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Некоторые подходы к обработке и интерпретации данных скважинных сейсмических наблюдений и результаты их применений.

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ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 1, ʋ2, 1998 ɝ.
ɫɬɪ.113-120
ɇɟɤɨɬɨɪɵɟ ɩɨɞɯɨɞɵ ɤ ɨɛɪɚɛɨɬɤɟ ɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɞɚɧɧɵɯ
ɫɤɜɚɠɢɧɧɵɯ ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɛɥɸɞɟɧɢɣ ɢ ɪɟɡɭɥɶɬɚɬɵ ɢɯ
ɩɪɢɦɟɧɟɧɢɣ
ɗ.Ⱥ. Ȼɥɹɫ1, Ʌ.ɂ. ɒɚɜɢɧɚ2
1
ɋɭɞɨɜɨɞɢɬɟɥɶɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɌɍ, ɤɚɮɟɞɪɚ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ
2
ɇɂɂ Ɇɨɪɝɟɨɮɢɡɢɤɚ
Ⱥɧɧɨɬɚɰɢɹ. ȼ ɪɚɛɨɬɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɨɛɳɢɣ ɩɨɞɯɨɞ ɤ ɨɛɪɚɛɨɬɤɟ ɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɞɚɧɧɵɯ ɫɤɜɚɠɢɧɧɵɯ
ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɛɥɸɞɟɧɢɣ. ɉɪɟɞɥɚɝɚɟɬɫɹ ɨɛɪɚɛɨɬɤɭ ɜɵɩɨɥɧɹɬɶ ɜ ɱɟɬɵɪɟ ɷɬɚɩɚ, ɧɚ ɤɚɠɞɨɦ ɢɡ ɤɨɬɨɪɵɯ
ɪɟɲɚɟɬɫɹ ɫɜɨɣ ɤɥɚɫɫ ɡɚɞɚɱ. ɉɨɞɪɨɛɧɨ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɨɞɧɚ ɢɡ ɡɚɞɚɱ – ɜɵɞɟɥɟɧɢɟ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɩɨ
ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɵɦ ɧɚɛɥɸɞɟɧɢɹɦ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɞɚɧɧɨɣ ɡɚɞɚɱɢ ɩɪɟɞɥɨɠɟɧ ɨɩɬɢɦɢɡɚɰɢɨɧɧɵɣ ɦɟɬɨɞ, ɧɚ
ɤɚɠɞɨɦ ɲɚɝɟ ɤɨɬɨɪɨɝɨ ɭɬɨɱɧɹɟɬɫɹ ɮɨɪɦɚ ɢ ɚɦɩɥɢɬɭɞɵ ɨɞɧɨɣ ɜɨɥɧɵ. Ɉɩɬɢɦɢɡɚɰɢɹ ɜɵɩɨɥɧɹɟɬɫɹ ɦɟɬɨɞɨɦ
ɫɨɩɪɹɠɟɧɧɵɯ ɝɪɚɞɢɟɧɬɨɜ, ɩɪɢ ɷɬɨɦ ɧɟɢɡɜɟɫɬɧɵɦɢ ɹɜɥɹɸɬɫɹ ɬɨɥɶɤɨ ɜɪɟɦɟɧɧɵɟ ɡɚɞɟɪɠɤɢ, ɚ ɚɦɩɥɢɬɭɞɵ ɢ
ɮɨɪɦɚ ɜɨɥɧɵ ɧɚɯɨɞɹɬɫɹ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɧɚ ɫɨɛɫɬɜɟɧɧɵɟ ɱɢɫɥɚ ɢ ɜɟɤɬɨɪɚ ɫɢɦɦɟɬɪɢɱɧɨɣ ɦɚɬɪɢɰɵ.
ɉɪɢɜɟɞɟɧɵ ɩɪɢɦɟɪɵ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦ ɧɚ ɞɚɧɧɵɯ ȼɋɉ ɜ ɋɟɜɟɪɧɨɦ ɋɚɦɨɬɥɨɪɟ. ɉɪɢɦɟɧɟɧɢɟ ɞɚɧɧɨɝɨ
ɩɨɞɯɨɞɚ ɩɨɡɜɨɥɢɥɨ ɩɨɥɭɱɢɬɶ ɝɥɭɛɢɧɧɵɟ ɪɚɡɪɟɡɵ ɫ ɱɚɫɬɨɬɚɦɢ ɞɨ 170Ƚɰ ɢ ɫɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɫɜɨɣɫɬɜɚ
ɩɪɨɞɭɤɬɢɜɧɵɯ ɫɥɨɟɜ ɜ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ.
Abstract. The paper describes a general approach to the processing and interpretation of borehole seismic
observations. The interpretation is advised to be carried out in four stages each solving its own problems. The
solution of one of them is considered in greater details - that is the task of regular wave definition from threecomponent observations. There is an optimization method offered to solve the problem, that specifies the shape
and amplitude of a single wave. The optimization is fulfilled with the help of a conjugated gradients' method, the
only unknown quantities are time delays, wave amplitudes and shapes find themselves on the eigenvalue
numbers and vectors of the symmetrical matrix. The paper shows the examples of software application to VSP
data from the Northern Samotlor field. The application of the given approach has given the possibility to obtain
deep sections with frequency up to 170 Hz and to predict the productive layer properties in the well vicinity.
1. ȼɜɟɞɟɧɢɟ
Ɉɛpɚɛɨɬɤɚ ɢ ɢɧɬɟpɩpɟɬɚɰɢɹ ɞɚɧɧɵɯ ɫɤɜɚɠɢɧɧɵɯ ɧɚɛɥɸɞɟɧɢɣ ɜɵɩɨɥɧɹɟɬɫɹ ɧɚ ɷɬɚɩɟ ɞɟɬɚɥɶɧɵɯ
pɚɛɨɬ ɩɨ ɭɬɨɱɧɟɧɢɸ ɫɬpɨɟɧɢɹ ɩpɨɞɭɤɬɢɜɧɵɯ ɫɥɨɟɜ ɜ ɨɤpɟɫɬɧɨɫɬɢ ɫɤɜɚɠɢɧɵ. ɇɚ ɷɬɨɣ ɫɬɚɞɢɢ pɚɛɨɬ
ɢɡɜɟɫɬɧɚ ɚɩpɢɨpɧɚɹ (ɩɪɢɛɥɢɠɟɧɧɚɹ) ɦɨɞɟɥɶ ɫpɟɞɵ ɜ ɫɤɜɚɠɢɧɟ, ɢ ɬɪɟɛɭɟɬɫɹ ɭɬɨɱɧɢɬɶ ɫɜɨɣɫɬɜɚ pɚɡpɟɡɚ ɜ
ɧɟɩɨɫpɟɞɫɬɜɟɧɧɨɣ ɛɥɢɡɨɫɬɢ ɨɬ ɫɤɜɚɠɢɧɵ – ɭɜɹɡɚɬɶ ɚɤɭɫɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɪɚɡɪɟɡɚ ɫ ɜɨɥɧɨɜɵɦ ɩɨɥɟɦ
ɩpɨɞɨɥɶɧɨɝɨ ȼɋɉ (ɜɟɪɬɢɤɚɥɶɧɨɟ ɫɟɣɫɦɢɱɟɫɤɨɟ ɩɪɨɮɢɥɢɪɨɜɚɧɢɟ), ɚ ɡɚɬɟɦ pɚɫɩpɨɫɬpɚɧɢɬɶ ɷɬɭ ɦɨɞɟɥɶ ɧɚ
ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɟ ɩpɨɫɬpɚɧɫɬɜɨ ɩɨ ɫɤɜɚɠɢɧɧɵɦ ɧɚɛɥɸɞɟɧɢɹɦ ɫ ɜɵɧɨɫɧɵɯ ɩɭɧɤɬɨɜ ɜɨɡɛɭɠɞɟɧɢɣ (ɜ
ɦɨpɫɤɢɯ ɭɫɥɨɜɢɹɯ ɷɬɨ ɦɨɝɭɬ ɛɵɬɶ ɦɧɨɝɨɭpɨɜɟɧɧɵɟ ɫɤɜɚɠɢɧɧɵɟ ɧɚɛɥɸɞɟɧɢɹ – ɋɈȽ). ɗɬɨ ɩɨɡɜɨɥɹɟɬ
ɩɨɥɭɱɚɬɶ ɞɟɬɚɥɶɧɭɸ ɢɧɮɨɪɦɚɰɢɸ ɨ ɫɬɪɨɟɧɢɢ ɩɪɨɞɭɤɬɢɜɧɵɯ ɫɥɨɟɜ, ɥɚɬɟɪɚɥɶɧɨɦ ɢɡɦɟɧɟɧɢɢ ɢɯ ɫɜɨɣɫɬɜ ɜ
ɨɤɪɟɫɬɧɨɫɬɢ ɫɤɜɚɠɢɧɵ ɪɚɞɢɭɫɨɦ ɩɨɪɹɞɤɚ 0,3 ɝɥɭɛɢɧɵ ɡɚɥɟɝɚɧɢɹ ɨɬɪɚɠɚɸɳɢɯ ɝɪɚɧɢɰ.
Ⱦɥɹ pɟɲɟɧɢɹ ɡɚɞɚɱɢ ɞɟɬɚɥɶɧɨɝɨ ɢɡɭɱɟɧɢɹ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ ɩpɨɫɬpɚɧɫɬɜɚ ɩpɟɞɥɚɝɚɟɬɫɹ
ɫɥɟɞɭɸɳɢɣ ɩɨɞɯɨɞ ɤ ɨɛpɚɛɨɬɤɟ ɢ ɢɧɬɟpɩpɟɬɚɰɢɢ ɞɚɧɧɵɯ ɫɤɜɚɠɢɧɧɵɯ ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɛɥɸɞɟɧɢɣ.
ɂɡɭɱɟɧɢɟ ɫɬɪɨɟɧɢɹ pɚɡpɟɡɚ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɩpɨɜɨɞɢɬɫɹ ɜ ɱɟɬɵpɟ ɷɬɚɩɚ, ɧɚ ɤɚɠɞɨɦ ɢɡ
ɤɨɬɨpɵɯ pɟɲɚɟɬɫɹ ɫɜɨɣ ɤpɭɝ ɡɚɞɚɱ.
ɇɚ ɩɟpɜɨɦ ɷɬɚɩɟ ɩɨ ɞɚɧɧɵɦ Ƚɂɋ ɢ ɩpɨɞɨɥɶɧɨɦɭ ɩɨɥɸ ȼɋɉ ɫɬpɨɢɬɫɹ ɞɟɬɚɥɶɧɚɹ ɨɞɧɨɦɟpɧɚɹ
ɦɨɞɟɥɶ pɚɡpɟɡɚ. ɋɧɚɱɚɥɚ ɩɨ ɞɚɧɧɵɦ Ƚɂɋ ɢ ȺɄ ɩɨɥɭɱɚɟɦ ɬɨɧɤɨɫɥɨɢɫɬɭɸ ɚɤɭɫɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ, ɞɥɹ
ɤɨɬɨpɨɣ pɚɫɫɱɢɬɵɜɚɟɬɫɹ ɜɨɥɧɨɜɨɟ ɩɨɥɟ ɨɬpɚɠɟɧɧɵɯ ɜɨɥɧ ɩpɨɞɨɥɶɧɨɝɨ ȼɋɉ. Ʉɚɤ ɩɨɤɚɡɵɜɚɟɬ ɩpɚɤɬɢɤɚ,
ɬɟɨpɟɬɢɱɟɫɤɨɟ ɜɨɥɧɨɜɨɟ ɩɨɥɟ ɨɬɪɚɠɟɧɧɵɯ ɜɨɥɧ ɧɟ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɩɨɥɟɦ, ɩɨɥɭɱɟɧɧɵɦ ɢɡ ɩpɨɞɨɥɶɧɨɝɨ
ȼɋɉ. ɗɬɢ ɨɬɥɢɱɢɹ ɜɵɡɵɜɚɸɬɫɹ ɦɧɨɝɢɦɢ ɩpɢɱɢɧɚɦɢ. ɇɟ ɜɞɚɜɚɹɫɶ ɜ ɩɨɞpɨɛɧɨɟ ɨɛɫɭɠɞɟɧɢɟ ɷɬɢɯ ɩpɢɱɢɧ,
ɨɬɦɟɬɢɦ ɬɨɥɶɤɨ, ɱɬɨ ɤpɨɦɟ ɩɨɝpɟɲɧɨɫɬɟɣ ɫɨɛɫɬɜɟɧɧɨ ɦɟɬɨɞɨɜ Ƚɂɋ ɢ ȺɄ, ɨɬɥɢɱɢɟ ɬɟɨpɟɬɢɱɟɫɤɨɝɨ ɢ
pɟɚɥɶɧɨɝɨ ɩɨɥɟɣ ɜɵɡɵɜɚɟɬɫɹ ɬɟɦ, ɱɬɨ ɩɨɥɟ ɫɟɣɫɦɢɱɟɫɤɢɯ ɜɨɥɧ ɮɨpɦɢpɭɟɬɫɹ ɨɛɥɚɫɬɶɸ ɫpɟɞɵ pɚɞɢɭɫɚ ɨɬ
ɞɟɫɹɬɤɨɜ ɦɟɬpɨɜ ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɫɨɬɟɧ (ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɝɥɭɛɢɧɵ ɡɚɥɟɝɚɧɢɹ ɢ ɩpɟɨɛɥɚɞɚɸɳɢɯ ɱɚɫɬɨɬ), ɜ
ɬɨ ɜpɟɦɹ ɤɚɤ pɚɞɢɭɫ ɢɫɫɥɟɞɨɜɚɧɢɹ Ƚɂɋ ɢ ȺɄ ɫɨɫɬɚɜɥɹɟɬ ɧɟɫɤɨɥɶɤɨ ɦɟɬpɨɜ. Ɏɚɤɬɢɱɟɫɤɢ ɞɥɹ ɩɨɫɬpɨɟɧɢɹ
ɦɨɞɟɥɢ pɚɡpɟɡɚ, ɫɨɝɥɚɫɨɜɚɧɧɨɣ ɫ ɜɨɥɧɨɜɵɦ ɩɨɥɟɦ ɩpɨɞɨɥɶɧɨɝɨ ȼɋɉ (ɬ.ɟ. ɜ ɫɟɣɫɦɢɱɟɫɤɨɦ ɞɢɚɩɚɡɨɧɟ
113
Ȼɥɹɫ ɗ.Ⱥ., ɒɚɜɢɧɚ Ʌ.ɂ. ɇɟɤɨɬɨɪɵɟ ɩɨɞɯɨɞɵ ɤ ɨɛɪɚɛɨɬɤɟ ...
ɱɚɫɬɨɬ), ɧɟɨɛɯɨɞɢɦɨ ɧɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɨɛɪɚɛɨɬɤɢ pɟɲɢɬɶ ɨɛpɚɬɧɭɸ ɞɢɧɚɦɢɱɟɫɤɭɸ ɡɚɞɚɱɭ. ɇɚ ɷɬɨɦ ɠɟ
ɷɬɚɩɟ ɜɵɩɨɥɧɹɟɬɫɹ ɪɚɡɞɟɥɟɧɢɟ ɢɫɯɨɞɧɨɝɨ ɩɨɥɹ ɩɪɨɞɨɥɶɧɨɝɨ ȼɋɉ ɧɚ ɩɚɞɚɸɳɢɟ ɢ ɨɬɪɚɠɟɧɧɵɟ ɜɨɥɧɵ,
ɨɩɬɢɦɚɥɶɧɚɹ ɞɟɤɨɧɜɨɥɸɰɢɹ ɩɨɥɹ ɨɬɪɚɠɟɧɧɵɯ ɜɨɥɧ ɢ ɜɵɫɨɤɨɬɨɱɧɚɹ ɩɪɢɜɹɡɤɚ ɨɬɪɚɠɟɧɢɣ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɩɟɪɜɨɝɨ ɷɬɚɩɚ ɪɚɡɪɚɛɨɬɚɧɵ ɦɟɬɨɞɵ ɨɩɪɟɞɟɥɟɧɢɹ ɨɞɧɨɦɟɪɧɨɣ ɬɨɧɤɨɫɥɨɢɫɬɨɣ
ɦɨɞɟɥɢ, ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɪɟɲɟɧɢɢ ɨɛɪɚɬɧɨɣ ɨɞɧɨɦɟɪɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ. Ɂɚɞɚɱɚ ɢɡɭɱɟɧɢɹ
ɚɤɭɫɬɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɪɚɡɪɟɡɚ ɩɨ ɞɚɧɧɵɦ ɩɪɨɞɨɥɶɧɨɝɨ ȼɋɉ (ɫ ɛɥɢɠɧɟɝɨ ɩɭɧɤɬɚ ɜɨɡɛɭɠɞɟɧɢɣ)
ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ ɞɜɚ ɲɚɝɚ. ɇɚ ɩɟɪɜɨɦ ɲɚɝɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɫɪɟɞɵ ɜɨ ɜɫɤɪɵɬɨɣ ɱɚɫɬɢ ɫɤɜɚɠɢɧɵ
ɩɭɬɟɦ ɪɟɲɟɧɢɹ ɨɞɧɨɦɟɪɧɨɣ ɨɛɪɚɬɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ, ɫɜɨɞɹɳɟɣɫɹ ɤ ɦɢɧɢɦɢɡɚɰɢɢ ɰɟɥɟɜɨɣ
ɮɭɧɤɰɢɢ, ɫɜɹɡɵɜɚɸɳɟɣ ɫɩɟɤɬɪɵ ɧɚɛɥɸɞɚɟɦɵɯ ɤɨɥɟɛɚɧɢɣ ɢ ɩɚɪɚɦɟɬɪɵ ɪɚɡɪɟɡɚ. Ɇɟɬɨɞɵ ɨɫɧɨɜɚɧɵ ɧɚ
ɧɟɥɢɧɟɣɧɨɣ ɨɩɬɢɦɢɡɚɰɢɢ ɜ ɫɩɟɤɬɪɚɥɶɧɨɣ ɨɛɥɚɫɬɢ, ɩɪɢ ɷɬɨɦ ɭɱɢɬɵɜɚɟɬɫɹ ɜɥɢɹɧɢɟ ɩɪɨɦɟɠɭɬɨɱɧɵɯ
ɝɪɚɧɢɰ ɧɚ ɛɚɡɟ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɞɟɥɢ. ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɞɟɬɚɥɶɧɨɣ ɦɨɞɟɥɢ ɫɪɟɞɵ ɜɵɩɨɥɧɹɟɬɫɹ ɪɚɡɞɟɥɟɧɢɟ
ɩɨɥɧɨɝɨ ɩɨɥɹ ɧɚ ɜɨɫɯɨɞɹɳɢɟ ɢ ɧɢɫɯɨɞɹɳɢɟ ɜɨɥɧɵ. ɉɨɥɟ ɨɬɪɚɠɟɧɧɵɯ ɜɨɥɧ ɮɢɥɶɬɪɭɟɬɫɹ ɩɨ ɮɨɪɦɟ
ɧɢɫɯɨɞɹɳɢɯ ɜɨɥɧ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɞɨɛɢɬɶɫɹ ɜɵɫɨɤɨɣ ɪɚɡɪɟɲɟɧɧɨɫɬɢ ɩɨɥɹ ɜɨɫɯɨɞɹɳɢɯ ɜɨɥɧ, ɜɵɩɨɥɧɢɬɶ
ɬɨɱɧɭɸ ɩɪɢɜɹɡɤɭ ɨɬɪɚɠɟɧɢɣ ɤ ɝɪɚɧɢɰɚɦ ɫɥɨɟɜ. Ɋɟɡɭɥɶɬɚɬɵ ɩɪɢɜɹɡɤɢ ɢ ɭɬɨɱɧɟɧɢɹ ɚɤɭɫɬɢɱɟɫɤɢɯ
ɩɚɪɚɦɟɬɪɨɜ ɫɪɟɞɵ ɩɪɨɜɟɪɹɸɬɫɹ ɩɪɢ ɩɨɦɨɳɢ ɩɪɨɝɪɚɦɦ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ. ɇɚ ɜɬɨɪɨɦ ɲɚɝɟ,
ɢɫɩɨɥɶɡɭɹ ɩɨɥɹ ɩɚɞɚɸɳɢɯ ɢ ɜɨɫɯɨɞɹɳɢɯ ɜɨɥɧ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɞɟɥɟɧɢɹ ɧɚɛɥɸɞɚɟɦɨɝɨ
ɜɨɥɧɨɜɨɝɨ ɩɨɥɹ ɧɚ ɧɢɫɯɨɞɹɳɢɟ ɢ ɜɨɫɯɨɞɹɳɢɟ ɜɨɥɧɵ, ɪɟɲɚɟɬɫɹ ɡɚɞɚɱɚ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɚɤɭɫɬɢɱɟɫɤɢɯ ɢ
ɩɨɝɥɨɳɚɸɳɢɯ ɫɜɨɣɫɬɜ ɪɚɡɪɟɡɚ ɧɢɠɟ ɡɚɛɨɹ ɫɤɜɚɠɢɧɵ. Ɋɟɲɟɧɢɟ ɞɚɧɧɨɣ ɡɚɞɚɱɢ ɬɚɤɠɟ ɫɜɨɞɢɬɫɹ ɤ
ɦɢɧɢɦɢɡɚɰɢɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ, ɫɜɹɡɵɜɚɸɳɟɣ ɜ ɫɩɟɤɬɪɚɥɶɧɨɣ ɨɛɥɚɫɬɢ ɫɩɟɤɬɪɵ ɜɵɞɟɥɟɧɧɵɯ ɜɨɥɧ ɢ
ɩɚɪɚɦɟɬɪɵ ɪɚɡɪɟɡɚ. Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɨɛɟ ɡɚɞɚɱɢ ɩɟɪɜɨɝɨ ɷɬɚɩɚ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɪɚɛɨɬɟ (Ȼɥɹɫ, ɋɟɪɟɞɚ, 1998).
ɇɚ ɜɬɨpɨɦ ɷɬɚɩɟ ɭɬɨɱɧɹɟɬɫɹ ɬɨɥɫɬɨɫɥɨɢɫɬɚɹ ɫɤɨpɨɫɬɧɚɹ ɦɨɞɟɥɶ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ ɩpɨɫɬpɚɧɫɬɜɚ
ɩɨ ɞɚɧɧɵɦ ɫɤɜɚɠɢɧɧɵɯ ɧɚɛɥɸɞɟɧɢɣ (ɋɈȽ ɢɥɢ ɫ ɜɵɧɨɫɧɨɝɨ ɩɭɧɤɬɚ), ɬ.ɟ. ɮɚɤɬɢɱɟɫɤɢ pɟɲɚɟɬɫɹ ɨɛpɚɬɧɚɹ
ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɡɚɞɚɱɚ. Ɂɞɟɫɶ ɧɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ ɩpɢɧɰɢɩɢɚɥɶɧɨɟ pɚɡɥɢɱɢɟ ɜ ɩɨɥɭɱɟɧɢɢ ɢɡɨɛpɚɠɟɧɢɣ
(ɜpɟɦɟɧɧɵɯ ɢɥɢ ɝɥɭɛɢɧɧɵɯ pɚɡpɟɡɨɜ) ɜ ɦɟɬɨɞɟ ɈȽɌ ɢ ɩɨ ɫɤɜɚɠɢɧɧɵɦ ɧɚɛɥɸɞɟɧɢɹɦ. ȿɫɥɢ ɜ ɦɟɬɨɞɟ ɈȽɌ
ɡɧɚɧɢɟ ɫɤɨpɨɫɬɧɨɣ ɦɨɞɟɥɢ ɫpɟɞɵ ɧɟ ɬpɟɛɭɟɬɫɹ, ɚ ɞɨɫɬɚɬɨɱɧɨ ɩpɨɜɟɫɬɢ ɫɤɨpɨɫɬɧɨɣ ɚɧɚɥɢɡ, ɬɨ ɞɥɹ
ɩɨɥɭɱɟɧɢɹ pɚɡpɟɡɨɜ ȼɋɉ-ɈȽɌ ɧɟɨɛɯɨɞɢɦɨ ɡɚɞɚɬɶ ɦɨɞɟɥɶ ɫpɟɞɵ, ɬɚɤ ɤɚɤ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ
ɦɢɝpɚɰɢɸ ɬɨɱɤɢ ɨɬpɚɠɟɧɢɹ ɩpɢ ɢɡɦɟɧɟɧɢɢ ɝɥɭɛɢɧɵ ɨɬpɚɠɚɸɳɟɣ ɝpɚɧɢɰɵ. ɉpɢ ɫɤɜɚɠɢɧɧɵɯ
ɧɚɛɥɸɞɟɧɢɹɯ ɞɚɠɟ ɧɟɛɨɥɶɲɢɟ ɩɨɝpɟɲɧɨɫɬɢ ɜ ɫɤɨpɨɫɬɧɨɣ ɦɨɞɟɥɢ ɩpɢɜɨɞɹɬ ɤ ɫɭɳɟɫɬɜɟɧɧɵɦ ɢɫɤɚɠɟɧɢɹɦ
ɫɭɦɦɚpɧɵɯ pɚɡpɟɡɨɜ, ɩɨɷɬɨɦɭ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɢɡɨɛpɚɠɟɧɢɣ ɫ ɦɢɧɢɦɚɥɶɧɵɦɢ ɢɫɤɚɠɟɧɢɹɦɢ ɧɟɨɛɯɨɞɢɦɨ
ɩpɟɞɜɚpɢɬɟɥɶɧɨ pɟɲɚɬɶ ɨɛpɚɬɧɭɸ ɤɢɧɟɦɚɬɢɱɟɫɤɭɸ ɡɚɞɚɱɭ - ɨɩpɟɞɟɥɹɬɶ ɩɥɚɫɬɨɜɵɟ ɫɤɨpɨɫɬɢ ɢ
ɨɬpɚɠɚɸɳɢɟ ɝpɚɧɢɰɵ ɩɨ ɝɨɞɨɝpɚɮɚɦ ɨɬpɚɠɟɧɧɵɯ ɢ ɩpɨɯɨɞɹɳɢɯ ɜɨɥɧ.
Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ ɩɨɫɬpɨɟɧɢɹ ɫɤɨpɨɫɬɧɨɣ ɦɨɞɟɥɢ pɚɡpɟɡɚ pɚɡɛɢɜɚɟɬɫɹ ɧɚ ɬpɢ ɲɚɝɚ: ɜɵɞɟɥɟɧɢɟ
ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɢ ɨɩpɟɞɟɥɟɧɢɟ ɢɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɯɚpɚɤɬɟpɢɫɬɢɤ, ɩɨɫɬpɨɟɧɢɟ ɫɤɨpɨɫɬɧɨɣ ɦɨɞɟɥɢ ɢ
ɩpɨɜɟpɤɚ pɟɡɭɥɶɬɚɬɨɜ ɭɬɨɱɧɟɧɢɹ ɫɤɨɪɨɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɪɚɡɪɟɡɚ ɩɭɬɟɦ ɫɪɚɜɧɟɧɢɹ ɪɟɚɥɶɧɵɯ ɢ
ɪɚɫɫɱɢɬɚɧɧɵɯ ɜɪɟɦɟɧ ɩɪɢɯɨɞɚ ɜɨɥɧ. Ɉɫɨɛɟɧɧɨɫɬɶɸ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɵɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɡɚɞɚɱ ɩɪɢ
ɫɤɜɚɠɢɧɧɵɯ ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɛɥɸɞɟɧɢɹɯ ɹɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ (ɢ ɧɟɨɛɯɨɞɢɦɨɫɬɶ) ɢɫɩɨɥɶɡɨɜɚɧɢɹ
ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ ɜɨɥɧ: ɜɨɫɯɨɞɹɳɢɯ ɢ ɧɢɫɯɨɞɹɳɢɯ, ɦɨɧɨɬɢɩɧɵɯ ɢ ɨɛɦɟɧɧɵɯ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɜɬɨɪɨɝɨ ɷɬɚɩɚ ɪɚɡɪɚɛɨɬɚɧɵ ɚɥɝɨɪɢɬɦɵ ɢ ɩɪɨɝɪɚɦɦɵ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɵɯ
ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɡɚɞɚɱ ɜ ɬɪɟɯɦɟɪɧɵɯ ɫɪɟɞɚɯ ɫ ɧɟɫɨɝɥɚɫɧɵɦɢ ɝɪɚɧɢɰɚɦɢ ɢ ɧɟɨɞɧɨɪɨɞɧɵɦɢ ɫɥɨɹɦɢ. Ɉɧɢ
ɩɨɡɜɨɥɹɸɬ ɨɩɪɟɞɟɥɹɬɶ ɬɨɥɫɬɨɫɥɨɢɫɬɵɟ ɦɨɞɟɥɢ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɩɨ ɜɨɥɧɚɦ ɪɚɡɥɢɱɧɵɯ
ɬɢɩɨɜ, ɤɚɤ ɜɨɫɯɨɞɹɳɢɦ, ɬɚɤ ɢ ɧɢɫɯɨɞɹɳɢɦ. ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɫɤɨɪɨɫɬɟɣ ɢ ɝɪɚɧɢɰ ɪɚɡɪɟɡɚ ɭɱɢɬɵɜɚɟɬɫɹ
ɩɪɟɥɨɦɥɟɧɢɟ ɥɭɱɟɣ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɫɧɨɫ ɜ ɬɪɟɯɦɟɪɧɵɯ ɥɚɬɟɪɚɥɶɧɨ-ɧɟɨɞɧɨɪɨɞɧɵɯ
ɫɪɟɞɚɯ. ɍɬɨɱɧɟɧɢɟ ɦɨɞɟɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɨɩɬɢɦɢɡɚɰɢɨɧɧɵɦ ɦɟɬɨɞɨɦ ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɢɡɚɰɢɢ ɪɚɡɥɢɱɢɣ
ɪɟɚɥɶɧɵɯ ɢ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɜɪɟɦɟɧ ɜɵɞɟɥɟɧɧɵɯ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ (Ȼɥɹɫ, 1998).
ɇɚ ɬpɟɬɶɟɦ ɷɬɚɩɟ ɜɵɩɨɥɧɹɟɬɫɹ ɜɵɱɢɬɚɧɢɟ pɟɝɭɥɹpɧɵɯ ɩɨɦɟɯ, ɩpɟɠɞɟ ɜɫɟɝɨ ɧɢɫɯɨɞɹɳɢɯ ɜɨɥɧ ɧɚ
ɫɟɣɫɦɨɝpɚɦɦɚɯ ȼɋɉ, ɚ ɬɚɤɠɟ ɧɢɡɤɨɫɤɨpɨɫɬɧɵɯ ɜɨɥɧ ɧɚ ɫɟɣɫɦɨɝpɚɦɦɚɯ ɋɈȽ. ɉɨɫɥɟ ɷɬɨɝɨ ɜɵɩɨɥɧɹɟɬɫɹ
ɩpɟɨɛpɚɡɨɜɚɧɢɟ ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ ɜɨ ɜpɟɦɟɧɧɵɟ ɢɥɢ ɝɥɭɛɢɧɧɵɟ ɢɡɨɛpɚɠɟɧɢɹ ɫpɟɞɵ ɜ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɦ
ɩpɨɫɬpɚɧɫɬɜɟ c ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɨɥɭɱɟɧɧɨɣ ɫɤɨpɨɫɬɧɨɣ ɦɨɞɟɥɢ. ȼɢɞ ɢɡɨɛpɚɠɟɧɢɣ ɡɚɜɢɫɢɬ ɨɬ ɫɯɟɦɵ
ɧɚɛɥɸɞɟɧɢɣ, ɜ ɩpɢɧɰɢɩɟ (ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɪɚɫɩɨɥɨɠɟɧɢɹɯ ɩɭɧɤɬɨɜ ɜɨɡɛɭɠɞɟɧɢɹ) ɦɨɠɧɨ ɩɨɥɭɱɚɬɶ
ɬpɟɯɦɟpɧɵɟ ɤɭɛɵ, ɚ ɡɚɬɟɦ ɢɡ ɧɢɯ ɜɵɛɢpɚɬɶ ɬɟ ɢɥɢ ɢɧɵɟ ɫɟɱɟɧɢɹ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɬɪɟɬɶɟɝɨ ɷɬɚɩɚ ɪɚɡɪɚɛɨɬɚɧɵ ɩɪɨɝɪɚɦɦɵ ɩɨɥɭɱɟɧɢɹ ɬɪɟɯɦɟɪɧɵɯ (ɢɥɢ
ɞɜɭɦɟɪɧɵɯ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɯɟɦɵ ɧɚɛɥɸɞɟɧɢɣ) ɜɪɟɦɟɧɧɵɯ ɢ ɝɥɭɛɢɧɧɵɯ ɢɡɨɛɪɚɠɟɧɢɣ
ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɫ ɭɱɟɬɨɦ ɩɪɟɥɨɦɥɟɧɢɹ ɥɭɱɟɣ ɧɚ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɝɪɚɧɢɰɚɯ ɫɥɨɟɜ. ɇɚ
ɜɯɨɞ ɞɚɧɧɨɣ ɩɪɨɰɟɞɭɪɵ ɩɨɞɚɟɬɫɹ ɫɤɨɪɨɫɬɧɚɹ ɦɨɞɟɥɶ, ɩɨɥɭɱɟɧɧɚɹ ɩɪɢ ɪɟɲɟɧɢɢ ɨɛɪɚɬɧɨɣ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ
ɡɚɞɚɱɢ ɧɚ ɩɪɟɞɵɞɭɳɟɦ ɷɬɚɩɟ. Ⱦɥɹ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨɩɪɚɜɤɢ ȼɋɉ-ɈȽɌ ɫ ɭɱɟɬɨɦ
ɩɪɟɥɨɦɥɟɧɢɹ ɥɭɱɟɣ ɢ ɢɯ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɫɧɨɫɚ. ɉɟɪɟɞ ɜɵɩɨɥɧɟɧɢɟɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ
ȼɋɉ ɫ ɜɵɧɨɫɧɵɯ ɩɭɧɤɬɨɜ ɧɟɨɛɯɨɞɢɦɨ ɜɵɞɟɥɢɬɶ ɨɬɪɚɠɟɧɧɵɟ ɜɨɥɧɵ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɞɚɧɧɨɣ ɡɚɞɚɱɢ
114
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 1, ʋ2, 1998 ɝ.
ɫɬɪ.113-120
ɪɚɡɪɚɛɨɬɚɧɵ ɚɥɝɨɪɢɬɦɵ ɢ ɩɪɨɝɪɚɦɦɵ ɪɚɡɞɟɥɟɧɢɹ ɩɨɥɟɣ ɫ ɭɱɟɬɨɦ ɜɵɧɨɫɚ ɩɭɧɤɬɨɜ ɜɨɡɛɭɠɞɟɧɢɹ, ɤɨɬɨɪɵɣ
ɩɪɢɜɨɞɢɬ ɤ ɧɟɩɚɪɚɥɥɟɥɶɧɨɫɬɢ ɝɨɞɨɝɪɚɮɨɜ ɜɨɥɧ, ɨɬɪɚɠɟɧɧɵɯ ɨɬ ɪɚɡɥɢɱɧɵɯ ɝɪɚɧɢɰ.
ɇɚ ɱɟɬɜɟpɬɨɦ ɷɬɚɩɟ ɜɵɩɨɥɧɹɟɬɫɹ ɩpɨɝɧɨɡɢpɨɜɚɧɢɟ ɞɟɬɚɥɶɧɨɣ ɚɤɭɫɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ, ɩɨɥɭɱɟɧɧɨɣ
ɩɨ ɞɚɧɧɵɦ Ƚɂɋ ɢ ɜɨɥɧɨɜɨɦɭ ɩɨɥɸ ɩpɨɞɨɥɶɧɨɝɨ ȼɋɉ, ɜ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɟ ɩpɨɫɬpɚɧɫɬɜɨ ɩɨ ɜpɟɦɟɧɧɵɦ
pɚɡpɟɡɚɦ ȼɋɉ-ɈȽɌ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɫɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɫɜɨɣɫɬɜɚ ɩɪɨɞɭɤɬɢɜɧɵɯ ɫɥɨɟɜ, ɩɪɨɜɟɪɢɬɶ
ɝɟɨɥɨɝɢɱɟɫɤɢɟ ɝɢɩɨɬɟɡɵ ɨ ɥɚɬɟɪɚɥɶɧɵɯ ɢɡɦɟɧɟɧɢɹɯ ɫɜɨɣɫɬɜ ɡɚɥɟɠɢ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɩɨɫɥɟɞɧɟɝɨ ɷɬɚɩɚ ɪɚɡɪɚɛɨɬɚɧɵ ɩɪɨɝɪɚɦɦɵ ɩɪɨɝɧɨɡɚ ɬɨɧɤɨɫɥɨɢɫɬɨɣ ɦɨɞɟɥɢ ɜ
ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɩɨ ɜɪɟɦɟɧɧɵɦ ɪɚɡɪɟɡɚɦ, ɩɨɥɭɱɟɧɧɵɦ ɧɚ ɩɪɟɞɵɞɭɳɟɦ ɷɬɚɩɟ. ȼ ɤɚɱɟɫɬɜɟ
ɦɨɞɟɥɢ ɜ ɫɤɜɚɠɢɧɟ ɛɟɪɟɬɫɹ ɦɨɞɟɥɶ, ɩɨɥɭɱɟɧɧɚɹ ɧɚ ɩɟɪɜɨɦ ɷɬɚɩɟ. Ⱦɥɹ ɭɬɨɱɧɟɧɢɹ ɚɤɭɫɬɢɱɟɫɤɢɯ
ɩɚɪɚɦɟɬɪɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɟɬɨɞ ɨɩɬɢɦɢɡɚɰɢɢ – ɚɜɬɨɦɚɬɢɱɟɫɤɢɣ ɩɨɞɛɨɪ ɦɨɞɟɥɢ ɢɡ ɭɫɥɨɜɢɹ ɦɚɤɫɢɦɚɥɶɧɨɣ
ɛɥɢɡɨɫɬɢ ɪɟɚɥɶɧɵɯ ɢ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɪɚɡɪɟɡɨɜ, ɩɪɢ ɷɬɨɦ ɢɦɟɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɭɱɟɬɚ ɤɪɚɬɧɵɯ ɜɨɥɧ,
ɨɛɪɚɡɭɸɳɢɯɫɹ ɧɚ ɫɢɥɶɧɵɯ ɝɪɚɧɢɰɚɯ ɫɥɨɟɜ.
2. ȼɵɞɟɥɟɧɢɟ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɩɨ ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɵɦ ɫɤɜɚɠɢɧɧɵɦ ɫɟɣɫɦɢɱɟɫɤɢɦ ɧɚɛɥɸɞɟɧɢɹɦ
Ɉɞɧɨɣ ɢɡ ɨɫɧɨɜɧɵɯ ɡɚɞɚɱ ɫɤɜɚɠɢɧɧɨɣ ɫɟɣɫɦɨɪɚɡɜɟɞɤɢ ɹɜɥɹɟɬɫɹ ɢɡɭɱɟɧɢɟ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ
ɫɬɪɨɟɧɢɹ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɨɬɪɚɠɟɧɧɵɯ ɜɨɥɧ. Ɍɪɟɯɤɨɦɩɨɧɟɧɬɧɚɹ
ɪɟɝɢɫɬɪɚɰɢɹ ɫɟɣɫɦɢɱɟɫɤɢɯ ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ ɜ ɫɤɜɚɠɢɧɟ ɩɨɡɜɨɥɹɟɬ ɩɪɢ ɜɵɞɟɥɟɧɢɢ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟ ɬɨɥɶɤɨ ɢɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɟ ɪɚɡɥɢɱɢɹ ɢ ɪɚɡɥɢɱɢɹ ɮɨɪɦɵ ɫɢɝɧɚɥɨɜ, ɧɨ ɢ ɨɬɥɢɱɢɟ ɜ
ɩɨɥɹɪɢɡɚɰɢɢ. ȼ ɪɚɛɨɬɚɯ ɋ.Ⱥ.ɇɚɯɚɦɤɢɧɚ, Ɏ.Ɇ.Ƚɨɥɶɰɦɚɧɚ, ȼ.ɇ.Ɍɪɨɹɧɚ ɪɚɡɪɚɛɨɬɚɧɵ ɚɥɝɨɪɢɬɦɵ ɜɵɞɟɥɟɧɢɹ
ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɧɚ ɮɨɧɟ ɩɨɦɟɯ, ɤɨɬɨɪɵɟ ɨɫɧɨɜɚɧɵ ɧɚ ɩɨɨɱɟɪɟɞɧɨɦ ɜɵɱɢɬɚɧɢɢ ɜɨɥɧ-ɩɨɦɟɯ. ɗɬɢ
ɚɥɝɨɪɢɬɦɵ ɦɨɠɧɨ ɨɛɨɛɳɢɬɶ ɧɚ ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɵɟ ɧɚɛɥɸɞɟɧɢɹ, ɧɨ ɨɧɢ ɧɟ ɹɜɥɹɸɬɫɹ ɨɩɬɢɦɚɥɶɧɵɦɢ.
Ʉɪɚɬɤɨ ɞɟɣɫɬɜɢɟ ɷɬɢɯ ɚɥɝɨɪɢɬɦɨɜ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ɋɧɚɱɚɥɚ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ,
ɱɬɨ ɧɚ ɫɟɣɫɦɨɝɪɚɦɦɟ ɡɚɪɟɝɢɫɬɪɢɪɨɜɚɧɚ ɨɞɧɚ (ɧɚɢɛɨɥɟɟ ɫɢɥɶɧɚɹ) ɪɟɝɭɥɹɪɧɚɹ ɜɨɥɧɚ, ɨɫɬɚɥɶɧɵɟ ɤɨɥɟɛɚɧɢɹ
ɫɱɢɬɚɸɬɫɹ ɩɨɦɟɯɚɦɢ. ɇɟɢɡɜɟɫɬɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ ɹɜɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɞɚɧɧɨɣ ɜɨɥɧɵ (ɜɟɤɬɨɪ ɚɦɩɥɢɬɭɞ,
ɮɨɪɦɚ ɜɨɥɧɵ ɢ ɜɪɟɦɟɧɧɵɟ ɩɨɞɜɢɠɤɢ ɧɚ ɪɚɡɥɢɱɧɵɯ ɬɪɚɫɫɚɯ), ɧɚɯɨɠɞɟɧɢɟ ɤɨɬɨɪɵɯ ɮɚɤɬɢɱɟɫɤɢ ɫɜɨɞɢɬɫɹ ɤ
ɩɪɨɟɤɬɢɪɨɜɚɧɢɸ ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɵ ɧɚ ɪɚɡɥɢɱɧɵɟ ɧɚɩɪɚɜɥɟɧɢɹ (ɬɨ ɟɫɬɶ ɩɟɪɟɛɨɪɭ
ɧɚɩɪɚɜɥɟɧɢɣ ɩɨɥɹɪɢɡɚɰɢɢ) ɢ ɫɭɦɦɢɪɨɜɚɧɢɸ ɬɪɚɫɫ ɫ ɪɚɡɥɢɱɧɵɦɢ ɡɚɞɟɪɠɤɚɦɢ (ɤɨɬɨɪɵɟ ɩɪɢ ɧɚɛɥɸɞɟɧɢɹɯ
ȼɋɉ ɥɢɧɟɣɧɨ ɡɚɜɢɫɹɬ ɨɬ ɧɟɤɨɬɨɪɨɝɨ ɩɚɪɚɦɟɬɪɚ). ɋɭɦɦɚɪɧɚɹ ɬɪɚɫɫɚ ɜɵɛɢɪɚɟɬɫɹ ɬɚɤ, ɱɬɨɛɵ ɟɟ ɷɧɟɪɝɢɹ
(ɩɪɢ ɩɟɪɟɛɨɪɟ ɡɚɞɟɪɠɟɤ) ɛɵɥɚ ɦɚɤɫɢɦɚɥɶɧɨɣ. ȼ ɞɚɥɶɧɟɣɲɢɯ ɦɨɞɢɮɢɤɚɰɢɹɯ ɜɵɱɢɫɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ
ɤɨɪɪɟɥɹɰɢɢ ɫɭɦɦɚɪɧɨɣ ɬɪɚɫɫɵ ɫ ɢɫɯɨɞɧɵɦɢ, ɢ ɩɨɫɥɟɞɧɢɟ ɜɧɨɜɶ ɫɭɦɦɢɪɭɸɬɫɹ ɫ ɜɟɫɚɦɢ, ɪɨɥɶ ɤɨɬɨɪɵɯ
ɢɝɪɚɸɬ ɧɚɣɞɟɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ.
Ɂɞɟɫɶ ɦɨɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɧɚ ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɵɯ ɧɚɛɥɸɞɟɧɢɹɯ ɪɚɡɥɢɱɧɵɟ ɜɨɥɧɵ (ɩɪɨɞɨɥɶɧɵɟ ɢ
ɩɨɩɟɪɟɱɧɵɟ) ɢɦɟɸɬ ɪɚɡɥɢɱɧɭɸ ɩɨɥɹɪɢɡɚɰɢɸ, ɩɨɷɬɨɦɭ ɜɵɛɨɪ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɹɪɢɡɚɰɢɢ ɜɵɞɟɥɹɟɦɨɣ
ɜɨɥɧɵ ɩɨɡɜɨɥɹɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɨɫɥɚɛɢɬɶ ɪɟɝɭɥɹɪɧɵɟ ɜɨɥɧɵ ɞɪɭɝɨɝɨ ɬɢɩɚ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɫɥɟ
ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɧɚ ɨɩɬɢɦɚɥɶɧɨɟ ɞɥɹ ɞɚɧɧɨɣ ɜɨɥɧɵ ɧɚɩɪɚɜɥɟɧɢɟ ɮɚɤɬɢɱɟɫɤɢ ɩɨɥɭɱɚɟɬɫɹ ɡɚɞɚɱɚ
ɜɵɞɟɥɟɧɢɹ ɜɨɥɧɵ ɩɨ ɨɞɧɨɤɨɦɩɨɧɟɧɬɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɟ, ɩɨɷɬɨɦɭ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɜɵɞɟɥɟɧɢɹ
ɪɟɝɭɥɹɪɧɨɣ ɜɨɥɧɵ ɦɨɠɧɨ ɨɝɪɚɧɢɱɢɬɶɫɹ ɨɞɧɨɤɨɦɩɨɧɟɧɬɧɵɦ ɜɨɥɧɨɜɵɦ ɩɨɥɟɦ.
Ⱦɚɥɟɟ, ɧɚɣɞɟɧɧɚɹ ɜɨɥɧɚ ɜɵɱɢɬɚɟɬɫɹ ɢɡ ɫɟɣɫɦɨɝɪɚɦɦɵ, ɩɨɫɥɟ ɱɟɝɨ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ
ɨɫɬɚɬɨɱɧɚɹ ɫɟɣɫɦɨɝɪɚɦɦɚ ɫɧɨɜɚ ɫɨɞɟɪɠɢɬ ɨɞɧɭ ɪɟɝɭɥɹɪɧɭɸ ɜɨɥɧɭ ɢ ɧɟɪɟɝɭɥɹɪɧɵɟ ɩɨɦɟɯɢ. Ⱦɥɹ
ɜɵɱɢɬɚɧɢɹ ɧɚɯɨɞɹɬɫɹ ɩɨɞɜɢɠɤɢ ɦɟɠɞɭ ɜɨɥɧɨɣ (ɤɨɬɨɪɚɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɦɦɭ ɬɪɚɫɫ ɫɟɣɫɦɨɝɪɚɦɦɵ ɫ
ɩɨɞɜɢɠɤɚɦɢ ɢ ɜɟɫɚɦɢ) ɢ ɤɚɠɞɨɣ ɬɪɚɫɫɨɣ, ɚ ɬɚɤɠɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ, ɤɨɬɨɪɵɟ ɫɥɭɠɚɬ ɜɟɫɚɦɢ
ɩɪɢ ɜɵɱɢɬɚɧɢɢ ɷɬɨɣ ɜɨɥɧɵ ɢɡ ɤɚɠɞɨɣ ɬɪɚɫɫɵ. ɉɨ ɨɫɬɚɬɨɱɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɟ ɫɧɨɜɚ ɜɵɩɨɥɧɹɟɬɫɹ ɬɚ ɠɟ
ɩɪɨɰɟɞɭɪɚ ɜɵɞɟɥɟɧɢɹ ɨɞɧɨɣ (ɜɬɨɪɨɣ) ɜɨɥɧɵ. ɇɚɣɞɟɧɧɚɹ ɜɬɨɪɚɹ ɜɨɥɧɚ, ɬɚɤɠɟ ɜɵɱɢɬɚɟɬɫɹ ɢɡ ɨɫɬɚɬɨɱɧɨɣ
ɫɟɣɫɦɨɝɪɚɦɦɵ. ɉɨɫɥɟ ɷɬɨɝɨ, ɜɵɞɟɥɟɧɧɚɹ ɩɟɪɜɚɹ ɜɨɥɧɚ ɩɨɞɫɭɦɦɢɪɭɟɬɫɹ ɤ ɨɫɬɚɬɤɭ, ɩɨɥɭɱɟɧɧɨɦɭ ɩɨɫɥɟ
ɜɵɱɢɬɚɧɢɹ ɨɛɟɢɯ ɪɚɧɟɟ ɧɚɣɞɟɧɧɵɯ ɜɨɥɧ. ɉɨɥɭɱɟɧɧɚɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɫɟɣɫɦɨɝɪɚɦɦɚ ɫɨɞɟɪɠɢɬ ɩɟɪɜɭɸ
(ɧɚɢɛɨɥɟɟ ɫɢɥɶɧɭɸ) ɜɨɥɧɭ ɢ ɨɫɬɚɬɨɱɧɵɟ ɤɨɥɟɛɚɧɢɹ. ȿɫɥɢ ɛɵ ɞɜɟ ɧɚɣɞɟɧɧɵɟ ɜɨɥɧɵ ɨɩɪɟɞɟɥɹɥɢɫɶ ɬɨɱɧɨ,
ɬɨ ɤ ɨɫɬɚɬɨɱɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɟ (ɩɨɫɥɟ ɜɵɱɢɬɚɧɢɹ ɷɬɢɯ ɞɜɭɯ ɜɨɥɧ) ɦɨɠɧɨ ɛɵɥɨ ɛɵ ɩɪɢɦɟɧɢɬɶ ɨɩɢɫɚɧɧɭɸ
ɩɪɨɰɟɞɭɪɭ. ɇɨ, ɬɚɤ ɤɚɤ ɩɟɪɜɚɹ ɜɨɥɧɚ ɧɚɯɨɞɢɥɚɫɶ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɞɪɭɝɢɯ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɧɟɬ (ɧɚ
ɫɚɦɨɦ ɞɟɥɟ ɫɟɣɫɦɨɝɪɚɦɦɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɢɧɬɟɪɮɟɪɟɧɰɢɸ ɧɟɫɤɨɥɶɤɢɯ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɢ
ɫɥɭɱɚɣɧɨɝɨ ɲɭɦɚ), ɬɨ ɟɟ ɩɚɪɚɦɟɬɪɵ ɨɩɪɟɞɟɥɹɥɢɫɶ ɧɟɬɨɱɧɨ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɩɨɫɥɟ ɜɵɱɢɬɚɧɢɹ ɩɟɪɜɨɣ
ɜɨɥɧɵ ɩɚɪɚɦɟɬɪɵ ɜɬɨɪɨɣ ɬɚɤɠɟ ɨɩɪɟɞɟɥɹɥɢɫɶ ɧɟɬɨɱɧɨ, ɩɨɷɬɨɦɭ ɬɪɟɛɭɟɬɫɹ ɭɬɨɱɧɟɧɢɟ ɨɛɟɢɯ ɜɵɞɟɥɟɧɧɵɯ
ɜɨɥɧ. ɉɨɫɥɟ ɩɨɞɫɭɦɦɢɪɨɜɚɧɢɹ ɩɟɪɜɨɣ ɜɨɥɧɵ ɤ ɨɫɬɚɬɨɱɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɟ, ɩɨɥɭɱɟɧɧɨɟ ɜɨɥɧɨɜɨɟ ɩɨɥɟ
ɫɨɞɟɪɠɢɬ ɩɟɪɜɭɸ ɜɨɥɧɭ, ɨɫɬɚɬɤɢ ɜɬɨɪɨɣ, ɨɫɬɚɥɶɧɵɟ ɪɟɝɭɥɹɪɧɵɟ ɜɨɥɧɵ (ɟɫɥɢ ɨɧɢ ɢɦɟɸɬɫɹ) ɢ
ɧɟɪɟɝɭɥɹɪɧɵɣ ɲɭɦ. Ɍɚɤ ɤɚɤ ɜɬɨɪɚɹ ɜɨɥɧɚ ɪɚɧɟɟ ɜɵɱɢɬɚɥɚɫɶ (ɩɭɫɬɶ ɞɚɠɟ ɧɟɬɨɱɧɨ), ɬɨ ɧɚ ɩɨɥɭɱɢɜɲɟɣɫɹ
ɫɟɣɫɦɨɝɪɚɦɦɟ ɟɟ ɭɪɨɜɟɧɶ ɦɟɧɶɲɟ, ɱɟɦ ɧɚ ɢɫɯɨɞɧɨɣ, ɩɨɷɬɨɦɭ ɩɟɪɜɚɹ ɜɨɥɧɚ ɞɨɥɠɧɚ ɜɵɞɟɥɢɬɶɫɹ ɥɭɱɲɟ,
ɱɟɦ ɧɚ ɢɫɯɨɞɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɟ. ɂɫɯɨɞɹ ɢɡ ɷɬɨɝɨ, ɩɪɟɞɵɞɭɳɚɹ ɩɪɨɰɟɞɭɪɚ ɩɨɜɬɨɪɹɟɬɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ
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Ȼɥɹɫ ɗ.Ⱥ., ɒɚɜɢɧɚ Ʌ.ɂ. ɇɟɤɨɬɨɪɵɟ ɩɨɞɯɨɞɵ ɤ ɨɛɪɚɛɨɬɤɟ ...
ɩɚɪɚɦɟɬɪɵ ɜɵɞɟɥɹɟɦɵɯ ɞɜɭɯ ɜɨɥɧ ɧɟ ɫɬɚɛɢɥɢɡɢɪɭɸɬɫɹ. Ⱦɚɥɟɟ, ɩɨɫɥɟ ɜɵɱɢɬɚɧɢɹ ɞɜɭɯ ɧɚɣɞɟɧɧɵɯ ɜɨɥɧ,
ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɪɟɬɶɹ (ɫɚɦɚɹ ɫɢɥɶɧɚɹ ɢɡ ɨɫɬɚɜɲɢɯɫɹ) ɜɨɥɧɚ ɢ ɬ.ɞ.
Ⱦɚɧɧɵɣ ɩɨɞɯɨɞ ɧɚɲɟɥ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɩɪɢ ɪɚɡɞɟɥɟɧɢɢ ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ ȼɋɉ, ɧɚ ɤɨɬɨɪɵɯ
ɪɟɝɢɫɬɪɢɪɭɸɬɫɹ ɱɟɬɵɪɟ ɨɫɧɨɜɧɵɟ ɜɨɥɧɵ: ɩɚɞɚɸɳɢɟ ɩɪɨɞɨɥɶɧɚɹ ɢ ɩɨɩɟɪɟɱɧɚɹ ɢ ɨɬɪɚɠɟɧɧɵɟ ɩɪɨɞɨɥɶɧɚɹ
ɢ ɩɨɩɟɪɟɱɧɚɹ. Ⱦɨɜɨɥɶɧɨ ɫɢɥɶɧɨɟ ɪɚɡɥɢɱɢɟ ɢɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ (ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɩɪɢ ɧɟ
ɨɱɟɧɶ ɛɨɥɶɲɢɯ ɭɞɚɥɟɧɢɹɯ ɢɫɬɨɱɧɢɤɚ ɨɬ ɫɤɜɚɠɢɧɵ) ɞɟɥɚɟɬ ɞɚɧɧɵɣ ɚɥɝɨɪɢɬɦ ɞɨɫɬɚɬɨɱɧɨ ɷɮɮɟɤɬɢɜɧɵɦ. ȼ
ɬɨ ɠɟ ɜɪɟɦɹ, ɩɪɢ ɪɟɲɟɧɢɢ ɬɨɧɤɢɯ ɡɚɞɚɱ ɩɨ ɞɟɬɚɥɶɧɨɦɭ ɢɡɭɱɟɧɢɸ ɫɬɪɨɟɧɢɹ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɝɨ
ɩɪɨɫɬɪɚɧɫɬɜɚ, ɠɟɥɚɬɟɥɶɧɨ ɜɵɞɟɥɹɬɶ ɩɨɥɟɡɧɵɟ ɜɨɥɧɵ ɫ ɦɢɧɢɦɚɥɶɧɵɦɢ ɩɨɝɪɟɲɧɨɫɬɹɦɢ.
ɑɢɫɥɟɧɧɵɟ ɪɚɫɱɟɬɵ ɧɚ ɦɨɞɟɥɹɯ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɩɨɫɥɟ ɧɟɫɤɨɥɶɤɢɯ (ɬɪɟɯ – ɩɹɬɢ) ɢɬɟɪɚɰɢɣ ɮɨɪɦɚ
ɜɵɞɟɥɹɟɦɵɯ ɜɨɥɧ ɫɬɚɛɢɥɢɡɢɪɭɟɬɫɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɨɫɬɚɬɤɢ (ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɢɫɯɨɞɧɨɣ ɫɟɣɫɦɨɝɪɚɦɦɨɣ ɢ
ɜɵɞɟɥɟɧɧɵɦɢ ɜɨɥɧɚɦɢ) ɧɟ ɫɬɪɟɦɹɬɫɹ ɤ ɧɭɥɸ, ɬɨ ɟɫɬɶ ɚɥɝɨɪɢɬɦ ɧɟ ɫɯɨɞɢɬɫɹ ɤ ɬɨɱɤɟ ɦɢɧɢɦɭɦɚ. ɇɢɠɟ ɦɵ
ɞɚɞɢɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɷɬɨɝɨ ɚɥɝɨɪɢɬɦɚ, ɨɬɤɭɞɚ ɛɭɞɟɬ ɹɫɧɨ, ɩɨɱɟɦɭ ɨɧ ɧɟ ɫɯɨɞɢɬɫɹ ɤ
ɨɩɬɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ, ɬɨ ɟɫɬɶ ɧɟ ɦɢɧɢɦɢɡɢɪɭɟɬ ɨɫɬɚɬɤɢ. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɧɨɜɵɣ
ɚɥɝɨɪɢɬɦ, ɤɨɬɨɪɵɣ ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɨɫɬɚɬɤɢ ɫɤɨɥɶ ɭɝɨɞɧɨ ɦɚɥɵɦɢ.
Ȼɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɫɥɟɞɭɸɳɭɸ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ, ɨɩɢɫɵɜɚɸɳɭɸ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ
ɞɚɧɧɵɟ, ɧɚɯɨɞɹɳɭɸ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɚɥɝɨɪɢɬɦɚɯ ɜɵɞɟɥɟɧɢɹ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɧɚ ɮɨɧɟ ɩɨɦɟɯ:
Rj(tj) = adi fd(tj - Wdi ) + aui fu(tj + Wui ) + bdi gd(tj - Tdi) + bui gu(tj + Tui) + [ij, i=1,2,...,n.
(1)
Ɂɞɟɫɶ Ri(t) = (Rxi(t), Ryi(t), Rzi(t)) – ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɚɹ ɫɟɣɫɦɨɝɪɚɦɦɚ, ɡɚɪɟɝɢɫɬɪɢɪɨɜɚɧɧɚɹ ɜ i-ɨɦ ɩɪɢɟɦɧɢɤɟ
ɜɨ ɜɪɟɦɟɧɚ t = tj, j=1,2,...,M; adi, aui – ɜɟɤɬɨɪɧɵɟ ɚɦɩɥɢɬɭɞɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɚɞɚɸɳɟɣ ɢ ɨɬɪɚɠɟɧɧɨɣ
ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ, bdi, bui – ɚɦɩɥɢɬɭɞɵ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ, Wdi , Wui – ɜɪɟɦɟɧɚ ɩɚɞɚɸɳɟɣ ɢ ɨɬɪɚɠɟɧɧɨɣ
ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ, Tdi, Tui – ɜɪɟɦɟɧɚ ɩɨɩɟɪɟɱɧɵɯ ɧɢɫɯɨɞɹɳɟɣ ɢ ɜɨɫɯɨɞɹɳɟɣ ɜɨɥɧ, fdi(t), fui(t), gdi(t), gui(t) –
ɮɨɪɦɚ ɩɨɩɟɪɟɱɧɵɯ ɢ ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ, [ij – ɧɟɪɟɝɭɥɹɪɧɚɹ ɩɨɦɟɯɚ, ɨɩɢɫɵɜɚɟɦɚɹ ɫɥɭɱɚɣɧɨɣ ɧɨɪɦɚɥɶɧɨ
ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɫɥɚɛɨ ɤɨɪɪɟɥɢɪɨɜɚɧɧɨɣ ɜɟɥɢɱɢɧɨɣ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɧɟɢɡɜɟɫɬɧɵɯ ɚɦɩɥɢɬɭɞ, ɜɪɟɦɟɧɧɵɯ
ɡɚɞɟɪɠɟɤ ɢ ɫɢɝɧɚɥɨɜ ɩɪɢɦɟɧɹɟɬɫɹ ɦɟɬɨɞ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɩɪɚɜɞɨɩɨɞɨɛɢɹ, ɤɨɬɨɪɵɣ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ
ɦɨɞɟɥɢ ɫɟɣɫɦɨɝɪɚɦɦɵ ɢ ɩɪɟɞɩɨɥɚɝɚɟɦɵɯ ɫɜɨɣɫɬɜɚɯ ɩɨɦɟɯ ɫɜɨɞɢɬɫɹ ɤ ɧɚɯɨɠɞɟɧɢɸ ɦɢɧɢɦɭɦɚ
ɮɭɧɤɰɢɨɧɚɥɚ Ɏc, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɪɚɜɟɧɫɬɜɨɦ
M n
Ɏc = ¦ ¦ ||Ri(tj) - adi fd(tj - Wdi ) - aui fu(tj + Wui ) - bdi gd(tj - Tdi) - bui gu(tj + Tui) ||2.
(2)
j=1 i=1
Ɂɞɟɫɶ ɧɟɢɡɜɟɫɬɧɵɦɢ ɹɜɥɹɸɬɫɹ ɜɟɤɬɨɪɧɵɟ ɚɦɩɥɢɬɭɞɵ adi, aui, bdi, bui, ɜɪɟɦɟɧɚ Wdi, Wui, Tdi, Tui ɢ ɮɨɪɦɚ ɜɨɥɧ
fd(t), fu(t), gd(t), gu(t), ||ai|| ɨɡɧɚɱɚɟɬ ɞɥɢɧɭ ɜɟɤɬɨɪɚ ai. ɉɪɢ ɧɚɯɨɠɞɟɧɢɹ ɦɢɧɢɦɭɦɚ ɷɬɨɣ ɮɭɧɤɰɢɢ ɛɭɞɟɦ
ɩɨɨɱɟɪɟɞɧɨ ɮɢɤɫɢɪɨɜɚɬɶ ɩɚɪɚɦɟɬɪɵ ɜɫɟɯ ɜɨɥɧ, ɤɪɨɦɟ ɨɞɧɨɣ. ɉɪɢ ɦɢɧɢɦɢɡɚɰɢɢ ɩɨ ɩɚɪɚɦɟɬɪɚɦ ɨɞɧɨɣ
ɜɨɥɧɵ ɛɭɞɟɦ ɬɚɤɠɟ ɮɢɤɫɢɪɨɜɚɬɶ ɩɨɨɱɟɪɟɞɧɨ ɤɢɧɟɦɚɬɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ (ɜɪɟɦɟɧɚ W, T) ɢ ɞɢɧɚɦɢɱɟɫɤɢɟ:
ɚɦɩɥɢɬɭɞɵ ɢ ɮɨɪɦɭ ɭɬɨɱɧɹɟɦɨɣ ɜɨɥɧɵ.
ɇɚ ɤɚɠɞɨɦ ɲɚɝɟ ɮɢɤɫɢɪɭɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɜɫɟɯ ɜɨɥɧ, ɤɪɨɦɟ ɭɬɨɱɧɹɟɦɨɣ. ɉɪɟɞɩɨɥɨɠɢɦ ɞɥɹ
ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ, ɱɬɨ ɭɬɨɱɧɹɟɬɫɹ ɩɚɞɚɸɳɚɹ ɩɪɨɞɨɥɶɧɚɹ ɜɨɥɧɚ fd(t–Wdi). ȼ ɞɚɥɶɧɟɣɲɟɦ ɞɥɹ ɫɨɤɪɚɳɟɧɢɹ
ɡɚɩɢɫɢ ɛɭɞɟɦ ɢɧɞɟɤɫ d ɨɩɭɫɤɚɬɶ. ɉɭɫɬɶ Rjc(tj) – ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɢɫɯɨɞɧɵɦ ɩɨɥɟɦ ɢ ɫɭɦɦɨɣ ɜɫɟɯ ɜɨɥɧ,
ɤɪɨɦɟ ɭɬɨɱɧɹɟɦɨɣ, ɬ.ɟ.:
Ric(tj) = Ri(tj) – aui fu(tj + Wui) – bdi gd(tj – Tdi) – bui gu(tj + Tui),
i=1,2,...,n;
j=1,2,...,M.
(3)
Ɍɨɝɞɚ ɨɩɪɟɞɟɥɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɭɬɨɱɧɹɟɦɨɣ ɜɨɥɧɵ ɫɜɨɞɢɬɫɹ ɤ ɦɢɧɢɦɢɡɚɰɢɢ ɮɭɧɤɰɢɢ
M
n
Ɏ = ¦ ¦ ||Rjc(tj) – ai f(tj - Wi)||2.
j=1 i=1
Ɍɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɡɧɚɱɟɧɢɹ ɜɟɤɬɨɪɚ ɚi, ɜɪɟɦɟɧ Wi ɢ ɮɭɧɤɰɢɢ f(tj) ɩɨ ɢɡɜɟɫɬɧɵɦ Rjc(tj). ɋɧɚɱɚɥɚ ɩɪɢɛɥɢɠɟɧɧɨ
ɧɚɣɞɟɦ ɜɪɟɦɟɧɚ W ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ ɚɜɬɨɤɨɪɪɟɥɹɰɢɢ ɩɨ ɢɫɯɨɞɧɵɦ ɬɪɚɫɫɚɦ ɢ ɡɚɮɢɤɫɢɪɭɟɦ ɢɯ. Ɍɨɝɞɚ
ɡɚɞɚɱɚ ɫɨɫɬɨɢɬ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɤɨɨɪɞɢɧɚɬ ɜɟɤɬɨɪɨɜ ai ɢ ɮɭɧɤɰɢɢ f(tj) ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ ɮɭɧɤɰɢɢ Ɏ.
ɉɪɟɠɞɟ ɱɟɦ ɪɟɲɚɬɶ ɞɚɧɧɭɸ ɡɚɞɚɱɭ, ɩɪɟɨɛɪɚɡɭɟɦ ɮɭɧɤɰɢɸ Ɏ ɚɧɚɥɨɝɢɱɧɨ (Ȼɵɤɨɜ, 1981). Ⱦɥɹ
ɷɬɨɝɨ ɜɜɟɞɟɦ ɜ ɬɪɚɫɫɵ i-ɝɨ ɤɚɧɚɥɚ ɜɪɟɦɟɧɧɵɟ ɫɞɜɢɝɢ Wi, ɬɨ ɟɫɬɶ ɤɚɠɞɭɸ ɬɪɚɫɫɭ ɫɟɣɫɦɨɝɪɚɦɦɵ ɫɞɜɢɧɟɦ ɧɚ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɜɪɟɦɹ. Ɇɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɪɟɦɟɧɧɨɟ ɨɤɧɨ, ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɬɫɹ ɮɭɧɤɰɢɹ Ɏ ɬɚɤɨɜɨ,
ɱɬɨ ɫɞɜɢɝɢ ɬɪɚɫɫ ɧɟ ɜɵɜɨɞɹɬ ɢɯ ɢɡ ɷɬɨɝɨ ɨɤɧɚ. Ɍɨɝɞɚ ɞɥɹ ɮɭɧɤɰɢɢ Ɏ ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɟɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ
M
n
Ɏ = ¦ ¦ ||Ric(tj + Wi) – ai f(tj)||2.
j=1 i=1
116
(4)
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 1, ʋ2, 1998 ɝ.
ɫɬɪ.113-120
Ɂɚɞɚɱɚ ɫɨɫɬɨɢɬ ɜ ɧɚɯɨɠɞɟɧɢɢ ɤɨɨɪɞɢɧɚɬ axi ɜɟɤɬɨɪɨɜ ai ɢ ɮɭɧɤɰɢɢ f(t), i=1,2,...,n. ɋɧɚɱɚɥɚ ɡɚɮɢɤɫɢɪɭɟɦ
ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɨɜ ai, ɬɨɝɞɚ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ (4) ɤɚɠɞɨɟ ɢɡ ɬɪɟɯ ɫɥɚɝɚɟɦɵɯ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɤɨɨɪɞɢɧɚɬɚɦ x, y ɢ z, ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɨɞɧɨɝɨ ɨɬɫɱɟɬɚ ɫɢɝɧɚɥɚ f(t), ɚ ɢɦɟɧɧɨ, ɨɬ fj = f(tj). Ɉɬɫɸɞɚ ɢ ɢɡ
ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ ɮɭɧɤɰɢɢ ɫɥɟɞɭɟɬ, ɱɬɨ, fj ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ wɎc/wfj = 0, ɤɨɬɨɪɨɟ, ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ
(4), ɢɦɟɟɬ ɜɢɞ
n
wɎ/wfj = ¦ (Ric(tj + Wi) – ai f(tj)) ai f(tj) = 0 ,
j=1,2,...,M.
(5)
i=1
ɂɡ ɞɚɧɧɨɝɨ ɪɚɜɟɧɫɬɜɚ ɫɪɚɡɭ ɩɨɥɭɱɚɟɦ, ɱɬɨ
n
n
f(tj) = [¦ Ric(tj + Wi)ai] / ¦||ak ||2 .
i=1
(6)
i=1
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɤɚɠɞɨɝɨ ɧɚɛɨɪɚ ɜɟɤɬɨɪɨɜ ak, k=1,2,..., M ɪɚɜɟɧɫɬɜɨ (6) ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɮɭɧɤɰɢɸ f(t),
ɞɥɹ ɤɨɬɨɪɨɣ Ɏ ɞɨɫɬɢɝɚɟɬ ɦɢɧɢɦɭɦɚ. ɍɱɢɬɵɜɚɹ ɷɬɨ, ɩɪɟɨɛɪɚɡɭɟɦ ɩɪɚɜɭɸ ɱɚɫɬɶ ɪɚɜɟɧɫɬɜɚ (4). Ɋɚɫɤɪɵɜɚɹ
ɤɜɚɞɪɚɬ ɧɨɪɦɵ ɜɟɤɬɨɪɚ, ɩɨɥɭɱɢɦ
M n
M n
M
n
M
n
Ɏ = ¦ ¦|| Ric(t+Wi) - ai f(t) ||2 = ¦ ¦ ||Ric(t+Wi)||2 - 2 ¦ f(t) ¦ Ric(t+Wi)ai + ¦ f2(t)¦ ||ai ||2.
t
i
t
i
t
i
t
i
Ɂɚɦɟɧɹɹ ɜ ɩɨɫɥɟɞɧɟɦ ɪɚɜɟɧɫɬɜɟ ɮɭɧɤɰɢɸ f(t) ɧɚ ɩɪɚɜɭɸ ɱɚɫɬɶ ɮɨɪɦɭɥɵ (6), ɩɨɥɭɱɢɦ
Mn
M
n
n
n
Ɏ=¦¦||Ric(t+Wi)||2 -2¦ {[¦ Ric(t+Wi)ak] / ¦||ak ||2}¦ Ric(t+Wi)ai +
t i
t
M
k
k
n
n
i
n
+ ¦{[¦Ric(t+Wi)ak] / ¦||ak ||2}2 ¦ ||ai ||2.
t
ɂɫɩɨɥɶɡɭɹ ɪɚɜɟɧɫɬɜɨ
k
k
n
(7)
i
n
n
[¦Ric(t+Wi)ak]2 = [¦ Ric(t+Wi)ak ] [¦Ri(t)ai]
k
k
i
n
ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ ¦||ak ||2 ɧɟ ɡɚɜɢɫɢɬ ɨɬ t, ɩɨɥɭɱɢɦ, ɱɬɨ
k
n
ɬ
n
n
n
n
n
n
¦ {[¦ Rk(t)ak] / ¦||ak ||2}¦Ri(t)ai = ¦ {[¦ Rk(t)ak] / ¦||ak ||2}2 ¦ ||ai ||2 .
t
k
k
i
t
k
k
i
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ (7) ɩɨɫɥɟɞɧɢɟ ɞɜɚ ɫɥɚɝɚɟɦɵɯ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ
ɩɨɞɨɛɧɵɟ ɱɥɟɧɵ, ɩɨɫɥɟ ɩɪɢɜɟɞɟɧɢɹ ɤɨɬɨɪɵɯ ɢ ɢɡɦɟɧɟɧɢɹ ɩɨɪɹɞɤɚ ɫɭɦɦɢɪɨɜɚɧɢɹ ɮɨɪɦɭɥɚ (6) ɩɪɢɧɢɦɚɟɬ
ɜɢɞ
M n
M n
Ɏ = ¦ ¦ ||Ri(t)||2 - [¦ ¦Dki ak ai] / (¦||ak ||2),
t i
t ki
k
M
ɝɞɟ Dik = ¦ Rk(t) Ri(t) – ɷɥɟɦɟɧɬɵ ɦɚɬɪɢɰɵ Ⱥ. Ɍɚɤ ɤɚɤ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɤɬɨɪɨɜ ak,
t
ɬɨ ɦɢɧɢɦɭɦ ɮɭɧɤɰɢɢ Ɏ ɞɨɫɬɢɝɚɟɬɫɹ ɩɪɢ ɬɟɯ ɠɟ ak, ɱɬɨ ɢ ɦɚɤɫɢɦɭɦ ɜɟɥɢɱɢɧɵ
n
n
n
F(a1, a2, ... an) = [¦ ¦Dki ak ai] / (¦||ak ||2) .
i
k
(8)
k
ȼɜɟɞɟɦ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɧɨɜɵɣ ɜɟɤɬɨɪ b, ɤɨɨɪɞɢɧɚɬɚɦɢ ɤɨɬɨɪɨɝɨ ɹɜɥɹɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɨɜ a1, a2, ...
an:
b1 = a1x , b2 = a1y , b3 = a1y , b4 = a2x , b5 = a1y , ... , b3n = anz .
Ʉɪɨɦɟ ɷɬɨɝɨ, ɪɚɫɫɦɨɬɪɢɦ ɜɟɤɬɨɪ U, ɤɨɨɪɞɢɧɚɬɵ ɤɨɬɨɪɨɝɨ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɤɨɨɪɞɢɧɚɬɚɦ ɜɟɤɬɨɪɚ b ɢ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɪɚɜɟɧɫɬɜɚɦɢ
U1 = Rx1 , U2 = Ry1 , U3 = Rz1 , U4 = Rx2 , ... , U1 = Rx1.
ȼ ɷɬɢɯ ɨɛɨɡɧɚɱɟɧɢɹɯ ɪɚɜɟɧɫɬɜɨ (8) ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ
n
n
n
F(b1, b2, ... b3n) = [¦ ¦Eki bk bi] / (¦|bk||2) ,
i
k
k
ɝɞɟ Eki – ɷɥɟɦɟɧɬɵ ɦɚɬɪɢɰɵ ȼ, ɨɩɪɟɞɟɥɟɧɧɵɟ ɪɚɜɟɧɫɬɜɚɦɢ
117
(9)
Ȼɥɹɫ ɗ.Ⱥ., ɒɚɜɢɧɚ Ʌ.ɂ. ɇɟɤɨɬɨɪɵɟ ɩɨɞɯɨɞɵ ɤ ɨɛɪɚɛɨɬɤɟ ...
M
Eki = ¦ Uk(t) Ui(t) .
t
ɇɚɯɨɠɞɟɧɢɟ ɦɚɤɫɢɦɭɦɚ ɮɭɧɤɰɢɢ F(b1, b2, ... b3n) ɪɚɜɧɨɫɢɥɶɧɨ ɧɚɯɨɠɞɟɧɢɸ ɤɨɨɪɞɢɧɚɬ ɫɨɛɫɬɜɟɧɧɨɝɨ
ɜɟɤɬɨɪɚ ɦɚɬɪɢɰɵ ȼ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɫɨɛɫɬɜɟɧɧɨɦɭ ɱɢɫɥɭ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɞɚɧɧɨɣ ɡɚɞɚɱɢ
ɪɚɡɪɚɛɨɬɚɧɵ ɱɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ ɢ ɫɬɚɧɞɚɪɬɧɵɟ ɩɪɨɝɪɚɦɦɵ.
Ɍɚɤɢɦ
ɨɛɪɚɡɨɦ,
ɧɚɯɨɠɞɟɧɢɟ
ɚɦɩɥɢɬɭɞ ɪɟɝɭɥɹɪɧɨɣ ɜɨɥɧɵ ɫɜɟɥɨɫɶ ɤ
ɧɚɯɨɠɞɟɧɢɸ
ɫɨɛɫɬɜɟɧɧɵɯ
ɱɢɫɟɥ
ɢ
ɜɟɤɬɨɪɨɜ ɦɚɬɪɢɰɵ, ɷɥɟɦɟɧɬɵ ɤɨɬɨɪɨɣ
ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɫɭɦɦɭ ɩɨɩɚɪɧɵɯ
ɩɪɨɢɡɜɟɞɟɧɢɣ ɩɪɨɟɤɰɢɣ ɧɚɛɥɸɞɚɟɦɵɯ
ɤɨɥɟɛɚɧɢɣ ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɱɤɚɯ ɩɪɢɟɦɚ.
ɦɚɬɪɢɰɵ
ɪɚɜɧɚ
ɱɢɫɥɭ
Ɋɚɡɦɟɪɧɨɫɬɶ
ɩɪɢɟɦɧɢɤɨɜ ɧɚ ɛɚɡɟ ɪɚɡɞɟɥɟɧɢɹ. ɉɨɫɥɟ
ɧɚɯɨɠɞɟɧɢɹ ɜɟɤɬɨɪɚ ɚɦɩɥɢɬɭɞ ɨɩɪɟɞɟɥɹɟɦ
ɮɨɪɦɭ ɫɢɝɧɚɥɚ ɤɚɤ ɥɢɧɟɣɧɭɸ ɤɨɦɛɢɧɚɰɢɸ
ɬɪɚɫɫ ɫ ɧɚɣɞɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ. Ɏɨɪɦɚ
ɭɬɨɱɧɹɟɦɨɣ
ɜɨɥɧɵ
ɨɩɪɟɞɟɥɹɟɬɫɹ
ɪɚɜɟɧɫɬɜɨɦ (6).
ɉɨɫɥɟ
ɨɩɪɟɞɟɥɟɧɢɹ
ɫɢɝɧɚɥɚ
ɭɬɨɱɧɹɸɬɫɹ ɜɪɟɦɟɧɚ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ
ɮɭɧɤɰɢɹ ɞɨɫɬɢɝɚɥɚ ɦɢɧɢɦɭɦɚ ɢ ɬ.ɞ. ɉɪɢ
ɧɚɯɨɠɞɟɧɢɹ ɜɪɟɦɟɧ ɡɚɞɚɱɚ ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ
ɧɟɡɚɜɢɫɢɦɵɟ
ɡɚɞɚɱɢ
ɦɢɧɢɦɢɡɚɰɢɢ
ɮɭɧɤɰɢɢ ɨɞɧɨɣ ɩɟɪɟɦɟɧɧɨɣ (ɦɢɧɢɦɢɡɚɰɢɹ
ɫɥɚɝɚɟɦɵɯ, ɨɬɧɨɫɹɳɢɯɫɹ ɤ ɨɞɧɨɣ ɬɨɱɤɟ
ɩɪɢɟɦɚ), ɤɨɬɨɪɚɹ ɪɟɲɚɟɬɫɹ ɦɟɬɨɞɨɦ
ɡɨɥɨɬɨɝɨ ɫɟɱɟɧɢɹ ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɦ
ɨɰɟɧɢɜɚɧɢɟɦ ɢɧɬɟɪɜɚɥɚ. Ɏɢɤɫɚɰɢɹ ɱɚɫɬɢ
ɩɟɪɟɦɟɧɧɵɯ
ɩɨɡɜɨɥɹɟɬ
ɫɭɳɟɫɬɜɟɧɧɨ
Ɋɢɫ.1.
ɫɨɤɪɚɬɢɬɶ ɜɪɟɦɹ ɜɵɱɢɫɥɟɧɢɣ. Ɉɬɦɟɬɢɦ,
ɱɬɨ ɞɚɧɧɵɣ ɩɨɞɯɨɞ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ ɦɢɧɢɦɢɡɚɰɢɢ ɤɜɚɞɪɚɬɢɱɧɵɯ ɧɟɜɹɡɨɤ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ
ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ, ɬɚɤɠɟ ɫɜɨɞɢɬɫɹ ɤ ɩɨɨɱɟɪɟɞɧɨɦɭ ɭɬɨɱɧɟɧɢɸ ɬɟɤɭɳɟɣ ɜɨɥɧɵ, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ
ɤɚɤ ɜɵɱɢɬɚɧɢɟ ɪɚɧɟɟ ɧɚɣɞɟɧɧɨɣ ɜɨɥɧɵ ɢ ɩɪɢɛɚɜɥɟɧɢɟ ɭɬɨɱɧɹɟɦɨɣ. ȼɵɱɢɬɚɹ ɜɨɥɧɭ, ɧɚɣɞɟɧɧɭɸ ɧɚ
ɩɪɟɞɵɞɭɳɟɦ ɲɚɝɟ, ɦɵ ɟɟ ɜɜɨɞɢɦ ɜ ɜɟɥɢɱɢɧɭ Ric(tj), ɨɩɪɟɞɟɥɟɧɧɭɸ ɪɚɜɟɧɫɬɜɨɦ (3), ɚ ɩɪɢɛɚɜɥɹɹ ɤ
ɨɫɬɚɬɨɱɧɨɦɭ ɩɨɥɸ ɧɨɜɭɸ ɜɨɥɧɭ (ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɭɬɨɱɧɹɬɶɫɹ), ɦɵ ɩɪɢɯɨɞɢɦ ɤ ɦɨɞɟɥɢ (4). Ɉɬɥɢɱɢɟ ɫɨɫɬɨɢɬ
ɜ ɬɨɦ, ɱɬɨ ɮɨɪɦɚ ɫɢɝɧɚɥɚ ɧɚɯɨɞɢɬɫɹ ɫ ɨɩɬɢɦɚɥɶɧɵɦɢ ɚɦɩɥɢɬɭɞɚɦɢ, ɢ ɦɢɧɢɦɢɡɚɰɢɹ ɩɪɨɜɨɞɢɬɫɹ ɫɪɚɡɭ ɩɨ
ɜɫɟɦ ɡɚɞɟɪɠɤɚɦ.
ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɚɬɶ ɨɩɬɢɦɚɥɶɧɵɟ (ɜ ɫɦɵɫɥɟ ɦɟɬɨɞɚ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɩɪɚɜɞɨɩɨɞɨɛɢɹ) ɨɰɟɧɤɢ
ɩɚɪɚɦɟɬɪɨɜ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ ɜ ɪɚɦɤɚɯ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɦɨɞɟɥɢ ɜɨɥɧɨɜɨɝɨ ɩɨɥɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɞɚɧɧɵɣ
ɩɨɞɯɨɞ ɦɨɠɟɬ ɛɵɬɶ ɨɛɨɛɳɟɧ ɞɥɹ ɭɱɟɬɚ ɧɟɥɢɧɟɣɧɨɣ ɩɨɥɹɪɢɡɚɰɢɢ ɪɟɝɭɥɹɪɧɵɯ ɜɨɥɧ, ɧɨ ɷɬɨɬ ɜɨɩɪɨɫ
ɜɵɯɨɞɢɬ ɡɚ ɪɚɦɤɢ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ.
Ɍɚɤ ɤɚɤ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ, ɦɢɧɢɦɢɡɢɪɭɸɳɢɟ ɮɭɧɤɰɢɸ ɩɪɢ
ɮɢɤɫɢɪɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɞɪɭɝɢɯ ɩɚɪɚɦɟɬɪɨɜ, ɬɨ ɞɚɧɧɵɣ ɚɥɝɨɪɢɬɦ ɫɯɨɞɢɬɫɹ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ
ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɦɚɬɪɢɰɵ Ƚɟɫɫɟ. ɋɯɨɞɢɦɨɫɬɶ ɞɨɫɬɢɝɚɟɬɫɹ ɡɚ ɫɱɟɬ ɨɩɬɢɦɚɥɶɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɜɟɫɨɜ
ɫɭɦɦɢɪɨɜɚɧɢɹ ɬɪɚɫɫ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɫɢɝɧɚɥɚ.
118
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 1, ʋ2, 1998 ɝ.
ɫɬɪ.113-120
3. ɉɪɢɦɟɧɟɧɢɟ ɪɚɡɪɚɛɨɬɚɧɧɨɝɨ ɩɨɞɯɨɞɚ ɤ ɨɛɪɚɛɨɬɤɟ ɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɞɚɧɧɵɯ ȼɋɉ
ɗɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɛɟɫɩɟɱɟɧɢɟ ɩɪɢɦɟɧɹɥɨɫɶ
ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɞɚɧɧɵɯ ȼɋɉ ɜ
ɫɤɜɚɠɢɧɚɯ Ȼɚɪɟɧɰɟɜɚ ɦɨɪɹ, Ʉɚɪɫɤɨɝɨ ɦɨɪɹ, ɨ. Ʉɨɥɝɭɟɜ,
Ɂɚɩɚɞɧɨɣ ɋɢɛɢɪɢ, ɩɨɥɭɱɟɧɧɵɯ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɫɤɜɚɠɢɧɧɨɣ ɫɟɣɫɦɢɱɟɫɤɨɣ ɚɩɩɚɪɚɬɭɪɵ “Ɂɨɧɞ-Ⱦ1” ɢ
ɩɧɟɜɦɚɬɢɱɟɫɤɢɯ ɢɫɬɨɱɧɢɤɨɜ “ɉɭɥɶɫ-1ɚ”, ɪɚɡɪɚɛɨɬɚɧɧɵɯ
ɜ ɇɂɂ Ɇɨɪɝɟɨɮɢɡɢɤɚ. ȿɝɨ ɩɪɢɦɟɧɟɧɢɟ ɩɨɡɜɨɥɢɥɨ
ɪɟɲɢɬɶ
ɪɹɞ
ɜɚɠɧɵɯ
ɝɟɨɥɨɝɢɱɟɫɤɢɯ
ɡɚɞɚɱ:
ɫɩɪɨɝɧɨɡɢɪɨɜɚɬɶ
ɥɢɬɨ-ɮɚɰɢɚɥɶɧɨɟ
ɡɚɦɟɳɟɧɢɟ
ɜ
ɩɪɨɞɭɤɬɢɜɧɵɯ ɫɥɨɹɯ ɜ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ,
ɭɬɨɱɧɢɬɶ ɫɜɨɣɫɬɜɚ ɬɨɧɤɢɯ (ɩɨɪɹɞɤɚ 5 - 10 ɦ) ɫɥɨɟɜ,
ɢɡɭɱɢɬɶ ɞɟɬɚɥɶɧɵɟ ɩɨɝɥɨɳɚɸɳɢɟ ɫɜɨɣɫɬɜɚ ɪɚɡɪɟɡɚ –
ɨɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ
ɩɨɝɥɨɳɟɧɢɹ
ɜ
ɫɥɨɹɯ
ɦɨɳɧɨɫɬɶɸ 10 - 15 ɦ. ɉɨɫɥɟɞɭɸɳɟɟ ɛɭɪɟɧɢɟ ɧɚ ɨ.
Ʉɨɥɝɭɟɜ ɩɨɞɬɜɟɪɞɢɥɨ ɩɪɚɜɢɥɶɧɨɫɬɶ ɩɪɨɝɧɨɡɚ ɫɜɨɣɫɬɜ
ɩɪɨɞɭɤɬɢɜɧɵɯ ɫɥɨɟɜ.
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ
ɪɟɡɭɥɶɬɚɬɵ, ɩɨɥɭɱɟɧɧɵɟ ɧɚ ɨɞɧɨɦ ɢɡ ɦɟɫɬɨɪɨɠɞɟɧɢɣ
ɋɟɜɟɪɧɨɝɨ ɋɚɦɨɬɥɨɪɚ ɜ Ɂɚɩɚɞɧɨɣ ɋɢɛɢɪɢ. Ɂɚɞɚɱɚ
ɫɨɫɬɨɹɥɚ ɜ ɢɡɭɱɟɧɢɢ ɫɬɪɨɟɧɢɹ ɩɪɨɞɭɤɬɢɜɧɵɯ ɩɥɚɫɬɨɜ ɜ
ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɨ ɧɚɛɥɸɞɟɧɢɹɦ ɫ
ɜɵɧɨɫɧɵɯ
ɉȼ.
ɋɧɚɱɚɥɚ
ɨɛɪɚɛɚɬɵɜɚɥɨɫɶ
ɢ
ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɥɨɫɶ ɜɨɥɧɨɜɨɟ ɩɨɥɟ ɩɪɨɞɨɥɶɧɨɝɨ ȼɋɉ
(ɭɞɚɥɟɧɢɟ ɨɬ ɫɤɜɚɠɢɧɵ 90 ɦ). ɉɨɫɥɟ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ
ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ ɦɟɬɨɞɨɦ, ɨɩɢɫɚɧɧɵɦ ɧɢɠɟ,
ɩɨɥɭɱɟɧɚ ɫɤɨɪɨɫɬɧɚɹ ɦɨɞɟɥɶ ɫɪɟɞɵ, ɤɨɬɨɪɚɹ ɯɨɪɨɲɨ
ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɦɨɞɟɥɶɸ, ɩɨɫɬɪɨɟɧɧɨɣ ɩɨ ɞɚɧɧɵɦ ȺɄ ɢ
Ƚɂɋ.
Ⱦɚɥɟɟ ɜɵɩɨɥɧɹɥɚɫɶ ɨɛɪɚɛɨɬɤɚ ɜɵɧɨɫɧɵɯ ɉȼ ɩɨ
ɨɩɢɫɚɧɧɨɣ ɜɵɲɟ ɦɟɬɨɞɢɤɟ. ɇɚ ɪɢɫ.1 ɩɨɤɚɡɚɧɨ ɢɫɯɨɞɧɨɟ
ɜɨɥɧɨɜɨɟ ɩɨɥɟ, ɩɨɥɭɱɟɧɧɨɟ ɫ ɉȼ, ɭɞɚɥɟɧɧɨɦ ɧɚ 1200 ɦ
ɨɬ ɫɤɜɚɠɢɧɵ - ɤɨɦɩɨɧɟɧɬɵ 1, 2, 3, ɡɚɪɟɝɢɫɬɪɢɪɨɜɚɧɧɵɟ
ɬɪɟɯɤɨɦɩɨɧɟɧɬɧɵɦ ɞɜɭɯɬɨɱɟɱɧɵɦ ɡɨɧɞɨɦ (ɚ), ɢ
ɤɨɦɩɨɧɟɧɬɵ X, Y, Z, ɩɨɥɭɱɟɧɧɵɟ ɩɨɫɥɟ ɩɨɜɨɪɨɬɚ ɡɨɧɞɚ
(ɛ). Ʉ ɤɨɦɩɨɧɟɧɬɚɦ X, Y, Z ɩɪɢɦɟɧɹɥɚɫɶ
ɩɪɟɞɫɤɚɡɵɜɚɸɳɚɹ ɞɟɤɨɧɜɨɥɸɰɢɹ, ɩɨɫɥɟ ɱɟɝɨ ɛɵɥɢ
ɜɵɞɟɥɟɧɵ ɧɢɫɯɨɞɹɳɢɟ ɢ ɜɨɫɯɨɞɹɳɢɟ ɩɪɨɞɨɥɶɧɵɟ ɢ
Ɋɢɫ.2.
ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ, ɩɨɤɚɡɚɧɧɵɟ ɧɚ ɪɢɫ.2.
ɉɨ ɜɵɞɟɥɟɧɧɵɦ ɝɨɞɨɝɪɚɮɚɦ ɨɬɪɚɠɟɧɧɵɯ ɜɨɥɧ
ɭɬɨɱɧɹɥɚɫɶ ɫɤɨɪɨɫɬɧɚɹ ɦɨɞɟɥɶ ɫɪɟɞɵ, ɤɨɬɨɪɚɹ ɡɚɬɟɦ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɝɥɭɛɢɧɧɵɯ ɪɚɡɪɟɡɨɜ.
ɉɪɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɪɚɡɪɟɡɨɜ ȼɋɉ-ɈȽɌ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɭɱɢɬɵɜɚɥɢɫɶ ɤɢɧɟɦɚɬɢɱɟɫɤɢɟ ɢ ɞɢɧɚɦɢɱɟɫɤɢɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɬɪɚɠɚɸɳɢɯ ɝɨɪɢɡɨɧɬɨɜ, ɫɮɨɪɦɢɪɨɜɚɜɲɢɯɫɹ ɨɬ ɨɛɴɟɤɬɨɜ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɢɯ ɥɚɬɟɪɚɥɶɧɚɹ
ɭɫɬɨɣɱɢɜɨɫɬɶ ɢɥɢ ɢɡɦɟɧɱɢɜɨɫɬɶ.
Ⱦɥɹ ɩɪɨɝɧɨɡɚ ɥɢɬɨɥɨɝɢɱɟɫɤɢɯ ɢɡɦɟɧɟɧɢɣ ɜ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ
ɚɩɪɢɨɪɧɚɹ ɝɟɨɥɨɝɨ-ɝɟɨɮɢɡɢɱɟɫɤɚɹ ɢɧɮɨɪɦɚɰɢɹ ɩɨ ɋɚɦɨɬɥɨɪɫɤɨɦɭ ɦɟɫɬɨɪɨɠɞɟɧɢɸ, ɦɚɬɟɪɢɚɥɵ Ƚɂɋ,
ɪɟɡɭɥɶɬɚɬɵ ɢɫɩɵɬɚɧɢɣ, ɤɟɪɧɨɜɵɟ ɞɚɧɧɵɟ ɩɨ ɫɨɫɟɞɧɢɦ ɫɤɜɚɠɢɧɚɦ, ɩɪɟɞɨɫɬɚɜɥɟɧɧɵɟ ɡɚɤɚɡɱɢɤɨɦ.
ɋɬɪɚɬɢɝɪɚɮɢɱɟɫɤɚɹ ɩɪɢɜɹɡɤɚ ɨɬɪɚɠɚɸɳɢɯ ɝɨɪɢɡɨɧɬɨɜ ɧɚ ɪɚɡɪɟɡɚɯ ȼɋɉ ɈȽɌ ɨɫɭɳɟɫɬɜɥɹɥɚɫɶ
ɩɭɬɟɦ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɪɚɡɪɟɡɨɜ, ɩɨɫɬɪɨɟɧɧɵɯ ɫ ɜɵɧɨɫɧɵɯ ɩɭɧɤɬɨɜ ɜɨɡɛɭɠɞɟɧɢɹ, ɫ ɪɚɡɪɟɡɨɦ ɩɨ ɛɥɢɠɧɟɦɭ
ɉȼ ɫ ɩɪɢɜɥɟɱɟɧɢɟɦ ɨɰɢɮɪɨɜɚɧɧɵɯ ɤɪɢɜɵɯ Ƚɂɋ.
ɇɚ ɪɢɫ.3 ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɚɡɪɟɡ ȼɋɉ-ɈȽɌ ɩɨ ɭɞɚɥɟɧɧɨɦɭ ɉȼ (ɜɵɧɨɫ 1100 ɦ) ɫ ɪɚɡɪɟɡɨɦ ɩɨ
ɛɥɢɠɧɟɦɭ ɉȼ1 ɢ ɤɪɢɜɵɦɢ Ʉɋ ɢ ɉɋ. Ɉɬɦɟɱɚɟɬɫɹ ɯɨɪɨɲɚɹ ɫɨɩɨɫɬɚɜɢɦɨɫɬɶ ɜɨɥɧɨɜɵɯ ɩɨɥɟɣ ɧɚ ɪɚɡɪɟɡɚɯ
ȼɋɉ-ɈȽɌ ɫ ɪɚɡɪɟɡɨɦ ɩɨ ɛɥɢɠɧɟɦɭ ɉȼ1. Ʉɪɨɜɥɹ ɢ ɩɨɞɨɲɜɚ ɩɪɨɞɭɤɬɢɜɧɵɯ ɩɥɚɫɬɨɜ, ɢɯ ɜɧɭɬɪɟɧɧɢɟ
ɥɢɬɨɥɨɝɢɱɟɫɤɢɟ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ, ɝɪɚɧɢɰɚ ɜɨɞɨɧɟɮɬɹɧɨɝɨ ɤɨɧɬɚɤɬɚ, ɜɵɞɟɥɟɧɧɵɟ ɩɨ ɉȼ1,
ɩɪɨɫɥɟɠɢɜɚɸɬɫɹ ɧɚ ɪɚɡɪɟɡɚɯ ɫ ɜɵɧɨɫɧɵɯ ɉȼ. ȼɵɫɨɤɨɱɚɫɬɨɬɧɚɹ ɨɛɪɚɛɨɬɤɚ ɦɚɬɟɪɢɚɥɨɜ ɫ ɭɞɚɥɟɧɧɵɯ ɉȼ
119
Ȼɥɹɫ ɗ.Ⱥ., ɒɚɜɢɧɚ Ʌ.ɂ. ɇɟɤɨɬɨɪɵɟ ɩɨɞɯɨɞɵ ɤ ɨɛɪɚɛɨɬɤɟ ...
ɩɨɡɜɨɥɢɥɚ ɜ ɜɨɥɧɨɜɨɦ ɩɨɥɟ ȼɋɉ ɩɪɨɫɥɟɞɢɬɶ ɨɬɪɚɠɟɧɢɹ ɫ ɱɚɫɬɨɬɨɣ ɞɨ 170 Ƚɰ ɢ, ɜɫɥɟɞɫɬɜɢɟ ɷɬɨɝɨ,
ɪɚɡɞɟɥɢɬɶ ɩɥɚɫɬɵ ɦɨɳɧɨɫɬɶɸ ɞɨ 5 - 10 ɦ.
Ɋɢɫ.3.
ɉɨ ɝɥɭɛɢɧɧɵɦ ɪɚɡɪɟɡɚɦ, ɩɨɥɭɱɟɧɧɵɦ ɧɚ ɋɟɜɟɪɧɨɦ ɋɚɦɨɬɥɨɪɟ, ɛɵɥɢ ɫɩɪɨɝɧɨɡɢɪɨɜɚɧɵ
ɢɡɦɟɧɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɩɪɨɞɭɤɬɢɜɧɵɯ ɩɥɚɫɬɨɜ, ɤɨɬɨɪɵɟ ɧɚɲɥɢ ɩɨɞɬɜɟɪɠɞɟɧɢɟ ɩɪɢ
ɩɨɫɥɟɞɭɸɳɟɦ ɛɭɪɟɧɢɢ.
Ʌɢɬɟɪɚɬɭɪɚ
Ȼɵɤɨɜ ɂ.Ⱥ., Ɍɢɯɨɧɨɜɚ ɂ.Ɇ. Ⱥɥɝɨɪɢɬɦɵ ɰɢɮɪɨɜɨɣ ɨɛɪɚɛɨɬɤɢ ɫɤɜɚɠɢɧɧɵɯ ɚɡɢɦɭɬɚɥɶɧɵɯ ɧɚɛɥɸɞɟɧɢɣ.
ȼɨɩɪɨɫɵ ɞɢɧɚɦɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɟɣɫɦɢɱɟɫɤɢɯ ɜɨɥɧ. Ʌ., ɜɵɩ. ɏɏ, ɫ.135-155, 1981.
Ȼɥɹɫ ɗ.Ⱥ., ɋɟɪɟɞɚ ȼ.ɂ. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɫɥɨɢɫɬɨɣ ɫɪɟɞɵ ɩɨ ɞɚɧɧɵɦ ȼɋɉ ɦɟɬɨɞɨɦ ɪɟɲɟɧɢɹ
ɨɛɪɚɬɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ. "ȼɟɫɬɧɢɤ ɆȽɌɍ", ɬ.1, ʋ1, ɫ.53-66, 1998.
Ȼɥɹɫ ɗ.Ⱥ. Ɉɩɪɟɞɟɥɟɧɢɟ ɬɪɟɯɦɟɪɧɨɣ ɫɥɨɢɫɬɨ-ɧɟɨɞɧɨɪɨɞɧɨɣ ɫɤɨɪɨɫɬɧɨɣ ɦɨɞɟɥɢ ɫɪɟɞɵ ɩɨ ɞɚɧɧɵɦ ɦɟɬɨɞɚ
ɨɬɪɚɠɟɧɧɵɯ ɜɨɥɧ. "ȼɟɫɬɧɢɤ ɆȽɌɍ", ɬ.1, ʋ2, c.95-112, 1998.
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