ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
161
3.
ȼɵɱɢɫɥɟɧɢɟ ɜɟɤɬɨɪɚ ɢɧɜɚɪɢɚɧɬɨɜ ɩɨ ɤɚɠɞɨɣ ɝɪɭɩɩɟ ɯɚɪɚɤɬɟ-
ɪɢɫɬɢɤ.
4.
Ɏɨɪɦɭɥɢɪɨɜɚɧɢɟ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɝɢɩɨɬɟɡɵ ɨ ɩɪɢɧɚɞɥɟɠɧɨɫɬɢ
ɧɚɛɥɸɞɚɟɦɨɝɨ ɨɛɪɚɡɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦɭ ɤɥɚɫɫɭ (ɨ ɛɥɢɡɨɫɬɢ ɜɵɱɢɫ-
ɥɟɧɧɨɝɨ ɜɟɤɬɨɪɚ ɢɧɜɚɪɢɚɧɬɨɜ ɤ ɜɟɤɬɨɪɭ ɢɧɜɚɪɢɚɧɬɨɜ, ɡɚɞɚɸɳɟɦɭ ɫɨ-
ɨɬɜɟɬɫɬɜɭɸɳɢɣ ɤɥɚɫɫ).
5.
ɉɪɨɜɟɪɤɚ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɝɢɩɨɬɟɡɵ ɩɪɨɬɢɜ ɚɥɶɬɟɪɧɚɬɢɜɵ.
ɋɩɟɤɬɪ Ɏɭɪɶɟ—Ɇɟɥɥɢɧɚ.
ɋɨɝɥɚɫɧɨ ɫɜɨɣɫɬɜɚɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
Ɏɭɪɶɟ, ɫɩɟɤɬɪɵ
1
,
F
2
F
ɢɡɨɛɪɚɠɟɧɢɣ
1
,
f
2
f
ɫɜɹɡɚɧɵ ɭɪɚɜɧɟɧɢɟɦ
2
,
x y
F
Z Z
1
2
exp 2
cos
sin
sin
cos
,
.
x
y
x
y
x
y
j
x
y
F
s
s
s
S
Z
Z
Z
T Z
T Z
T Z
T
' '
§
·
¨
¸
©
¹
(2)
ɉɟɪɟɯɨɞ ɤ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢ-ɩɨɥɹɪɧɵɦ ɤɨɨɪɞɢɧɚɬɚɦ
exp cos ;
exp sin
x
y
Z
U
M
Z
U
M
­
°
®
°¯
ɢ ɜɡɹɬɢɟ ɚɦɩɥɢɬɭɞɵ ɨɬ ɩɪɚɜɨɣ ɢ ɥɟɜɨɣ ɱɚɫɬɟɣ ɭɪɚɜɧɟɧɢɹ (2) ɞɚɟɬ
ln
ln
2
1 2
1
cos ,
sin
cos
,
sin
;
s
s
F e
e
F e
e
s
U
U
U
U
M
M
T M
T M
2
1 2
1 ,
ln ,
,
LP
LP
F
F
s
s
U M
U
T M
(3)
ɝɞɟ
2
LP
F
ɢ
1
LP
F
—
ɫɩɟɤɬɪɵ
2
F
ɢ
1
,
F
ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɥɨɝɚɪɢɮɦɢ-
ɱɟɫɤɢ-ɩɨɥɹɪɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ.
ɋɨɨɬɧɨɲɟɧɢɟ (3) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɨɜɨɪɨɬ ɧɚ ɭɝɨɥ
T
ɢ ɦɚɫɲɬɚɛɢ-
ɪɨɜɚɧɢɟ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ
s
ɹɜɥɹɸɬɫɹ ɫɞɜɢɝɚɦɢ ɜɞɨɥɶ ɫɨɨɬɜɟɬɫɬɜɭ-
ɸɳɢɯ ɨɫɟɣ ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢ-ɩɨɥɹɪɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ. ȼɡɹɬɢɟ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ Ɏɭɪɶɟ ɨɬ ɮɭɧɤɰɢɢ
LP
F
ɞɚɟɬ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɫɩɟɤɬɪ
Ɏɭɪɶɟ—Ɇɟɥɥɢɧɚ, ɢɧɜɚɪɢɚɧɬɧɵɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɢɤɥɢɱɟɫɤɨɝɨ ɫɞɜɢɝɚ,
ɩɨɜɨɪɨɬɚ ɢ ɪɚɫɬɹɠɟɧɢɹ (ɫɠɚɬɢɹ). ɇɟɤɨɬɨɪɵɟ ɫɜɨɣɫɬɜɚ ɩɪɟɨɛɪɚɡɨɜɚ-
ɧɢɹ Ɏɭɪɶɟ—Ɇɟɥɥɢɧɚ [3] ɭɤɚɡɚɧɵ ɜ ɬɚɛɥ. 1.
Ɍɚɛɥɢɰɚ 1
ɋɜɨɣɫɬɜɚ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ Ɏɭɪɶɟ—Ɇɟɥɥɢɧɚ
ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɨɛɥɚɫɬɶ
Ɉɛɥɚɫɬɶ ɫɩɟɤɬɪɚ Ɏɭɪɶɟ—Ɇɟɥɥɢɧɚ
ɉɨɜɨɪɨɬ ɧɚ ɭɝɨɥ
M
ɐɢɤɥɢɱɟɫɤɢɣ ɫɞɜɢɝ ɧɚ ɜɟɥɢɱɢɧɭ
T M
'
Ɇɚɫɲɬɚɛɢɪɨɜɚɧɢɟ ɜ
s
ɪɚɡ
ɋɞɜɢɝ ɧɚ ɜɟɥɢɱɢɧɭ log
s
U
'