ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
10
Ⱦɥɹ 2-ɣ ɫɢɫɬɟɦɵ ɧɢɬɟɣ ɬɟɧɡɨɪ
( )
ɉ
ijkl
D
c
ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ (4),
ɜ ɤɨɬɨɪɨɣ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɢɬɶ ɰɢɤɥɢɱɟɫɤɭɸ ɩɟɪɟɫɬɚɧɨɜɤɭ ɢɧɞɟɤ-
ɫɨɜ: 1 2,
o
2 3, 3 1.
o o
Ɍɟɧɡɨɪ ɦɨɞɭɥɟɣ ɭɩɪɭɝɨɫɬɢ ɧɢɬɟɣ ɜ ɫɨɛɫɬɜɟɧɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢ-
ɧɚɬ
i
O
c
[
ɹɜɥɹɟɬɫɹ ɨɛɪɚɬɧɵɦ ɞɥɹ ɬɟɧɡɨɪɚ ɭɩɪɭɝɢɯ ɩɨɞɚɬɥɢɜɨɫɬɟɣ:
( )
( ) 1
(
ɉ ) .
ijkl
ijkl
C
D
D
c
c
ȼ ɪɚɡɜɢɜɚɟɦɨɣ ɡɞɟɫɶ ɦɨɞɟɥɢ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ
ɧɢɬɶ ɦɨɠɟɬ ɱɚɫɬɢɱɧɨ ɪɚɡɪɭɲɢɬɶɫɹ, ɤɨɝɞɚ ɡɧɚɱɟɧɢɹ 1 ɞɨɫɬɢɝɧɟɬ ɩɚɪɚ-
ɦɟɬɪ ɩɨɜɪɟɠɞɚɟɦɨɫɬɢ
( )
1
;
z
D
ɩɪɢ ɷɬɨɦ ɨɛɧɭɥɹɸɬɫɹ ɜɫɟ ɦɨɞɭɥɢ ɭɩɪɭɝɨ-
ɫɬɢ, ɤɪɨɦɟ
( )
.
C
c
D
DDDD
Ɍɚɤɨɟ ɱɚɫɬɢɱɧɨɟ ɪɚɡɪɭɲɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɢɡ-ɡɚ
ɪɚɡɪɭɲɟɧɢɹ ɦɚɬɪɢɰɵ ɜ ɫɨɫɬɚɜɟ ɧɢɬɢ, ɛɟɡ ɪɚɡɪɵɜɚ ɦɨɧɨɜɨɥɨɤɨɧ. ȿɫɥɢ
ɡɧɚɱɟɧɢɹ 1 ɞɨɫɬɢɝɚɟɬ ɩɚɪɚɦɟɬɪ ɩɨɜɪɟɠɞɚɟɦɨɫɬɢ
( )
2
,
z
D
ɬɨ ɩɪɨɢɫɯɨɞɢɬ
ɩɨɥɧɨɟ ɪɚɡɪɭɲɟɧɢɟ ɧɢɬɢ (ɜ ɞɚɧɧɨɣ ɬɨɱɤɟ) ɢɡ-ɡɚ ɪɚɡɪɭɲɟɧɢɹ ɦɨɧɨɜɨ-
ɥɨɤɨɧ ɜ ɧɟɣ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɦɚɬɪɢɰɵ, ɨɤɪɭɠɚɸɳɟɣ ɦɨɧɨɜɨɥɨɤɧɚ.
ɉɪɢ ɩɨɥɧɨɦ ɪɚɡɪɭɲɟɧɢɢ ɧɢɬɢ ɨɛɧɭɥɹɸɬɫɹ ɜɫɟ ɦɨɞɭɥɢ ɭɩɪɭɝɨɫɬɢ
( )
.
ijkl
C
c
D
ɋ ɭɱɟɬɨɦ ɢɡɥɨɠɟɧɧɨɝɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɦɨ-
ɞɭɥɟɣ ɭɩɪɭɝɨɫɬɢ ɧɢɬɢ ɜ ɫɨɛɫɬɜɟɧɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɦɨɠɧɨ ɡɚɩɢ-
ɫɚɬɶ ɬɚɤ:
^
( )
( )
( )
1
2
1 (
1) 1 (
1)
ijkl
C
h z
h z
D
D
D
c ª
º ª
º u
¬
¼
¬
¼
`
( ) 1
( )
( )
2
(
ɉ )
(
1)
,
ijkl
i
j
k l
h z
C
D
D
D
DDDD D D
D
D
G G G G
c
c
u
(5)
ɝɞɟ
( )
2
(
1)
h z
D
—
ɮɭɧɤɰɢɹ ɏɟɜɢɫɚɣɞɚ:
( )
2
(
1) 0,
h z
D
ɟɫɥɢ
( )
2
1,
z
D
ɢ
( )
2
(
1) 1,
h z
D
ɟɫɥɢ
( )
2
1.
z
t
D
Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɦɨɞɭɥɟɣ ɭɩɪɭɝɨɫɬɢ ɧɢɬɢ ɜ
ɟɞɢɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ
i
O
[
ɢɫɩɨɥɶɡɭɟɦ ɮɨɪɦɭɥɵ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ 4-ɝɨ ɪɚɧɝɚ ɩɪɢ ɩɨɜɨɪɨɬɟ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɧɚ
ɭɝɨɥ
( ) :
k
D
M [
( )
( ) ( )
( ) ( )
( )
( )
( )
1
2
( ,
,
)
( )
( )
( )
( ),
l
m
n
s
r
ijkl
ijkl
i
k j
k k
k l
k
C z z
C Q Q Q Q
c
D
D
D
D
D
D
D
D
[
[
[
[
[
(6)
ɝɞɟ
( )
( )
m
i
k
Q
D
[
—
ɦɚɬɪɢɰɵ ɩɨɜɨɪɨɬɚ:
1
1
(1)
1
1
cos ( ) 0 sin ( )
( )
0
1
0 ;
sin ( ) 0 cos ( )
k
k
m
i
k
k
k
Q
§
·
¨
¸
¨
¸
¨
¸
©
¹
M [
M [
[
M [
M [
(7)