɩɟɪɟɧɨɫɚ ɢ ɞɢɮɮɭɡɢɢ ɬɪɚɫɫɟɪɨɜ
X
(
ɬɟɦɩɟɪɚɬɭɪɵ ɢ
ɫɨɥɟɧɨɫɬɢ)
2
.
h
v
d
X
X k X k
C
dt
z
z
w w §
·
’ ¨
¸
©
¹
w w
Ɂɞɟɫɶ
u
,
v
,
w
—
ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ ɢ ɜɟɪɬɢɤɚɥɶɧɚɹ ɤɨɦɩɨɧɟɧɬɵ ɜɟɤɬɨɪɚ
ɫɤɨɪɨɫɬɢ;
Ȝ
—
ɩɟɪɟɦɟɧɧɵɣ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɮɪɢɤɰɢɨɧɧɵɣ ɤɨɷɮɮɢ-
ɰɢɟɧɬ, ɭɜɟɥɢɱɢɜɚɸɳɢɣɫɹ ɤ ɛɟɪɟɝɨɜɵɦ ɝɪɚɧɢɰɚɦ ɢ ɷɤɜɚɬɨɪɭ ɢ ɨɩɪɟ-
ɞɟɥɹɸɳɢɣ ɜɥɢɹɧɢɟ ɮɪɢɤɰɢɨɧɧɨɝɨ ɱɥɟɧɚ;
U
,
T
,
S
,
p
—
ɩɥɨɬɧɨɫɬɶ, ɬɟɦ-
ɩɟɪɚɬɭɪɚ, ɫɨɥɟɧɨɫɬɶ ɢ ɞɚɜɥɟɧɢɟ ɦɨɪɫɤɨɣ ɜɨɞɵ;
,
x y
W W
—
ɤɨɦɩɨɧɟɧɬɵ
ɧɚɩɪɹɠɟɧɢɹ ɬɪɟɧɢɹ ɜɟɬɪɚ;
,
h v
k k
—
ɤɨɷɮɮɢɰɢɟɧɬɵ ɬɭɪɛɭɥɟɧɬɧɨɣ
ɞɢɮɮɭɡɢɢ ɬɪɚɫɫɟɪɨɜ ɩɨ ɝɨɪɢɡɨɧɬɚɥɢ ɢ ɜɟɪɬɢɤɚɥɢ;
ɋ
—
ɢɫɬɨɱɧɢɤɢ
ɬɪɚɫɫɟɪɨɜ.
ɍɤɚɡɚɧɧɚɹ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɪɟɲɚɟɬɫɹ ɜ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ
ɤɨɨɪɞɢɧɚɬ ɞɥɹ ɜɫɟɝɨ Ɇɢɪɨɜɨɝɨ ɨɤɟɚɧɚ ɫ ɪɟɚɥɶɧɨɣ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɧ-
ɧɨɣ ɝɥɭɛɢɧɨɣ. ɇɚ ɝɪɚɧɢɰɚɯ ɦɚɬɟɪɢɤɨɜ ɬɚɤɠɟ ɩɪɢɧɢɦɚɸɬɫɹ ɪɚɜɧɵɦɢ
ɧɭɥɸ ɧɨɪɦɚɥɶɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɩɨɬɨɤɨɜ ɬɟɩɥɨɬɵ ɢ ɫɨɥɟɣ. Ɉɤɟɚɧ
ɩɨɞɜɟɪɝɚɟɬɫɹ ɜɨɡɞɟɣɫɬɜɢɸ ɧɚɩɪɹɠɟɧɢɹ ɬɪɟɧɢɹ ɜɟɬɪɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ.
ɉɨɬɨɤɢ
T
ɢ
S
ɜɛɥɢɡɢ ɞɧɚ ɩɨɥɚɝɚɸɬɫɹ ɪɚɜɧɵɦɢ ɧɭɥɸ, ɚ ɧɚ ɩɨɜɟɪɯɧɨ-
ɫɬɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɫ ɚɬɦɨɫɮɟɪɨɣ.