ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
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ɉɟɪɟɯɨɞ ɤ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɫɨɤɪɚɳɚɸɳɟɣ ɱɢɫɥɨ ɭɡɥɨɜ ɩɨ
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɤɨɨɪɞɢɧɚɬɚɦ.
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɧɟɪɚɜɧɨɦɟɪɧɵɯ
ɫɟɬɨɤ ɩɪɢ ɱɢɫɥɟɧɧɨɦ ɪɟɲɟɧɢɢ ɭɪɚɜɧɟɧɢɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ ɜ
ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɩɪɟɫɥɟɞɭɟɬ ɰɟɥɶ ɭɦɟɧɶɲɢɬɶ ɱɢɫɥɨ ɪɚɫɱɟɬɧɵɯ ɭɡɥɨɜ,
ɜ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬ ɢɫɤɨɦɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɛɟɡ ɩɨɬɟɪɢ ɬɨɱɧɨɫɬɢ ɚɩ-
ɩɪɨɤɫɢɦɚɰɢɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɨɩɟɪɚɬɨɪɨɜ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɯɚɪɚɤ-
ɬɟɪ ɢɡɦɟɧɟɧɢɹ ɮɭɧɤɰɢɣ, ɢɫɫɥɟɞɭɟɦɵɯ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɭɪɚɜɧɟɧɢɣ
ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ, ɨɛɵɱɧɨ ɫɭɳɟɫɬɜɟɧɧɨ ɪɚɡɥɢɱɚɟɬɫɹ ɜ ɪɚɡɧɵɯ
ɱɚɫɬɹɯ ɨɛɥɚɫɬɢ ɢɯ ɨɩɪɟɞɟɥɟɧɢɹ. ȼ ɱɚɫɬɧɨɫɬɢ, ɝɪɚɞɢɟɧɬ ɷɬɢɯ ɮɭɧɤɰɢɣ
ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɱɚɫɬɢ ɝɪɚɧɢɰ ɢɯ ɨɛɥɚɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɵɱɧɨ ɫɭɳɟ-
ɫɬɜɟɧɧɨ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɹ ɷɬɨɝɨ ɝɪɚɞɢɟɧɬɚ ɜ ɟɟ ɝɥɭɛɢɧɧɵɯ ɱɚɫɬɹɯ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɧɟɪɚɜɧɨɦɟɪɧɵɯ ɫɟɬɨɤ ɜɨɡɧɢɤɚɟɬ ɞɨɫɬɚɬɨɱɧɨ
ɫɟɪɶɟɡɧɚɹ ɩɪɨɛɥɟɦɚ, ɫɜɹɡɚɧɧɚɹ ɫ ɨɛɟɫɩɟɱɟɧɢɟɦ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɚɩ-
ɩɪɨɤɫɢɦɚɰɢɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɨɩɟɪɚɬɨɪɨɜ.
ȼ ɤɚɱɟɫɬɜɟ ɨɞɧɨɝɨ ɢɡ ɭɞɚɱɧɵɯ ɩɨɞɯɨɞɨɜ ɤ ɪɟɲɟɧɢɸ ɷɬɨɣ ɩɪɨɛɥɟɦɵ
ɦɨɠɧɨ ɭɤɚɡɚɬɶ ɪɚɛɨɬɭ [4], ɝɞɟ ɩɪɟɞɥɨɠɟɧɚ ɫɯɟɦɚ ɚɩɩɪɨɤɫɢɦɚɰɢɢ
ɭɪɚɜɧɟɧɢɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ ɧɚ ɧɟɪɚɜɧɨɦɟɪɧɨɣ ɫɟɬɤɟ ɨɫɨɛɨɝɨ
ɬɢɩɚ. ɋɨɫɟɞɧɢɟ ɲɚɝɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜ ɧɟɣ ɥɢɛɨ ɪɚɜɧɵ, ɥɢɛɨ ɪɚɡɥɢ-
ɱɚɸɬɫɹ ɪɨɜɧɨ ɜ 2 ɪɚɡɚ. ɉɪɢ ɷɬɨɦ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɜɬɨɪɨɣ ɩɨɪɹɞɨɤ ɬɨɱ-
ɧɨɫɬɢ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɨɩɟɪɚ-
ɬɨɪɨɜ ɩɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɡɧɚɱɢɬɟɥɶɧɨɦ ɭɫɥɨɠɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ ɜɵ-
ɱɢɫɥɢɬɟɥɶɧɨɝɨ ɩɪɨɰɟɫɫɚ.
ɇɢɠɟ ɩɪɟɞɥɚɝɚɟɬɫɹ ɞɪɭɝɨɣ ɩɨɞɯɨɞ ɤ ɪɟɲɟɧɢɸ ɭɤɚɡɚɧɧɨɣ ɡɚɞɚɱɢ,
ɤɨɬɨɪɵɣ ɢɫɩɨɥɶɡɭɟɬ ɪɚɡɛɢɟɧɢɟ ɨɛɥɚɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɮɭɧɤɰɢɢ ɧɚ ɦɨ-
ɧɨɬɨɧɧɨ ɢɡɦɟɧɹɸɳɢɟɫɹ ɲɚɝɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ
ɤɨɨɪɞɢɧɚɬɚɦ (ɩɪɢ ɪɟɲɟɧɢɢ ɲɢɪɨɤɨɝɨ ɤɪɭɝɚ ɩɪɚɤɬɢɱɟɫɤɢɯ ɡɚɞɚɱ ɜɨɡ-
ɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɪɚɡɛɢɟɧɢɹ ɨɛɥɚɫɬɢ ɨɩɪɟɞɟɥɟ-
ɧɢɹ ɢɫɤɨɦɵɯ ɮɭɧɤɰɢɣ ɩɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɤɨɨɪɞɢɧɚɬɚɦ ɢɦɟɧɧɨ
ɬɚɤɨɝɨ ɬɢɩɚ).
ɋɭɬɶ ɷɬɨɝɨ ɩɨɞɯɨɞɚ ɩɪɨɢɥɥɸɫɬɪɢɪɭɟɦ ɧɚ ɩɪɢɦɟɪɟ ɭɪɚɜɧɟɧɢɹ (14),
ɩɪɢ ɪɟɲɟɧɢɢ ɤɨɬɨɪɨɝɨ ɰɟɥɟɫɨɨɛɪɚɡɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɧɟɪɚɜɧɨɦɟɪ-
ɧɵɯ ɫɟɬɨɤ ɨɛɭɫɥɨɜɥɟɧɚ ɫɥɟɞɭɸɳɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ:
x
ɲɚɝ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ ɤɨɨɪɞɢɧɚɬɟ
x
ɠɟɥɚɬɟɥɶɧɨ ɢɡɦɟɧɹɬɶ ɬɚ-
ɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɨɧ ɛɵɥ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɨɞɭɥɸ ɩɪɨɢɡ-
ɜɨɞɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɷɬɨɣ ɤɨɨɪɞɢɧɚɬɟ, ɤɨɬɨɪɵɣ ɨɛɵɱɧɨ ɢɦɟɟɬ ɬɟɧ-
ɞɟɧɰɢɸ ɤ ɭɦɟɧɶɲɟɧɢɸ ɫ ɪɨɫɬɨɦ ɤɨɨɪɞɢɧɚɬɵ
ɯ
;
x
ɲɚɝ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ ɤɨɨɪɞɢɧɚɬɟ
y
ɠɟɥɚɬɟɥɶɧɨ ɢɡɦɟɧɹɬɶ ɬɚ-
ɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɨɧ ɛɵɥ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɩɪɨɢɡɜɨɞɧɨɣ
w
z
ɩɨ ɷɬɨɣ ɤɨɨɪɞɢɧɚɬɟ, ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɬɟɧɞɟɧɰɢɸ ɤ ɭɜɟɥɢɱɟɧɢɸ ɫ ɪɨɫɬɨɦ
ɤɨɨɪɞɢɧɚɬɵ
ɭ
.
ɍɤɚɡɚɧɧɵɦ ɬɪɟɛɨɜɚɧɢɹɦ, ɜ ɱɚɫɬɧɨɫɬɢ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɪɟɨɛɪɚɡɨ-
ɜɚɧɢɟ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɜɢɞɚ
^ ` ^ `
,
,
,
x y
K [
o
(22)