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ȼɚɠɧɟɣɲɟɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɞɟɥɚ ɮɚɡ ɹɜɥɹɟɬɫɹ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ ɧɚ ɝɪɚɧɢɰɟ ɠɢɞɤɨɫɬɶ - ɝɚɡ ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɝɢɯ ɮɚɤɬɨɪɨɜ: ɯɢɦɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ, ɬɟɦɩɟɪɚɬɭɪɵ, ɞɚɜɥɟɧɢɹ ɢ ɞɪ. ɮɚɤɬɨɪɨɜ. ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ ɭɦɟɧɶɲɚɟɬɫɹ. ɋɥɨɠɧɟɟ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɧɚɬɹɠɟɧɢɹ ɧɚ ɝɪɚɧɢɰɟ ɧɟɮɬɶ - ɠɢɞɤɨɫɬɶ. ȿɫɥɢ ɧɟɮɬɶ ɞɟɝɚɡɢɪɨɜɚɧɚ ɢ ɩɨɱɬɢ ɧɟ ɫɨɞɟɪɠɢɬ ɩɨɥɹɪɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ, ɟɟ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ ɧɚ ɝɪɚɧɢɰɟ ɫ ɜɨɞɨɣ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ. ȿɫɥɢ ɠɟ ɜ ɧɟɮɬɢ ɫɨɞɟɪɠɚɬɫɹ ɩɨɥɹɪɧɵɟ ɤɨɦɩɨɧɟɧɬɵ, ɪɚɫɬɜɨɪɢɦɵɟ ɜ ɜɨɞɟ, ɬɨ ɫ ɪɨɫɬɨɦ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ ɟɟ ɧɚ ɝɪɚɧɢɰɟ ɫ ɜɨɞɨɣ ɦɨɠɟɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ. ɉɪɢ ɧɚɥɢɱɢɢ ɪɚɫɬɜɨɪɢɦɵɯ ɝɚɡɨɜ ɡɚɜɢɫɢɦɨɫɬɶ ɭɫɥɨɠɧɹɟɬɫɹ.

ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡɦɟɪɢɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɬɪɭɞɧɨ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɜɟɪɯɧɨɫɬɧɨɟ ɧɚɬɹɠɟɧɢɟ ɨɰɟɧɢɜɚɟɬɫɹ ɤɨɫɜɟɧɧɨ - ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɤɪɚɟɜɨɝɨ ɭɝɥɚ ɫɦɚɱɢɜɚɧɢɹ, ɤɨɬɨɪɵɣ ɬɚɤɠɟ ɫɥɭɠɢɬ ɢ ɦɟɪɨɣ ɫɦɚɱɢɜɚɧɢɹ ɠɢɞɤɨɫɬɶɸ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ. ɉɨɜɟɪɯɧɨɫɬɶ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɫɦɚɱɢɜɚɟɬɫɹ ɬɟɦ ɥɭɱɲɟ, ɱɟɦ ɦɟɧɶɲɟ ɪɚɡɧɨɫɬɶ ɩɨɥɹɪɧɨɫɬɟɣ ɦɟɠɞɭ ɬɟɥɨɦ ɢ ɠɢɞɤɨɫɬɶɸ. ȼɵɫɨɤɨɩɨɥɹɪɧɵɟ ɠɢɞɤɨɫɬɢ, ɬ.ɟ. ɨɛɥɚɞɚɸɳɢɟ ɜɵɫɨɤɢɦ ɩɨɜɟɪɯɧɨɫɬɧɵɦ ɧɚɬɹɠɟɧɢɟɦ, ɫɦɚɱɢɜɚɸɬ ɬɜɟɪɞɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɯɭɠɟ, ɱɟɦ ɦɚɥɨɩɨɥɹɪɧɵɟ. ɇɚɩɪɢɦɟɪ, ɪɬɭɬɶ ɫɦɚɱɢɜɚɟɬ ɥɢɲɶ ɧɟɤɨɬɨɪɵɟ ɦɟɬɚɥɥɵ, ɬɨɝɞɚ ɤɚɤ ɦɟɧɟɟ ɩɨɥɹɪɧɚɹ ɠɢɞɤɨɫɬɶ - ɜɨɞɚ - ɫɦɚɱɢɜɚɟɬ ɧɟ ɬɨɥɶɤɨ ɦɟɬɚɥɥɵ, ɧɨ ɢ ɦɧɨɝɢɟ ɞɪɭɝɢɟ ɦɢɧɟɪɚɥɵ, ɚ ɦɚɥɨ ɩɨɥɹɪɧɵɟ ɦɚɫɥɚ - ɜɫɟ ɬɜɟɪɞɵɟ ɬɟɥɚ.

ȼɟɥɢɱɢɧɚ ɭɝɥɚ ɫɦɚɱɢɜɚɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɝɢɯ ɮɚɤɬɨɪɨɜ. Ɉɫɨɛɟɧɧɨ ɛɨɥɶɲɨɟ ɜɥɢɹɧɢɟ ɧɚ ɧɟɟ ɨɤɚɡɵɜɚɟɬ ɩɪɨɰɟɫɫɵ ɚɞɫɨɪɛɰɢɢ. ɇɚɩɪɢɦɟɪ, ɨɛɪɚɛɨɬɤɨɣ ɉȺȼ ɦɨɠɧɨ ɡɧɚɱɢɬɟɥɶɧɨ ɭɜɟɥɢɱɢɬɶ ɫɦɚɱɢɜɚɟɦɨɫɬɶ ɢ ɧɚɨɛɨɪɨɬ ɭɦɟɧɶɲɢɬɶ.

ȼ ɩɟɪɢɨɞ ɜɫɤɪɵɬɢɹ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ ɢ ɜ ɩɟɪɢɨɞ ɨɫɜɨɟɧɢɹ ɝɪɚɧɢɰɵ ɪɚɡɞɟɥɚ ɮɚɡ ɧɟ ɨɫɬɚɸɬɫɹ ɫɬɚɛɢɥɶɧɵɦɢ: ɩɪɢ ɜɫɤɪɵɬɢɢ - ɧɟɮɬɶ ɨɬɬɟɫɧɹɟɬɫɹ ɨɬ ɫɤɜɚɠɢɧɵ, ɩɪɢ ɨɫɜɨɟɧɢɢ - ɧɚɨɛɨɪɨɬ. ɉɪɢ ɬɚɤɨɦ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɦɟɧɹɟɬɫɹ ɢ ɭɝɨɥ ɫɦɚɱɢɜɚɟɦɨɫɬɢ.

21

1.9.ɉɨɧɹɬɢɟ ɨ ɤɨɷɮɮɢɰɢɟɧɬɟ ɚɧɨɦɚɥɶɧɨɫɬɢ, ɢɧɞɟɤɫɟ ɞɚɜɥɟɧɢɹ ɩɨɝɥɨɳɟɧɢɹ ɢ ɩɨɪɨɜɨɦ ɞɚɜɥɟɧɢɢ.

ɉɨɞ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɚɧɨɦɚɥɶɧɨɫɬɢ (Ʉɚ) ɜ ɛɭɪɟɧɢɢ ɩɨɧɢɦɚɸɬ ɨɬɧɨɲɟɧɢɟ ɩɥɚɫɬɨɜɨɝɨ ɞɚɜɥɟɧɢɹ (Ɋɩɥ) ɧɚ ɝɥɭɛɢɧɟ zɩɥ ɤ ɞɚɜɥɟɧɢɸ ɫɬɨɥɛɚ ɩɪɟɫɧɨɣ ɜɨɞɵ ɬɚɤɨɣ ɠɟ ɜɵɫɨɬɵ:

Pɩɥ

(1.10.)

Kɚ Uɜ q zɩɥ

ɂɧɞɟɤɫɨɦ ɞɚɜɥɟɧɢɹ ɩɨɝɥɨɳɟɧɢɹ ɧɚɡɵɜɚɸɬ ɨɬɧɨɲɟɧɢɟ ɞɚɜɥɟɧɢɹ (Ɋɩ) ɧɚ ɫɬɟɧɤɢ ɫɤɜɚɠɢɧɵ, ɩɪɢ ɤɨɬɨɪɨɦ ɜɨɡɧɢɤɚɟɬ ɩɨɝɥɨɳɟɧɢɟ ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ, ɤ ɞɚɜɥɟɧɢɣ ɫɬɨɥɛɚ ɜɨɞɵ ɜɵɫɨɬɨɣ ɨɬ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɨɛɴɟɤɬɚ ɞɨ ɭɫɬɶɹ.

 

K n

 

Pɩ

 

 

Uɜ q zɩɥ

 

 

 

ɉɨɞ ɝɪɚɞɢɟɧɬɨɦ

ɩɥɚɫɬɨɜɨɝɨ

ɞɚɜɥɟɧɢɹ gradPɩɥ ɢ ɝɪɚɞɢɟɧɬɨɦ ɞɚɜɥɟɧɢɹ

ɩɨɝɥɨɳɟɧɢɹ gradPɩ

ɩɨɧɢɦɚɸɬ

ɨɬɧɨɲɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɞɚɜɥɟɧɢɹ ɤ

ɝɥɭɛɢɧɟ ɡɚɥɟɝɚɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɩɥɚɫɬɚ:

gradPɩɥ Pɩɥ

zɩɥ ,

gradPɩ Pɩ zɩɥ

22

2. ȼɋɄɊɕɌɂȿ ɉɊɈȾɍɄɌɂȼɇɕɏ ɉɅȺɋɌɈȼ ɉɊɂ ȻɍɊȿɇɂɂ

ȼɫɤɪɵɬɢɟ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ (ɪɚɡɜɟɞɵɜɚɟɦɨɝɨ ɢɥɢ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɨɝɨ ɨɛɴɟɤɬɚ) - ɷɬɨ ɨɩɟɪɚɰɢɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɛɭɪɟɧɢɟɦ ɫɬɜɨɥɚ ɫɤɜɚɠɢɧɵ ɜ ɢɧɬɟɪɜɚɥɟ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ ɧɚ ɩɨɥɧɭɸ ɟɝɨ ɦɨɳɧɨɫɬɶ ɢɥɢ ɱɚɫɬɢɱɧɨ. ɉɪɨɰɟɫɫ ɛɭɪɟɧɢɹ ɜ ɩɪɨɞɭɤɬɢɜɧɨɦ ɩɥɚɫɬɟ ɢɦɟɟɬ ɨɩɪɟɞɟɥɟɧɧɭɸ ɫɩɟɰɢɮɢɤɭ. Ɉɧɚ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɩɪɢ ɜɫɤɪɵɬɢɢ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢɨɛɪɟɬɚɸɬ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɤɨɬɨɪɵɟ ɩɪɨɢɫɯɨɞɹɬ ɜ ɨɤɪɟɫɬɧɨɫɬɹɯ ɫɬɜɨɥɚ ɫɤɜɚɠɢɧɵ ɢ ɩɪɢɜɨɞɹɬ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɵ ɩɥɚɫɬɚ. ɉɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɨɣ ɩɥɚɫɬɚ ɧɚɡɵɜɚɸɬ ɧɟɤɨɬɨɪɵɣ ɨɛɴɟɦ ɩɨɫɥɟɞɧɟɝɨ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɢɣɫɹ ɨɬ ɫɬɟɧɨɤ ɫɬɜɨɥɚ ɫɤɜɚɠɢɧɵ ɜ ɝɥɭɛɶ ɩɥɚɫɬɚ ɢ ɩɨɞɜɟɪɠɟɧɧɵɣ ɩɪɢ ɜɫɤɪɵɬɢɢ ɞɟɣɫɬɜɢɸ ɩɪɨɰɟɫɫɨɜ, ɧɚɪɭɲɚɸɳɢɯ ɩɟɪɜɨɧɚɱɚɥɶɧɨɟ ɦɟɯɚɧɢɱɟɫɤɨɟ ɢ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɨɟ ɫɨɫɬɨɹɧɢɟ ɤɨɥɥɟɤɬɨɪɚ ɢ ɫɨɞɟɪɠɚɳɟɣɫɹ ɜ ɧɟɦ ɩɨɞɜɢɠɧɨɣ (ɠɢɞɤɨɣ ɢɥɢ ɝɚɡɨɨɛɪɚɡɧɨɣ) ɮɚɡɵ

[1].

Ɉɫɧɨɜɧɚɹ ɡɚɞɚɱɚ ɩɪɢ ɜɫɤɪɵɬɢɢ ɩɥɚɫɬɚ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨɛɵ ɧɟ ɞɨɩɭɫɬɢɬɶ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɧɚɪɭɲɟɧɢɹ ɟɫɬɟɫɬɜɟɧɧɵɯ ɫɜɨɣɫɬɜ ɢ ɫɨɫɬɨɹɧɢɹ ɝɨɪɧɨɣ ɩɨɪɨɞɵɤɨɥɥɟɤɬɨɪɚ ɢ ɩɪɚɜɢɥɶɧɨ ɡɚɞɚɬɶ ɜɟɥɢɱɢɧɭ ɡɚɝɥɭɛɥɟɧɢɹ ɜ ɩɥɚɫɬ. ȿɟ ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɨɥɨɠɟɧɢɹ ɜɨɞɨɧɟɮɬɹɧɨɝɨ ɤɨɧɬɚɤɬɚ, ɛɥɢɡɨɫɬɢ ɩɨɞɨɲɜɟɧɧɵɯ ɜɨɞ ɢ ɬ.ɩ. ɉɪɢ ɛɭɪɟɧɢɢ ɜ ɩɪɨɞɭɤɬɢɜɧɨɣ ɬɨɥɳɟ ɞɨɥɠɧɚ ɛɵɬɶ ɨɛɟɫɩɟɱɟɧɚ ɬɚɤɚɹ ɝɥɭɛɢɧɚ ɜɫɤɪɵɬɢɹ, ɤɨɬɨɪɚɹ ɝɚɪɚɧɬɢɪɨɜɚɥɚ ɛɵ ɞɥɢɬɟɥɶɧɭɸ ɛɟɡɜɨɞɧɭɸ ɷɤɫɩɥɭɚɬɚɰɢɸ ɫɤɜɚɠɢɧɵ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɜ ɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ ɝɢɞɪɚɜɥɢɱɟɫɤɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɢ ɩɨɫɬɭɩɥɟɧɢɢ ɧɟɮɬɢ ɢɥɢ ɝɚɡɚ ɜ ɫɤɜɚɠɢɧɭ.

ȼ ɪɟɡɭɥɶɬɚɬɟ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɨɝɨ ɢ ɮɢɡɢɤɨ-ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɩɪɢ ɩɟɪɜɢɱɧɨɦ ɜɫɤɪɵɬɢɢ ɢɡɦɟɧɹɸɬɫɹ ɮɢɥɶɬɪɚɰɢɨɧɧɨ-ɟɦɤɨɫɬɧɵɟ ɫɜɨɣɫɬɜɚ ɩɨɪɨɞ-ɤɨɥɥɟɤɬɨɪɨɜ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ [2].

Ɏɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɩɪɢɫɤɜɚɠɢɧɧɭɸ ɡɨɧɭ ɨɛɭɫɥɨɜɥɟɧɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɩɨɪɨɞ ɢ ɮɥɸɢɞɨɜ ɩɥɚɫɬɚ ɫ ɮɢɥɶɬɪɚɬɚɦɢ ɩɪɨɦɵɜɨɱɧɵɯ ɠɢɞɤɨɫɬɟɣ, ɩɨɫɪɟɞɫɬɜɨɦ ɞɟɣɫɬɜɢɹ ɚɞɫɨɪɛɰɢɨɧɧɵɯ, ɤɚɩɢɥɥɹɪɧɵɯ ɢ ɞɢɮɮɭɡɢɨɧɧɨɨɫɦɨɬɢɱɟɫɤɢɯ ɫɢɥ.

23

Ɏɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɩɪɨɞɭɤɬɢɜɧɵɣ ɝɨɪɢɡɨɧɬ ɨɤɚɡɵɜɚɸɬ ɫɥɟɞɭɸɳɢɟ ɮɚɤɬɨɪɵ:

-ɪɚɡɝɪɭɡɤɚ ɝɨɪɧɨɝɨ ɦɚɫɫɢɜɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɛɭɪɢɜɚɧɢɹ (ɫɨɨɪɭɠɟɧɢɹ ɜɵɪɚɛɨɬɤɢ) ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ;

-ɢɡɦɟɧɹɸɳɟɟɫɹ ɩɪɨɬɢɜɨɞɚɜɥɟɧɢɟ ɫɬɨɥɛɚ ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ;

-ɤɨɥɶɦɚɬɚɰɢɹ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɞɢɫɩɟɪɫɧɨɣ ɮɚɡɨɣ ɩɪɨɦɵɜɨɱɧɵɯ ɠɢɞɤɨɫɬɟɣ ɢ ɱɚɫɬɢɰɚɦɢ ɜɵɛɭɪɟɧɧɨɣ ɩɨɪɨɞɵ;

-ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɟɠɢɦɚ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ;

-ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɢ ɦɟɯɚɧɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɩɨɪɨɞɵ ɪɚɡɛɭɪɢɜɚɟɦɨɝɨ ɩɥɚɫɬɚ ɞɜɢɠɭɳɢɦɫɹ ɛɭɪɨɜɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ.

ɉɪɢ ɷɬɨɦ ɫɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ ɩɥɚɫɬɚ ɩɪɢ ɩɟɪɜɢɱɧɨɦ ɜɫɤɪɵɬɢɢ, ɹɜɥɹɸɬɫɹ ɫɥɟɞɫɬɜɢɟɦ ɮɢɡɢɤɨ-ɦɟɯɚɧɢɱɟɫɤɢɯ ɜɨɡɞɟɣɫɬɜɢɣ. ɇɚɩɪɢɦɟɪ, ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɩɨɪɨɞ-ɤɨɥɥɟɤɬɨɪɨɜ ɫ ɮɢɥɶɬɪɚɬɨɦ ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ ɨɛɭɫɥɨɜɥɟɧɨ ɩɪɨɧɢɤɧɨɜɟɧɢɟɦ ɩɨɫɥɟɞɧɟɝɨ ɜɧɭɬɪɶ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɜɵɡɜɚɧɧɨɝɨ ɪɟɩɪɟɫɫɢɟɣ. ɂɥɢ ɜɵɩɚɞɟɧɢɟ ɨɫɚɞɤɨɜ ɜɧɭɬɪɢ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢɡ ɧɚɫɵɳɚɸɳɢɯ ɟɝɨ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ ɦɨɠɟɬ ɛɵɬɶ ɫɩɪɨɜɨɰɢɪɨɜɚɧɨ ɢɡɦɟɧɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɟɠɢɦɚ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɵ.

2.1.ɗɥɟɦɟɧɬɵ ɬɟɨɪɢɢ ɮɢɥɶɬɪɚɰɢɢ

Ȼɭɪɟɧɢɟ ɧɟɮɬɹɧɵɯ ɢ ɝɚɡɨɜɵɯ ɫɤɜɚɠɢɧ ɧɟɢɡɛɟɠɧɨ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɪɚɡɥɢɱɧɵɦɢ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɦɢ ɩɪɨɰɟɫɫɚɦɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɛɭɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ ɫɨ ɫɥɚɝɚɸɳɢɦɢ ɫɬɟɧɤɢ ɝɨɪɧɨɣ ɜɵɪɚɛɨɬɤɢ ɩɨɪɨɞɚɦɢ. Ʉ ɷɬɢɦ ɩɪɨɰɟɫɫɚɦ ɨɬɧɨɫɹɬɫɹ ɮɢɥɶɬɪɚɰɢɹ, ɞɢɮɮɭɡɢɹ, ɬɟɩɥɨɨɛɦɟɧ, ɤɚɩɢɥɥɹɪɧɚɹ ɩɪɨɩɢɬɤɚ ɢ ɞɪ. Ɉɞɢɧ ɢɡ ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɵɯ ɩɪɨɰɟɫɫɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɛɭɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ ɫ ɨɤɪɭɠɚɸɳɢɦɢ ɫɤɜɚɠɢɧɭ ɩɨɪɨɞɚɦɢ - ɮɢɥɶɬɪɚɰɢɹ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɩɨɝɥɨɳɟɧɢɣ ɛɭɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ ɢ ɧɟɮɬɟɝɚɡɨɜɨɞɨɩɪɨɹɜɥɟɧɢɣ, ɝɥɢɧɢɡɚɰɢɸ ɫɬɟɧɨɤ ɫɤɜɚɠɢɧɵ, ɤɨɥɶɦɚɬɚɰɢɸ ɩɪɢɫɬɜɨɥɶɧɨɣ ɡɨɧɵ ɩɪɨɞɭɤɬɢɜɧɵɯ ɩɥɚɫɬɨɜ, ɫɭɮɮɨɡɢɸ ɜ ɮɢɥɶɬɪɨɜɨɣ ɡɨɧɟ ɫɤɜɚɠɢɧɵ ɜ ɩɪɨɰɟɫɫɟ ɜɵɡɨɜɚ ɩɪɢɬɨɤɚ ɢ ɩɨɫɥɟɞɭɸɳɟɣ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɪɚɡɭɩɥɨɬɧɟɧɢɟ ɢ ɧɚɛɭɯɚɧɢɟ ɝɥɢɧɢɫɬɵɯ ɨɬɥɨɠɟɧɢɣ

24

ɢ ɦɧɨɝɢɟ ɞɪɭɝɢɟ ɹɜɥɟɧɢɹ, ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɸɳɢɟ ɧɚ ɤɚɱɟɫɬɜɨ ɡɚɤɚɧɱɢɜɚɧɢɹ ɫɤɜɚɠɢɧ. Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɧɚɭɱɧɨ ɨɛɨɫɧɨɜɚɧɧɵɯ ɩɪɢɟɦɨɜ ɩɪɟɞɨɬɜɪɚɳɟɧɢɹ ɪɹɞɨɜ ɨɫɥɨɠɧɟɧɢɣ, ɞɨɫɬɢɠɟɧɢɹ ɷɮɮɟɤɬɢɜɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɩɪɢ ɜɫɤɪɵɬɢɢ ɢ ɨɫɜɨɟɧɢɢ ɩɥɚɫɬɨɜ, ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɰɟɫɫɨɜ ɛɭɪɟɧɢɹ ɫ ɦɢɧɢɦɚɥɶɧɵɦɢ ɩɪɨɬɢɜɨɞɚɜɥɟɧɢɹɦɢ ɧɚ ɩɥɚɫɬɵ ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɩɨɥɚɝɚɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɵɦɢ ɡɚɜɢɫɢɦɨɫɬɹɦɢ, ɨɩɢɫɵɜɚɸɳɢɦɢ ɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ ɜ ɩɥɚɫɬɚɯ, ɢɡɭɱɟɧɢɟ ɤɨɬɨɪɵɯ ɫɨɫɬɚɜɥɹɟɬ ɩɪɟɞɦɟɬ ɬɟɨɪɢɢ ɮɢɥɶɬɪɚɰɢɢ [4].

2.1.1. Ɂɚɤɨɧɵ ɮɢɥɶɬɪɚɰɢɢ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ.

Ⱦɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɟɣ ɜ ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ ɧɚɡɵɜɚɸɬ ɮɢɥɶɬɪɚɰɢɟɣ. ɉɨɪɢɫɬɵɟ ɫɪɟɞɵ ɢɥɢ ɦɚɬɟɪɢɚɥɵ – ɷɬɨ ɬɜɟɪɞɵɟ ɬɟɥɚ, ɢɦɟɸɳɢɟ ɜ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɦ ɤɨɥɢɱɟɫɬɜɟ ɩɭɫɬɨɬɵ, ɯɚɪɚɤɬɟɪɧɵɟ ɪɚɡɦɟɪɵ ɤɨɬɨɪɵɯ ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɪɚɡɦɟɪɚɦɢ ɬɟɥɚ. ɋɬɪɭɤɬɭɪɚ ɩɨɪɢɫɬɵɯ ɦɚɬɟɪɢɚɥɨɜ ɦɨɠɟɬ ɛɵɬɶ ɜɟɫɶɦɚ ɪɚɡɧɨɨɛɪɚɡɧɨɣ. Ɍɚɤ, ɫɚɦɵɟ ɦɚɥɵɟ ɩɭɫɬɨɬɵ, ɜ ɤɨɬɨɪɵɯ ɫɢɥɵ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɠɢɞɤɨɫɬɢ ɫ ɬɜɟɪɞɵɦɢ ɫɬɟɧɤɚɦɢ ɜɟɫɶɦɚ ɜɟɥɢɤɢ, ɧɚɡɵɜɚɸɬ ɦɨɥɟɤɭɥɹɪɧɵɦɢ ɩɨɪɚɦɢ. ɉɪɨɬɢɜɨɩɨɥɨɠɧɨɫɬɶɸ ɢɦ ɹɜɥɹɸɬɫɹ ɩɨɪɵ, ɜ ɤɨɬɨɪɵɯ ɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɢ ɥɢɲɶ ɜɟɫɶɦɚ ɧɟɡɧɚɱɢɬɟɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɨ ɫɬɟɧɤɚɦɢ, ɢ ɢɯ ɧɚɡɵɜɚɸɬ ɤɚɜɟɪɧɚɦɢ. ɉɨɥɨɫɬɢ, ɡɚɧɢɦɚɸɳɢɟ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɩɨɥɨɠɟɧɢɟ ɦɟɠɞɭ ɤɚɜɟɪɧɚɦɢ ɢ ɦɨɥɟɤɭɥɹɪɧɵɦɢ ɩɨɪɚɦɢ, ɧɚɡɵɜɚɸɬ ɩɪɨɫɬɨ ɩɨɪɚɦɢ. ɉɨɪɵ ɦɨɝɭɬ ɛɵɬɶ ɫɨɨɛɳɚɸɳɢɦɢɫɹ ɢ ɧɟɫɨɨɛɳɚɸɳɢɦɢɫɹ. ɉɟɪɜɵɟ ɨɛɪɚɡɭɸɬ ɚɤɬɢɜɧɨɟ ɩɨɪɨɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɚ ɜɫɟ ɩɨɪɵ - ɨɛɳɟɟ ɩɨɪɨɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ.

ɇɚɢɛɨɥɟɟ ɜɚɠɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɨɪɢɫɬɵɯ ɦɚɬɟɪɢɚɥɨɜ – ɩɨɪɢɫɬɨɫɬɶ, ɬ.ɟ. ɞɨɥɹ ɨɛɴɟɦɚ, ɩɪɢɯɨɞɹɳɚɹɫɹ ɧɚ ɩɨɪɵ m:

m

Vɩ

, ɞ.ɟ.,

(2.1)

 

 

V

 

25

ɝɞɟ Vɩ

ɨɛɴɟɦ ɩɨɪ;

V

ɨɛɴɟɦ ɬɟɥɚ.

ɉɪɢ ɷɬɨɦ ɩɨɪɢɫɬɨɫɬɶ ɦɨɠɧɨ ɬɚɤɠɟ ɪɚɡɞɟɥɢɬɶ ɧɚ ɚɤɬɢɜɧɭɸ ɢ ɚɛɫɨɥɸɬɧɭɸ ɢɥɢ ɩɨɥɧɭɸ.

ɉɨɪɢɫɬɨɫɬɶ ɢɡɦɟɪɹɟɬɫɹ ɪɚɡɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ. ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɵɟ ɫɩɨɫɨɛɵ ɢɡɦɟɪɟɧɢɹ ɚɛɫɨɥɸɬɧɨɣ ɩɨɪɢɫɬɨɫɬɢ - ɩɪɹɦɨɣ, ɚ ɬɚɤɠɟ ɫɩɨɫɨɛ ɢɡɦɟɪɟɧɢɹ ɩɥɨɬɧɨɫɬɢ. ɉɨ ɩɟɪɜɨɦɭ ɫɩɨɫɨɛɭ ɢɡɦɟɪɹɸɬ ɨɛɴɟɦ ɨɛɪɚɡɰɚ, ɞɥɹ ɱɟɝɨ ɨɛɪɚɡɟɰ ɩɨɤɪɵɜɚɸɬ ɜɨɞɨɧɟɩɪɨɧɢɰɚɟɦɵɦ ɩɨɤɪɵɬɢɟɦ ɢ ɨɩɪɟɞɟɥɹɸɬ ɨɛɴɟɦ ɜɵɬɟɫɧɟɧɧɨɣ ɜɨɞɵ, ɚ ɡɚɬɟɦ, ɢɡɦɟɥɶɱɢɜ ɨɛɪɚɡɟɰ, ɢɡɦɟɪɹɸɬ ɨɛɴɟɦ ɬɜɟɪɞɨɣ ɮɚɡɵ. ɉɨ ɜɬɨɪɨɦɭ ɫɩɨɫɨɛɭ ɨɩɪɟɞɟɥɹɸɬ ɨɛɴɟɦ ɢ ɩɥɨɬɧɨɫɬɶ ɨɛɪɚɡɰɚ, ɚ ɡɚɬɟɦ ɨɛɴɟɦ ɢ

ɩɥɨɬɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ ɨɛɪɚɡɰɚ. Ɍɨɝɞɚ ɢɡ ɭɫɥɨɜɢɹ:

 

 

U0 V0

Uɦ Vɦ

(2.2)

ɢɦɟɟɦ:

 

 

 

 

 

m 1

U0

, ɞ.ɟ. ,

(2.3)

 

 

 

 

Uɦ

 

ɝɞɟ ȡ0, ȡɦ

– ɩɥɨɬɧɨɫɬɶ ɨɛɪɚɡɰɚ, ɦɚɬɟɪɢɚɥɚ ɨɛɪɚɡɰɚ, ɤɝ/ɦ3;

 

V0, Vɦ

– ɨɛɴɟɦ ɨɛɪɚɡɰɚ, ɦɚɬɟɪɢɚɥɚ ɨɛɪɚɡɰɚ, ɦ3.

 

Ⱦɥɹ ɢɡɦɟɪɟɧɢɹ ɚɤɬɢɜɧɨɣ ɩɨɪɢɫɬɨɫɬɢ ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɸɬ ɦɟɬɨɞ ɧɚɝɧɟɬɚɧɢɹ ɪɬɭɬɢ ɢɥɢ ɩɪɨɩɢɬɤɢ ɜɨɞɨɣ. ɉɨ ɩɟɪɜɨɦɭ ɫɩɨɫɨɛɭ ɨɛɪɚɡɟɰ ɩɨɦɟɳɚɸɬ ɜ ɫɨɫɭɞ ɫ ɪɬɭɬɶɸ ɢ ɨɩɪɟɞɟɥɹɸɬ ɟɝɨ ɨɛɴɟɦ ɩɨ ɢɡɦɟɧɟɧɢɸ ɭɪɨɜɧɹ, ɬɚɤ ɤɚɤ ɪɬɭɬɶ ɧɟ ɫɦɚɱɢɜɚɟɬ ɨɛɪɚɡɟɰ. Ɂɚɬɟɦ ɭɜɟɥɢɱɢɜɚɸɬ ɞɚɜɥɟɧɢɟ ɜ ɫɨɫɭɞɟ, ɢ ɜɨɲɟɞɲɢɣ ɜ

26

ɨɛɪɚɡɟɰ ɨɛɴɟɦ ɪɬɭɬɢ ɨɩɪɟɞɟɥɹɟɬ ɨɛɴɟɦ ɚɤɬɢɜɧɨɝɨ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ. ɉɪɢ ɷɬɨɦ ɨɛɴɟɦɨɦ ɫɠɚɬɨɝɨ ɜɨɡɞɭɯɚ ɩɪɟɧɟɛɪɟɝɚɸɬ, ɱɬɨ ɹɜɥɹɟɬɫɹ ɧɟɞɨɫɬɚɬɤɨɦ ɦɟɬɨɞɚ. ɉɨ ɜɬɨɪɨɦɭ ɫɩɨɫɨɛɭ, ɲɢɪɨɤɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɦɭ ɜ ɧɟɮɬɹɧɨɣ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ, ɢɫɩɨɥɶɡɭɸɬ ɫɜɨɣɫɬɜɨ ɱɢɫɬɵɯ ɝɨɪɧɵɯ ɩɨɪɨɞ ɯɨɪɨɲɨ ɫɦɚɱɢɜɚɬɶɫɹ ɜɨɞɨɣ. Ɉɛɪɚɡɟɰ, ɢɡ ɤɨɬɨɪɨɝɨ ɨɬɤɚɱɚɥɢ ɜɨɡɞɭɯ, ɩɨɝɪɭɠɚɸɬ ɜ ɜɨɞɭ, ɢ ɩɪɢɦɟɪɧɨ ɱɟɪɟɡ ɧɟɞɟɥɸ ɟɝɨ ɚɤɬɢɜɧɨɟ ɩɨɪɨɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɰɟɥɢɤɨɦ ɡɚɩɨɥɧɹɟɬɫɹ ɜɨɞɨɣ.

Ɉɩɪɟɞɟɥɢɜ ɟɝɨ ɦɚɫɫɭ, ɩɨɥɭɱɢɦ:

m M'-Ɇ , ɞ.ɟ., (2.4) V Uɜ

ɝɞɟ Ɇc Ɇ –

ɦɚɫɫɚ ɨɛɪɚɡɰɚ ɫ ɜɨɞɨɣ, ɦɚɫɫɚ ɜɨɞɵ, ɤɝ;

V

ɨɛɴɟɦ ɨɛɪɚɡɰɚ ɫ ɜɨɞɨɣ, ɦ3;

ȡɜ

ɩɥɨɬɧɨɫɬɶ ɜɨɞɵ, ɤɝ/ɦ3.

ɉɨɪɢɫɬɨɫɬɶ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɤɨɥɟɛɥɟɬɫɹ ɜ ɞɨɫɬɚɬɨɱɧɨ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ (Ɍɚɛɥɢɰɚ 2.1).

Ɍɚɛɥɢɰɚ 2.1 – ɉɨɪɢɫɬɨɫɬɶ ɪɚɡɥɢɱɧɵɯ ɦɚɬɟɪɢɚɥɨɜ.

ɇɚɡɜɚɧɢɟ ɦɚɬɟɪɢɚɥɚ

ɉɨɪɢɫɬɨɫɬɶ,

 

ɞ.ɟ.,

 

0,08-0,38

ɉɟɫɱɚɧɢɤɢ

 

0,04-0,10

ɂɡɜɟɫɬɧɹɤɢ

 

0,03-0,48

Ƚɥɢɧɵ

 

0,02-0,07

Ȼɟɬɨɧ

 

0,37-0,49

Ʉɜɚɪɰɟɜɵɣ ɩɟɫɨɤ

 

0,37-0,50

Ɋɵɯɥɵɟ ɩɟɫɤɢ

 

 

27

dV Q dt,

Ⱦɥɹ ɪɟɚɥɶɧɵɯ ɩɥɚɫɬɨɜ-ɤɨɥɥɟɤɬɨɪɨɜ ɧɟɮɬɢ ɢ ɝɚɡɚ ɡɧɚɱɟɧɢɹ ɩɨɪɢɫɬɨɫɬɢ ɨɛɵɱɧɨ ɧɚɯɨɞɹɬɫɹ ɜ ɩɪɟɞɟɥɚɯ 0,15-0,22 ɫ ɜɨɡɦɨɠɧɵɦɢ ɨɬɤɥɨɧɟɧɢɹɦɢ ɜ ɬɭ ɢɥɢ ɞɪɭɝɭɸ ɫɬɨɪɨɧɭ.

ɉɨɬɨɤ ɠɢɞɤɨɫɬɢ, ɞɜɢɠɭɳɟɣɫɹ ɜ ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ, ɦɨɠɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɟɝɨ ɨɛɴɟɦɧɵɦ ɪɚɫɯɨɞɨɦ Q, ɦ3/ɫ. ɉɪɢ ɷɬɨɦ ɨɬɧɨɲɟɧɢɟ ɟɝɨ ɤ ɩɥɨɳɚɞɢ

ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɨɛɪɚɡɰɚ S, ɦ2 ɟɫɬɶ ɫɤɨɪɨɫɬɶ ɮɢɥɶɬɪɚɰɢɢ (ȣ):

 

X

Q

, ɦ/ɫ.

(2.5)

 

S

 

 

ɗɬɚ ɫɤɨɪɨɫɬɶ – ɮɢɤɬɢɜɧɚɹ ɜɟɥɢɱɢɧɚ, ɬɚɤ ɤɚɤ ɠɢɞɤɨɫɬɶ ɞɜɢɠɟɬɫɹ ɥɢɲɶ ɩɨ ɚɤɬɢɜɧɨɦɭ ɩɨɪɨɜɨɦɭ ɩɪɨɫɬɪɚɧɫɬɜɭ ɢ ɮɚɤɬɢɱɟɫɤɚɹ ɟɟ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɛɨɥɶɲɟ ȣ. ȿɫɥɢ ɩɥɨɳɚɞɶ ɩɪɨɫɜɟɬɨɜ ɜ ɫɟɱɟɧɢɢ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ ɨɛɨɡɧɚɱɢɬɶ ɱɟɪɟɡ Sɩ, ɦ2, ɬɨ ɮɚɤɬɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɪɚɜɧɚ:

Z

X

, ɦ/ ɫ,

(2.6)

 

n

 

 

ɝɩɪɨɫɜɟɬɧɨɫɬɶ, ɞ.ɟ.;

ɞɟ

n

Sɩ

.

(2.7)

 

 

S

 

ɇɚɪɹɞɭ ɫ ɷɬɢɦ ɞɥɹ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɨɛɴɟɦɚ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ ɦɟɠɞɭ ɫɟɱɟɧɢɹɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ dɯ, ɱɟɪɟɡ ɤɨɬɨɪɵɣ ɩɪɨɬɟɤɥɨ ɤɨɥɢɱɟɫɬɜɨ ɠɢɞɤɨɫɬɢ dV:

(2.8)

ɢɦɟɟɦ ɫɨɨɬɧɨɲɟɧɢɟ:

m S dx Q dt,

(2.9)

ɢɥɢ

28

Z

dx

Q

X

,

(2.10)

dt

m S

n

 

 

 

ɬɨ ɟɫɬɶ

X

n

.

(2.11)

 

 

Z

 

ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɥɭɱɚɟɦ:

X

Q

(2.12)

m

Sɩ

 

ɢɥɢ

m

Sɩ

,

(2.13)

 

 

S

 

ɬ.ɟ. ɨɬɧɨɲɟɧɢɟ ɩɥɨɳɚɞɢ ɩɪɨɫɜɟɬɨɜ ɤ ɩɥɨɳɚɞɢ ɫɟɱɟɧɢɹ ɨɛɪɚɡɰɚ ɪɚɜɧɨ ɩɨɪɢɫɬɨɫɬɢ. ɇɚ ɷɬɨɦ ɨɫɧɨɜɚɧɢɢ ɩɨɫɬɪɨɟɧɵ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɩɨɫɨɛɵ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɪɢɫɬɨɫɬɢ.

ȼ ɬɟɨɪɢɢ ɮɢɥɶɬɪɚɰɢɢ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɫɤɨɪɨɫɬɶ ɮɢɥɶɬɪɚɰɢɢ, ɞɥɹ ɤɨɬɨɪɨɣ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɬɟɱɟɧɢɹ. ɗɬɢ ɦɨɞɟɥɢ ɢɥɢ ɡɚɤɨɧɵ ɮɢɥɶɬɪɚɰɢɢ ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɫɜɹɡɶ ɦɟɠɞɭ ɩɨɬɟɪɹɦɢ ɧɚɩɨɪɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɠɢɞɤɨɫɬɢ ɜ ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ, ɟɟ ɫɜɨɣɫɬɜɚɦɢ ɢ ɩɚɪɚɦɟɬɪɚɦɢ ɠɢɞɤɨɫɬɟɣ.

Ɉɞɢɧ ɢɡ ɨɫɧɨɜɧɵɯ ɡɚɤɨɧɨɜ ɮɢɥɶɬɪɚɰɢɢ – ɡɚɤɨɧ Ⱦɚɪɫɢ, ɤɨɬɨɪɵɣ ɡɚɩɢɫɵɜɚɟɬɫɹ ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɬɟɱɟɧɢɹ ɜ ɜɢɞɟ:

 

 

Q

k

§ p

p

 

 

z

 

z

 

·

 

 

X

S

 

¨ 1

l

2

J

 

1

l

2

¸, ɦ/ ɫ,

(2.14)

 

P

 

 

 

©

 

 

 

 

 

¹

 

ɝɞɟ k

– ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ, ɦ2;

 

29

ȝ– ɜɹɡɤɨɫɬɶ ɮɢɥɶɬɪɭɸɳɟɣɫɹ ɠɢɞɤɨɫɬɢ, ɉɚ·ɫ;

p1, p2

ɞɚɜɥɟɧɢɹ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɜ ɫɟɱɟɧɢɹɯ 1 ɢ 2, ɨɬɫɬɨɹɳɢɯ ɧɚ

 

 

ɪɚɫɫɬɨɹɧɢɢ l, ɦ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɉɚ;

z1, z2

ɜɵɫɨɬɵ ɩɨɥɨɠɟɧɢɣ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɫɟɱɟɧɢɣ 1 ɢ 2, ɦ.

ȼ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɟ ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɮɢɥɶɬɪɚɰɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɢ ɩɪɢ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɫɢɥɚɦɢ ɬɹɠɟɫɬɢ ɡɚɤɨɧ Ⱦɚɪɫɢ ɢɦɟɟɬ ɜɢɞ:

X

 

k

dp

 

k

 

p2

p1

,

(2.15)

P

P

x 2

 

 

 

 

 

dl

 

 

x1

 

ɝɞɟ ɯ21=dl – ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɫɟɱɟɧɢɹɦɢ 1

ɢ 2 ɜɞɨɥɶ ɨɫɢ ɚɛɫɰɢɫɫ, ɦ.

ȼ ɦɧɨɝɨɦɟɪɧɨɦ ɫɥɭɱɚɟ:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

k

gradp.

 

 

 

 

 

X

 

 

 

 

 

(2.16)

 

 

 

 

 

 

 

 

 

 

 

 

P

 

 

 

 

 

 

 

Ɂɧɚɤ ɦɢɧɭɫ ɜ ɷɬɢɯ ɜɵɪɚɠɟɧɢɹɯ ɭɤɚɡɵɜɚɟɬ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɫɬɶ ɧɚɩɪɚɜɥɟɧɢɣ ɫɤɨɪɨɫɬɢ ɮɢɥɶɬɪɚɰɢɢ ɢ ɝɪɚɞɢɟɧɬɚ ɞɚɜɥɟɧɢɹ.

ȼ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɪɚɠɟɧɢɹɯ ɮɢɝɭɪɢɪɭɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɨɜɨɝɨ ɫɜɨɣɫɬɜɚ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ – ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɧɢɰɚɟɦɨɫɬɢ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɩɥɨɳɚɞɢ:

k

>X@ >P@ >l@

ɦ ɫ-1 ɉɚ ɫ ɦ

ɦ

2

.

(2.17)

>p@

 

ɉɚ

 

 

 

 

 

 

30