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ɉɪɢ z  z

ɜ (6.60) ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɫɬɚɜɥɹɬɶ z

/z = 1.

ɂɡ ɫɨɜɦɟɫɬɧɨɝɨ ɪɟɲɟɧɢɹ (6.21) ɢ (6.23) ɩɨɥɭɱɚɟɦ

U Jlp

ɢɥɢ

gJlH /

(6. 24)

ɝɞɟ J=

zww /)(



– ɭɫɤɨɪɟɧɢɟ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɪɢ ɭɞɚɪɟ, ɦ/ɫ

ȿɫɥɢ ɪ

– ɞɚɜɥɟɧɢɟ, ɞɨɩɭɫɤɚɟɦɨɟ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɨ ɭɫɥɨɜɢɸ

ɩɪɨɱɧɨɫɬɢ, ɚ ɪ

– ɪɚɛɨɱɟɟ ɞɚɜɥɟɧɢɟ, ɬɨ ɞɨɩɭɫɬɢɦɨɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɭɞɚɪ-

ɧɨɟ ɞɚɜɥɟɧɢɟ

)(

ɪɞɭ

ppp 

(6. 25)

Ⱦɨɩɭɫɬɢɦɨɟ ɭɫɤɨɪɟɧɢɟ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɦ/ɫ

, ɤɨɬɨɪɨɟ

ɞɨɥɠɧɨ ɭɱɢɬɵɜɚɬɶɫɹ ɩɪɢ ɜɵɛɨɪɟ ɛɵɫɬɪɨɞɟɣɫɬɜɢɹ ɪɟɝɭɥɢɪɭɸɳɢɯ ɢ

ɞɪɨɫɫɟɥɢɪɭɸɳɢɯ ɤɥɚɩɚɧɨɜ,



ɪɞ

(6. 26)

ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɡ ɫɨɜɦɟɫɬɧɨɝɨ ɪɟɲɟɧɢɹ (6.24) ɢ (6.26).

ɍɪɚɜɧɟɧɢɟ (6.23) ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɜ ɫɥɟɞɭɸɳɟɣ ɮɨɪɦɟ:

zzsV

/ɭ/

ɭɜ

(6. 27)

ɝɞɟ s

= ɚ

/f– ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɉɚ ɫ/ɦ

(ɞɥɹ ɞɚɧ-

ɧɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ ɜɟɥɢɱɢɧɚ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɧɚɹ);

– ɢɡɦɟɧɟ-

ɧɢɟ ɨɛɴɟɦɧɨɝɨ ɪɚɫɯɨɞɚ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɪɢ ɭɞɚɪɟ, ɦ

/ɫ

= w

f – ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɞɨ ɭɞɚɪɚ, ɦ

/ɫ ;

= w

f – ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɨɫɥɟ ɭɞɚɪɚ, ɦ

/ɫ);

f–ɩɥɨɳɚɞɶ ɫɟɱɟɧɢɹ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɦ

Ⱥɧɚɥɨɝɢɱɧɨ

zzsVH //

ɧɭ

(6. 27ɚ)

ɝɞɟ

– ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɬɪɭ6ɨɩɪɨɜɨɞɚ, ɦ·ɫ/ɦ

ɉɪɢ z z

, ɬ. ɟ. ɤɨɝɞɚ ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɚɹ ɩɨɬɨɤɚ ɜɨɞɵ ɪɚɜɧɨ ɢɥɢ

ɦɟɧɶɲɟ ɮɚɡɵ ɭɞɚɪɚ

ɭ/ sV

ɢɥɢ

ɧɭ

/ sVH '

(6. 28)

ȼɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɜɧɨ ɞɚɜɥɟɧɢɸ (ɧɚɩɨɪɭ) ɝɢɞɪɚɜɥɢɱɟɫɤɨ-

ɝɨ ɭɞɚɪɚ, ɜɨɡɧɢɤɚɸɳɟɦɭ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜ ɧɟɦ ɨɛɴɟɦɧɨ-

ɝɨ ɪɚɫɯɨɞɚ ɧɚ 1ɦ

/c ɡɚ ɜɪɟɦɹ z z

ɍɞɚɪɧɨɟ ɞɚɜɥɟɧɢɟ, ɜɨɡɧɢ-

ɤɚɸɳɟɟ ɜ ɫɢɫɬɟɦɟ ɬɟɩɥɨɫɧɚɛɠɟ-

ɧɢɹ ɩɪɢ ɜɧɟɡɚɩɧɨɣ ɨɫɬɚɧɨɜɤɟ

ɫɟɬɟɜɵɯ ɧɚɫɨɫɨɜ, ɦɨɠɟɬ ɛɵɬɶ

ɧɚɣɞɟɧɨ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ,

ɩɪɟɞɥɨɠɟɧɧɵɦ ɜ ɪɚɛɨɬɟ.

ȼɧɟɡɚɩɧɚɹ ɨɫɬɚɧɨɜɤɚ ɫɟɬɟ-

ɜɵɯ ɧɚɫɨɫɨɜ ɜɵɡɵɜɚɟɬ ɜɨɥɧɨɜɨɣ

ɩɪɨɰɟɫɫ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɣɫɹ

Ɋɢɫ. 6.15. ɋɯɟɦɚ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ

/ – ɧɚɫɨɫ; ll – ɨɛɪɚɬɧɵɣ ɡɚɬɜɨɪ, /// – ɩɪɨ-

ɬɢɜɨɭɞɚɪɧɚɹ ɩɟɪɟɦɵɱɤɚ; /V – ɚɛɨɧɟɧɬ-

ɫɤɢɟ ɭɫɬɚɧɨɜɤ

ɭɦɟɧɶɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɧɚ ɧɚɝɧɟɬɚɬɟɥɶɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɧɚɫɨɫɧɨɣ ɭɫɬɚ-

ɧɨɜɤɢ (ɪɢɫ. 6.15, ɬɨɱɤɚ 1) ɢ ɩɨɜɵɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɧɚ ɜɫɚɫɵɜɚɸɳɟɦ

ɤɨɥɥɟɤɬɨɪɟ (ɬɨɱɤɚ 2).

Ɂɚɜɢɫɢɦɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɧɚɩɨɪɨɜ (ɞɚɜɥɟɧɢɣ) ɧɚ ɤɨɥɥɟɤɬɨɪɚɯ ɧɚ-

ɫɨɫɧɨɣ ɨɬ ɢɡɦɟɧɟɧɢɹ ɪɚɫɯɨɞɚ ɜɨɞɵ ɱɟɪɟɡ ɧɚɫɨɫ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɨɥɧɨɜɵɦ

ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɩɨɞɚɸɳɢɯ ɢ ɨɛɪɚɬɧɵɯ ɦɚɝɢɫɬɪɚɥɶɧɵɯ ɬɪɭɛɨɩɪɨɜɨɞɨɜ,

ɫɨɟɞɢɧɟɧɧɵɯ ɫ ɤɨɥɥɟɤɬɨɪɚɦɢ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ:

ɜɨ

ɜɩ

sss  ,

(6.29)

ɝɞɟ

ɜɩ

=ɚ/(gȈf

) – ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɨɞɚɸɳɢɯ ɦɚɝɢɫɬɪɚɥɟɣ,

ɦ·ɫ/ɦ

;

ɜɨ

= ɚ/(gȈf

) – ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɪɚɬɧɵɯ ɦɚɝɢɫɬɪɚɥɟɣ,

ɦ·ɫ/ɦ; Ȉf

ɢ Ȉf

– ɫɭɦɦɚɪɧɚɹ ɩɥɨɳɚɞɶ ɫɟɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨɞɚɸɳɢɯ ɢ

ɨɛɪɚɬɧɵɯ ɦɚɝɢɫɬɪɚɥɟɣ, ɨɬɯɨɞɹɳɢɯ ɨɬ ɤɨɥɥɟɤɬɨɪɨɜ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ, ɦ

ɇɚ ɪɢɫ. 6.16 ɜ ɇ, V-ɤɨɨɪɞɢɧɚɬɚɯ ɩɨɤɚɡɚɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɫɨɫ-

ɧɨɣ ɭɫɬɚɧɨɜɤɢ, Ɍɨɱɤɚ Ⱥ

ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɚɱɚɥɶɧɨɦɭ ɪɟɠɢɦɭ ɪɚɛɨɬɵ ɫɢɫ-

ɬɟɦɵ (ɞɨ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɜɨɡɦɭɳɟɧɢɹ) ɩɪɢ ɧɨɪɦɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟ-

ɧɢɹ ɧɚɫɨɫɧɵɯ ɚɝɪɟɝɚɬɨɜ, ɪɚɜɧɨɣ n.

ɉɪɢ ɜɧɟɡɚɩɧɨɦ ɜɵɤɥɸɱɟɧɢɢ

ɞɜɢɝɚɬɟɥɟɣ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɧɚɫɨɫɨɜ

ɫɧɢɠɚɟɬɫɹ ɨɬ n ɞɨ ɧɭɥɹ ɢ ɫɢɫɬɟɦɚ ɩɟ-

ɪɟɯɨɞɢɬ ɜ ɫɨɫɬɨɹɧɢɟ Ⱥ

. Ɋɚɫɯɨɞ ɜɨɞɵ

ɱɟɪɟɡ ɧɚɫɨɫɧɭɸ ɭɫɬɚɧɨɜɤɭ ɭɦɟɧɶɲɚɟɬ-

ɫɹ ɧɚ ǻV =V

– V

, ɩɪɢ ɷɬɨɦ ɜɨɡɧɢɤɚɟɬ

ɭɞɚɪɧɵɣ ɧɚɩɨɪ ɇ

. ɍɞɚɪɧɚɹ ɯɚɪɚɤɬɟɪɢ-

ɫɬɢɤɚ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ – ɩɪɹɦɚɹ Ⱥ

ɫɨɟɞɢɧɹɸɳɚɹ ɧɚɱɚɥɶɧɨɟ ɢ ɤɨɧɟɱɧɨɟ

ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ, ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜ-

ɧɟɧɢɟɦ ɜɨɥɧɨɜɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

(6.27ɚ), ɝɞɟ

s – ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟ-

ɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɩɨ (6.29).

Ɋɢɫ. 6.16. ɉɨɫɬɪɨɟɧɢɟ ɭɞɚɪɧɨɣ

ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɫɨɫɧɨɣ ɭɫɬɚ-

ɧɨɜɤɢ

Ɍɚɧɝɟɧɫ ɭɝɥɚ ɧɚɤɥɨɧɚ ɩɪɹɦɨɣ Ⱥ

ɤ ɨɫɢ ɚɛɫɰɢɫɫ

zzs /tgĮ

ɭɜ

Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɭɞɚɪɧɨɝɨ ɧɚɩɨɪɚ ɦɟɠɞɭ ɩɨɞɚɸɳɢɦ ɢ ɨɛɪɚɬɧɵɦ ɤɨɥɥɟɤ-

ɬɨɪɚɦɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɢɯ ɜɨɥɧɨɜɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ, ɚ ɢɦɟɧɧɨ:

ɜ.ɨ

ɧɭɭ.ɨ

ɜ.ɩ

ɧɭɭ.ɩ

ssHH

(6.30)

ɝɞɟ ɇ

ɭɩ

ɢ ɇ

ɭɨ

– ɭɞɚɪɧɵɟ ɧɚɩɨɪɵ ɜ ɩɨɞɚɸɳɟɦ ɢ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɚɯ.

ɇɚ ɪɢɫ. 6.17, ɚ ɩɨɤɚɡɚɧ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɧɚɩɨɪɨɜ ɧɚ ɩɨɞɚɸɳɟɦ

ɢ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɚɯ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ ɩɪɢ ɜɧɟɡɚɩɧɨɦ ɜɵɤɥɸɱɟ-

ɧɢɢ ɞɜɢɝɚɬɟɥɟɣ ɧɚɫɨɫɨɜ. Ɂɚ ɜɪɟɦɹ z, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɱɚɫɬɨɬɚ ɜɪɚɳɟ-

ɧɢɹ ɧɚɫɨɫɚ ɭɦɟɧɶɲɚɟɬɫɹ ɨɬ ɧɨɪɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ n ɞɨ ɧɭɥɹ, ɧɚɩɨɪ ɧɚ

ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɩɨɜɵɲɚɟɬɫɹ ɧɚ

, ɚ ɧɚ ɩɨɞɚɸɳɟɦ ɤɨɥɥɟɤɬɨɪɟ

ɫɧɢɠɚɟɬɫɹ ɧɚ

. ɋɭɦɦɚɪɧɵɣ ɧɚɩɨɪ ɧɚ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɞɨɫɬɢɝɚ-

ɟɬ ɇ

, ɚ ɧɚ ɩɨɞɚɸɳɟɦ H

–

. ɑɟɪɟɡ ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɜɨɥɧɨɜɨɣ

ɩɪɨɰɟɫɫ ɡɚɬɭɯɚɟɬ ɢ ɜ ɫɢɫɬɟɦɟ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɫɬɚɬɢɱɟɫɤɢɣ ɧɚɩɨɪ H

ɫɬ

Ɋɢɫ. 6.17. ɂɡɦɟɧɟɧɢɟ ɧɚɩɨɪɨɜ ɧɚ ɤɨɥɥɟɤɬɨɪɚɯ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ ɩɪɢ ɧɚ-

ɪɭɲɟɧɢɢ ɪɟɠɢɦɚ

ɚ – ɜɧɟɡɚɩɧɨɟ ɨɬɤɥɸɱɟɧɢɟ, ɛ – ɜɧɟɡɚɩɧɨɟ ɜɤɥɸɱɟɧɢɟ

ɉɪɢ ɡɚɩɭɫɤɟ ɧɚɫɨɫɨɜ ɢɡ ɧɟɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɨɹɧɢɹ «ɧɚ ɫɟɬɶ» ɫ ɨɬ-

ɤɪɵɬɵɦɢ ɡɚɞɜɢɠɤɚɦɢ ɧɚ ɩɨɞɚɸɳɟɦ ɢ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɚɯ ɬɚɤɠɟ ɜɨɡ-

ɧɢɤɚɟɬ ɜɨɥɧɨɜɨɣ ɩɪɨɰɟɫɫ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɣɫɹ ɩɨɜɵɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ

(ɧɚɩɨɪɚ) ɧɚ ɩɨɞɚɸɳɟɦ ɤɨɥɥɟɤɬɨɪɟ (ɫɦ. ɪɢɫ. 6.15, ɬɨɱɤɚ 1) ɢ ɫɧɢɠɟɧɢɟɦ

ɧɚɩɨɪɚ ɧɚ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɧɚɫɨɫɧɨɣ (ɬɨɱɤɚ 2). ɇɚ ɪɢɫ. 6.16 ɷɬɨɬ

ɩɪɨɰɟɫɫ ɩɨɤɚɡɚɧ ɫ ɩɨɦɨɳɶɸ ɭɞɚɪɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɩɪɹɦɨɣ 0Ⱥ, ɨɩɢ-

ɫɵɜɚɟɦɨɣ (6.27).

ɇɚ ɪɢɫ. 6.17, ɛ ɜ z, H-ɤɨɨɪɞɢɧɚɬɚɯ ɩɨɤɚɡɚɧ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ

ɧɚɩɨɪɨɜ ɧɚ ɤɨɥɥɟɤɬɨɪɚɯ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ ɩɪɢ ɡɚɩɭɫɤɟ ɟɟ ɧɚ ɫɟɬɶ ɫ

ɨɬɤɪɵɬɵɦɢ ɡɚɞɜɢɠɤɚɦɢ.

Ɉɛɵɱɧɵɟ ɚɜɬɨɦɚɬɵ, ɩɪɟɞɨɯɪɚɧɹɸɳɢɟ ɜ ɫɬɚɰɢɨɧɚɪɧɵɯ ɭɫɥɨɜɢɹɯ

ɫɢɫɬɟɦɭ ɨɬ ɨɩɚɫɧɵɯ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɦɨɝɭɬ

ɡɚɳɢɬɢɬɶ ɟɟ

ɨɬ ɜɨɥɧɨɜɵɯ ɹɜɥɟɧɢɣ, ɜɨɡɧɢɤɚɸɳɢɯ ɩɪɢ ɝɢɞɪɚɜɥɢɱɟɫɤɨɦ

ɭɞɚɪɟ.

Ⱦɥɹ ɡɚɳɢɬɵ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɨɬ ɧɟɞɨɩɭɫɬɢɦɨɝɨ ɩɨɜɵɲɟ-

ɧɢɹ ɞɚɜɥɟɧɢɹ ɩɪɢ ɝɢɞɪɚɜɥɢɱɟɫɤɨɦ ɭɞɚɪɟ ɩɪɢɦɟɧɹɸɬɫɹ ɫɩɟɰɢɚɥɶɧɵɟ

ɭɫɬɪɨɣɫɬɜɚ, ɤɨɬɨɪɵɟ ɩɨ ɩɪɢɧɰɢɩɭ ɪɚɛɨɬɵ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɫɥɟɞɭɸ-

ɳɢɟ ɝɪɭɩɩɵ:

1) ɭɫɬɪɨɣɫɬɜɚ, ɢɡɦɟɧɹɸɳɢɟ ɡɧɚɤ ɜɨɥɧɵ ɞɚɜɥɟɧɢɣ. Ʉ ɧɢɦ ɨɬɧɨɫɹɬ-

ɫɹ ɨɛɪɚɬɧɵɟ ɤɥɚɩɚɧɵ ɧɚ ɩɟɪɟɦɵɱɤɚɯ, ɫɨɟɞɢɧɹɸɳɢɯ ɬɪɭɛɨɩɪɨɜɨɞɵ, ɜ

ɤɨɬɨɪɵɯ ɜɨɥɧɵ

ɞɚɜɥɟɧɢɣ ɢɦɟɸɬ ɪɚɡɧɵɟ ɡɧɚɤɢ. ȼ ɱɚɫɬɧɨɫɬɢ, ɬɚɤɢɟ ɩɟ-

ɪɟɦɵɱɤɢ ɱɚɫɬɨ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɦɟɠɞɭ ɨɛɪɚɬɧɵɦ ɢ ɩɨɞɚɸɳɢɦɢ ɤɨɥ-

ɥɟɤɬɨɪɚɦɢ ɧɚɫɨɫɧɵɯ ɧɚ Ɍɗɐ ɢɥɢ ɜ ɤɪɭɩɧɵɯ ɤɨɬɟɥɶɧɵɯ (ɫɦ., ɧɚɩɪɢɦɟɪ,

ɩɟɪɟɦɵɱɤɭ III ɧɚ ɪɢɫ. 6.15). ɉɪɢ ɜɧɟɡɚɩɧɨɣ ɨɫɬɚɧɨɜɤɟ ɧɚɫɨɫɨɜ, ɤɨɝɞɚ

ɞɚɜɥɟɧɢɟ ɜ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɩɪɟɜɵɲɚɟɬ ɞɚɜɥɟɧɢɹ

ɜ ɩɨɞɚɸɳɟɦ ɤɨɥ-

ɥɟɤɬɨɪɟ, ɨɬɤɪɵɜɚɟɬɫɹ ɨɛɪɚɬɧɵɣ ɤɥɚɩɚɧ ɢɥɢ

ɡɚɬɜɨɪ II ɧɚ ɩɪɨɬɢɜɨɭɞɚɪɧɨɣ

ɩɟɪɟɦɵɱɤɟ ɢ ɞɚɜɥɟɧɢɹ ɜ ɤɨɥɥɟɤɬɨɪɚɯ ɜɵɪɚɜɧɢɜɚɸɬɫɹ;

2) ɭɫɬɪɨɣɫɬɜɚ, ɬɨɪɦɨɡɹɳɢɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɨɥɧɨɜɨɝɨ ɩɪɨɰɟɫɫɚ.

Ʉ ɧɢɦ

ɨɬɧɨɫɹɬɫɹ ɝɚɡɨɜɵɟ ɢ ɜɨɡɞɭɲɧɵɟ ɤɨɥɩɚɤɢ;

3) ɭɫɬɪɨɣɫɬɜɚ ɞɥɹ ɫɛɪɨɫɚ ɞɚɜɥɟɧɢɣ. Ʉ ɧɢɦ

ɨɬɧɨɫɹɬɫɹ ɭɪɚɜɧɢɬɟɥɶ-

ɧɵɟ ɪɟɡɟɪɜɭɚɪɵ, ɪɚɡɪɵɜɧɵɟ ɞɢɚɮɪɚɝɦɵ ɢ ɩɪɟɞɨɯɪɚɧɢɬɟɥɶɧɵɟ ɤɥɚɩɚɧɵ.

ɉɪɟɞɨɯɪɚɧɢɬɟɥɶɧɵɟ ɤɥɚɩɚɧɵ ɦɚɥɨɧɚɞɟɠɧɵ ɢɡ-ɡɚ

ɜɨɡɦɨɠɧɨɝɨ ɩɪɢɤɢɩɚ-

ɧɢɹ ɢ ɧɟɞɨɫɬɚɬɨɱɧɨɝɨ ɛɵɫɬɪɨɞɟɣɫɬɜɢɹ;

4) ɭɫɬɪɨɣɫɬɜɚ, ɢɡɦɟɧɹɸɳɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɢɫɬɨɱɧɢɤɚ ɜɨɡɦɭɳɟ-

ɧɢɹ. Ʉ ɧɢɦ ɨɬɧɨɫɢɬɫɹ ɭɫɬɚɧɨɜɤɚ ɦɚɯɨɜɵɯ ɤɨɥɟɫ ɧɚ ɜɚɥɭ ɧɚɫɨɫɚ, ɤɨɬɨɪɵɟ

ɭɜɟɥɢɱɢɜɚɸɬ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɚɝɪɟɝɚɬɚ, ɛɥɚɝɨɞɚɪɹ ɱɟɦɭ ɜɨɡɪɚɫɬɚɟɬ ɟɝɨ

ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ z

ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɜɪɟɦɟɧɢ z, ɡɚ ɤɨɬɨ-

ɪɨɟ ɩɪɢ ɨɬɤɥɸɱɟɧɢɢ ɷɥɟɤɬɪɨɩɢɬɚɧɢɹ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɧɚɫɨɫɚ ɢɡɦɟɧɹ-

ɟɬɫɹ ɨɬ ɧɨɪɦɚɥɶɧɨɣ ɞɨ ɧɭɥɹ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɧɢɠɚɟɬ ɭɞɚɪɧɵɣ ɧɚɩɨɪ,

ɪɚɜɧɵɣ ɇ

/z. ȼɪɟɦɹ, ɡɚ ɤɨɬɨɪɨɟ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɧɚɫɨɫɚ ɩɪɢ ɨɬɤɥɸ-

ɱɟɧɢɢ ɷɥɟɤɬɪɨɩɢɬɚɧɢɹ ɢɡɦɟɧɹɟɬɫɹ ɜ n

ɪɚɡ, ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɨ

ɩɨ ɫɥɟɞɭɸɳɟɣ ɩɪɢɛɥɢɠɟɧɧɨɣ ɮɨɪɦɭɥɟ:

)1/(

oɚ



nnzz

(6.31a)

ɝɞɟ z

– ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɧɚɫɨɫɧɨɝɨ ɚɝɪɟɝɚɬɚ, ɪɚɜɧɚɹ ɜɪɟɦɟɧɢ z

, ɡɚ

ɤɨɬɨɪɨɟ ɩɪɢ ɨɬɤɥɸɱɟɧɢɢ ɷɥɟɤɬɪɨɩɢɬɚɧɢɹ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɧɚɫɨɫɚ ɢɡ-

ɦɟɧɹɟɬɫɹ ɜ 2 ɪɚɡɚ

. ɋ ɩɨɦɨɳɶɸ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ z

, ɤɨɬɨ-

ɪɭɸ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɨɩɵɬɧɵɦ ɩɭɬɟɦ, ɥɟɝɤɨ ɩɨɫɬɪɨɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ

ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɧɚɫɨɫɚ n

ɨɬ ɜɪɟɦɟɧɢ z

, ɩɪɨɲɟɞɲɟɝɨ ɩɨɫɥɟ ɨɬɤɥɸɱɟ-

ɧɢɹ ɷɥɟɤɬɪɨɩɢɬɚɧɢɹ, ɩɨ ɮɨɪɦɭɥɟ

ɚo

zzn



(6.31ɛ)

Ʉ ɷɬɨɣ ɠɟ ɝɪɭɩɩɟ ɨɬɧɨɫɹɬɫɹ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɢɟ ɭɫɬɪɨɣɫɬɜɚ ɞɥɹ

ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɜɤɥɸɱɟɧɢɹ ɪɟɡɟɪɜɧɨɝɨ ɧɚɫɨɫɚ ɩɪɢ ɜɵɯɨɞɟ ɢɡ ɫɬɪɨɹ ɪɚ-

ɛɨɱɟɝɨ ɧɚɫɨɫɚ.

ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɭɞɚɪɚ,

ɜɵɡɵɜɚɸɳɟɝɨ ɜɨɥɧɨɜɨɣ ɩɪɨɰɟɫɫ ɢɡɦɟɧɟɧɢɹ ɞɚɜɥɟɧɢɹ, ɩɪɢ ɩɪɟɤɪɚɳɟɧɢɢ

ɰɢɪɤɭɥɹɰɢɢ ɜɨɞɵ ɦɨɠɟɬ ɭɫɬɚɧɨɜɢɬɶɫɹ ɩɨɜɵɲɟɧɧɨɟ ɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜɥɟ-

ɧɢɟ ɜ ɫɢɫɬɟɦɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɬɟɧɰɢɚɥɶɧɨɣ

ɷɧɟɪɝɢɢ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨ-

ɜɨɞɚɯ, ɧɚɯɨɞɹɳɢɯɫɹ ɩɨɞ ɞɚɜɥɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɛɥɢɠɟɧɧɨ

ɨɩɪɟɞɟɥɟɧɨ ɩɨ ɮɨɪɦɭɥɟ

VgVHp /

ɫɬ

U'6

(6.32)

ɝɞɟ ɇ – ɧɚɩɨɪ, ɨɬɫɱɢɬɚɧɧɵɣ ɨɬ ɨɛɳɟɣ ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ, ɩɨɞ ɤɨɬɨ-

ɪɵɦ ɩɪɢ ɰɢɪɤɭɥɹɰɢɢ ɧɚɯɨɞɢɬɫɹ ɷɥɟɦɟɧɬɚɪɧɵɣ ɨɛɴɟɦ ɜɨɞɵ ǻV

, ɦ

; V –

ɩɨɥɧɵɣ ɨɛɴɟɦ ɜɨɞɵ ɜ ɫɢɫɬɟɦɟ, ɦ

;

ɫɬ

– ɞɚɜɥɟɧɢɟ, ɉɚ.

ȼ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹɯ ɞɚɜɥɟɧɢɟ ɪ„ ɦɨɠɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɩɪɟɜɵɫɢɬɶ

ɞɨɩɭɫɬɢɦɨɟ. Ⱦɥɹ ɩɪɟɞɭɩɪɟɠɞɟɧɢɹ ɬɚɤɢɯ ɪɟɠɢɦɨɜ ɨɫɬɚɧɨɜɤɚ ɰɢɪɤɭɥɹɰɢɢ

ɜɨɞɵ ɜ ɤɪɭɩɧɵɯ ɬɟɩɥɨɜɵɯ ɫɟɬɹɯ ɞɨɥɠɧɚ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɩɨ ɩɪɨ- ɝɪɚɦɦɟ,

ɩɪɟɞɭɫɦɚɬɪɢɜɚɸ ɳɟɣ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɟ ɫɧɢɠɟɧɢɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪ-

ɝɢɢ ɫɢɫɬɟɦ ɞɨ ɩɪɟɤɪɚɳɟɧɢɹ ɰɢɪɤɭɥɹɰɢɢ, ɧɚɩɪɢɦɟɪ, ɩɭɬɟɦ ɞɪɨɫɫɟɥɢɪɨ-

ɜɚɧɢɹ ɞɚɜɥɟɧɢɹ ɜɨɞɵ ɧɚ ɧɚɝɧɟɬɚɬɟɥɶɧɨɣ ɥɢɧɢɢ ɫɟɬɟɜɵɯ ɧɚɫɨɫɨɜ.

6.5. ȼɨɩɪɨɫɵ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɩɟɪɫɩɟɤɬɢɜɵ ɪɚɡɜɢɬɢɹ ɫɢɫɬɟɦ

ɷɧɟɪɝɨɫɧɚɛɠɟɧɢɹ

Ʉɚɤ ɭɬɜɟɪɠɞɚɥ ɚɜɬɨɪ ɪɚɛɨɬɵ [1], ɞɨ ɧɚɫɬɨɹɳɟɝɨ ɜɪɟɦɟɧɢ ɪɚɡɜɢɬɢɟ

ɫɢɫɬɟɦ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɝɨ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢɡɨɜɚɥɨɫɶ ɫɥɟɞɭɸ-

ɳɢɦɢ ɬɟɧɞɟɧɰɢɹɦɢ:

x Ɋɨɫɬ ɤɨɥɢɱɟɫɬɜɚ ɢɫɬɨɱɧɢɤɨɜ ɬɟɩɥɨɬɵ, ɪɚɛɨɬɚɸɳɢɯ ɜ ɟɞɢɧɨɣ

ɫɢɫɬɟɦɟ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɝɨɪɨɞɨɜ;

ɍɫɥɨɠɧɟɧɢɟ ɫɬɪɭɤɬɭɪɵ ɩɨɬɪɟɛɥɟɧɢɹ ɬɟɩɥɨɬɵ ɢɡ-ɡɚ ɞɨɛɚɜɥɟ-

ɧɢɹ ɤ ɨɬɨɩɥɟɧɢɸ, ɜɟɧɬɢɥɹɰɢɢ ɢ ɝɨɪɹɱɟɦɭ ɜɨɞɨɫɧɚɛɠɟɧɢɸ

ɧɚɝɪɭɡɨɤ ɩɨ ɤɨɧɞɢɰɢɨɧɢɪɨɜɚɧɢɸ ɜɨɡɞɭɯɚ ɢ ɪɚɡɥɢɱɧɵɯ ɬɟɯ-

ɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ;

ɍɜɟɥɢɱɟɧɢɸ ɱɢɫɥɚ ɩɨɬɪɟɛɢɬɟɥɟɣ, ɧɟ ɞɨɩɭɫɤɚɸɳɢɯ ɩɟɪɟɪɵ-

ɜɨɜ ɜ ɩɨɫɬɚɜɤɚɯ ɬɟɩɥɚ;

ɇɢɡɤɚɹ ɤɨɧɤɭɪɟɧɬɨɫɩɨɫɨɛɧɨɫɬɶ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɝɨ ɬɟɩɥɨ-

ɫɧɚɛɠɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɪɭɝɢɦɢ ɢɫɬɨɱɧɢɤɚɦɢ ɬɟɩɥɚ.

Ⱦɥɢɬɟɥɶɧɵɣ ɨɩɵɬ ɷɤɫɩɥɭɚɬɚɰɢɢ ɤɪɭɩɧɵɯ ɫɢɫɬɟɦ ɰɟɧɬɪɚɥɢɡɨɜɚɧ-

ɧɨɝɨ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɩɨɤɚɡɚɥ ɢɯ ɩɨɧɢɠɟɧɧɭɸ ɧɚɞɟɠɧɨɫɬɶ, ɤɨɬɨɪɚɹ ɨɛɴ-

ɹɫɧɹɟɬɫɹ ɭɫɥɨɜɢɹɦɢ ɢɯ ɫɨɨɪɭɠɟɧɢɹ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ:

ɋɥɨɠɧɵɟ ɭɫɥɨɜɢɹ ɜɵɩɨɥɧɟɧɢɹ ɫɬɪɨɢɬɟɥɶɧɨ-ɦɨɧɬɚɠɧɵɯ ɪɚ-

ɛɨɬ;

ɋɥɨɠɧɨɫɬɶ ɤɨɧɬɪɨɥɹ ɫɨɫɬɨɹɧɢɹ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɜ ɭɫɥɨɜɢɹɯ

ɷɤɫɩɥɭɚɬɚɰɢɢ;

ɇɟɛɥɚɝɨɩɪɢɹɬɧɵɟ ɜɧɟɲɧɢɟ ɭɫɥɨɜɢɹ ɷɤɫɩɥɭɚɬɚɰɢɢ ɬɟɩɥɨɜɵɯ

ɫɟɬɟɣ;

ɇɢɡɤɨɟ ɤɚɱɟɫɬɜɨ ɦɚɬɟɪɢɚɥɚ ɬɪɭɛɨɩɪɨɜɨɞɨɜ;

ɋɥɚɛɚɹ ɡɚɳɢɬɚ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɨɬ ɤɨɪɪɨɡɢɢ;

ɇɢɡɤɨɟ ɤɚɱɟɫɬɜɨ ɫɟɬɟɜɨɣ ɜɨɞɵ ɢɡ-ɡɚ ɧɟɫɨɛɥɸɞɟɧɢɹ ɜɨɞɧɨ-

ɯɢɦɢɱɟɫɤɨɝɨ ɪɟɠɢɦɚ;

ɋɥɚɛɨɫɬɶ ɢ ɧɢɡɤɚɹ ɨɫɧɚɳɟɧɧɨɫɬɶ ɫɥɭɠɛ ɚɜɚɪɢɣɧɨ ɜɨɫɫɬɚɧɨ-

ɜɢɬɟɥɶɧɨɝɨ ɪɟɦɨɧɬɚ.

ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɜ ɫɢɫɬɟɦɚɯ ɷɧɟɪɝɨɫɧɚɛɠɟɧɢɹ ɝɨɪɨɞɨɜ, ɠɢɥɵɯ

ɦɚɫɫɢɜɨɜ ɢ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɡɥɨɜ ɫɥɨɠɢɥɚɫɶ ɫɢɬɭɚɰɢɹ, ɛɥɢɡɤɚɹ ɤ ɤɚɬɚ-

ɫɬɪɨɮɢɱɟɫɤɨɣ. ɉɪɟɠɞɟ ɜɫɟɝɨ, ɷɬɨ ɩɪɨɢɫɯɨɞɢɬ ɢɡ-ɡɚ ɢɡɧɨɲɟɧɧɨɫɬɢ ɨɛɨ-

ɪɭɞɨɜɚɧɢɹ ɬɟɩɥɨɜɵɯ ɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɟɬɟɣ, ɤɨɬɨɪɚɹ ɜ ɨɬɞɟɥɶɧɵɯ ɫɥɭɱɚ-

ɹɯ ɞɨɫɬɢɝɚɟɬ 60–70 %. Ʉɪɨɦɟ ɬɨɝɨ, ɞɨɩɭɳɟɧɧɵɟ ɩɪɨɫɱɟɬɵ ɩɪɢ

ɜɵɛɨɪɟ

ɫɬɪɚɬɟɝɢɢ ɪɚɡɜɢɬɢɹ ɫɢɫɬɟɦ ɷɧɟɪɝɨɫɧɚɛɠɟɧɢɹ ɜ ɩɟɪɢɨɞ ɫɨɰɢɚɥɢɡɦɚ ɩɪɢ-

ɜɟɥɢ ɤ ɩɨɬɟɪɟ ɢɧɜɟɫɬɢɰɢɨɧɧɨɣ ɩɪɢɜɥɟɤɚɬɟɥɶɧɨɫɬɢ ɷɬɢɯ ɫɢɫɬɟɦ ɜ ɭɫɥɨ-

ɜɢɹɯ ɪɵɧɤɚ.

ɋɥɨɠɧɨɫɬɶ ɚɞɚɩɬɚɰɢɢ ɫɢɫɬɟɦ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɤ ɭɫɥɨɜɢɹɦ ɪɵɧɤɚ

ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɨɧɢ ɫɬɪɨɢɥɢɫɶ ɩɨ ɩɪɢɧɰɢɩɭ ɜɡɚɢɦɨɫɜɹɡɢ ɷɥɟɦɟɧ-

ɬɨɜ ɩɨ ɬɟɩɥɨɧɨɫɢɬɟɥɸ. ɋɟɬɟɜɚɹ ɜɨɞɚ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɹɜɥɹɟɬɫɹ

ɨɛɳɢɦ ɬɟɩɥɨɧɨɫɢɬɟɥɟɦ ɤɚɤ ɞɥɹ ɢɫɬɨɱɧɢɤɨɜ ɬɟɩɥɚ, ɬɚɤ ɢ ɞɥɹ ɬɪɚɧɡɢɬɧɵɯ

ɬɟɩɥɨɦɚɝɢɫɬɪɚɥɟɣ, ɚ ɬɚɤɠɟ ɢ ɞɥɹ ɩɨɬɪɟɛɢɬɟɥɟɣ, ɩɨɞɤɥɸɱɟɧɧɵɯ ɤ ɬɟɩɥɨ-

ɫɟɬɢ ɩɨ ɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɜɨɫɩɨɥɧɟɧɢɟ ɩɨɬɟɪɶ ɬɟɩɥɨɧɨ-

ɫɢɬɟɥɹ, ɜɨɡɧɢɤɲɢɯ ɜ ɥɸɛɨɦ ɦɟɫɬɟ ɫɢɫɬɟɦɵ, ɞɨɥɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶɫɹ ɤɚ-

ɤɢɦ ɥɢɛɨ ɯɨɡɹɣɫɬɜɭɸɳɢɦ ɷɥɟɦɟɧɬɨɦ, ɡɚɬɪɚɬɵ ɤɨɬɨɪɨɝɨ ɞɨɥɠɧɵ ɛɵɬɶ

ɤɨɦɩɟɧɫɢɪɨɜɚɧɵ ɜɫɟɣ ɫɢɫɬɟɦɨɣ. Ʉɚɤ ɷɬɨ ɫɞɟɥɚɬɶ, ɟɫɥɢ ɱɚɫɬɨ ɞɚɠɟ ɬɪɭɞ-

ɧɨ ɭɫɬɚɧɨɜɢɬɶ ɦɟɫɬɨ ɭɬɟɱɤɢ ɬɟɩɥɨɧɨɫɢɬɟɥɹ. ȿɫɥɢ ɠɟ ɩɨɞɩɢɬɤɚ ɬɟɩɥɨɫɟɬɢ

ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɧɟ ɨɞɧɢɦ, ɚ ɧɟɫɤɨɥɶɤɢɦɢ ɩɪɟɞɩɪɢɹɬɢɹɦɢ, ɬɨ ɩɪɚɤɬɢɱɟ-

ɫɤɢ ɬɪɭɞɧɨ ɧɚɞɟɹɬɶɫɹ, ɱɬɨ ɤɚɱɟɫɬɜɨ ɩɨɞɩɢɬɨɱɧɨɣ ɜɨɞɵ ɜɫɟɝɞɚ ɛɭɞɟɬ ɨɬ-

ɜɟɱɚɬɶ ɬɪɟɛɨɜɚɧɢɹɦ ɧɨɪɦ. Ɋɟɡɤɨ ɩɟɪɟɦɟɧɧɵɣ ɯɚɪɚɤɬɟɪ

ɪɚɫɯɨɞɚ ɩɨɞɩɢ-

ɬɨɱɧɨɣ ɜɨɞɵ ɜ ɨɬɤɪɵɬɵɯ ɫɢɫɬɟɦɚɯ ɬɨɥɶɤɨ ɭɫɥɨɠɧɹɟɬ ɡɚɞɚɱɭ ɤɚɱɟɫɬɜɟɧ-

ɧɨɣ ɟɟ ɩɨɞɝɨɬɨɜɤɢ.

ȼɨɩɪɨɫɵ ɷɤɫɩɥɭɚɬɚɰɢɢ ɫɭɳɟɫɬɜɭɸɳɢɯ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ, ɧɚɞɟɠɧɨ-

ɫɬɢ ɢɯ ɷɥɟɦɟɧɬɨɜ ɢ ɷɧɟɪɝɨɫɧɚɛɠɟɧɢɹ ɩɨɬɪɟɛɢɬɟɥɟɣ ɞɨɫɬɚɬɨɱɧɨ ɩɨɞɪɨɛ-

ɧɨ ɢɡɥɨɠɟɧɵ ɜ [1], ɢ ɱɢɬɚɬɟɥɶ ɦɨɠɟɬ ɬɚɦ ɫ ɧɢɦɢ ɨɡɧɚɤɨɦɢɬɶɫɹ. Ɂɞɟɫɶ ɠɟ

ɦɵ ɩɨɩɵɬɚɟɦɫɹ ɢɡɥɨɠɢɬɶ ɫɜɨɟ ɜɢɞɟɧɢɟ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɢ ɪɚɡɜɢɬɢɹ

ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɵɯ ɫɢɫɬɟɦ

ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ.

ɂɡɥɨɠɟɧɧɵɟ ɜɵɲɟ ɩɪɨɛɥɟɦɵ ɷɤɫɩɥɭɚɬɚɰɢɢ ɫɭɳɟɫɬɜɭɸɳɢɯ ɬɟɩɥɨ-

ɜɵɯ ɫɟɬɟɣ ɬɪɟɛɭɸɬ ɪɟɲɢɬɟɥɶɧɵɯ ɦɟɪ ɩɨ ɢɯ ɦɨɞɟɪɧɢɡɚɰɢɢ ɢ ɪɟɤɨɧɫɬ-

ɪɭɤɰɢɢ.

ȿɫɥɢ ɨɛɪɚɬɢɬɶɫɹ ɤ ɨɩɵɬɭ ɫɨɡɞɚɧɢɹ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɫɢɫɬɟɦ ɰɟɧɬɪɚ-

ɥɢɡɨɜɚɧɧɨɝɨ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɜ ɫɬɪɚɧɚɯ ɫ ɪɚɡɜɢɬɨɣ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢ-

ɤɨɣ, ɬɨ ɦɨɠɧɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɷɬɢ ɫɢɫɬɟɦɵ ɜɨɡɧɢɤɥɢ ɤɚɤ ɤɨɧɤɭɪɟɧɬɧɨ

ɫɩɨɫɨɛɧɵɟ ɩɭɬɟɦ ɨɛɴɟɞɢɧɟɧɢɹ ɪɹɞɚ ɢɫɬɨɱɧɢɤɨɜ ɬɟɩɥɚ

ɢ ɩɨɬɪɟɛɢɬɟɥɟɣ

ɱɟɪɟɡ ɦɚɝɢɫɬɪɚɥɶɧɵɟ ɬɟɩɥɨɜɵɟ ɫɟɬɢ. ɉɪɢ ɷɬɨɦ ɤɚɠɞɵɣ ɢɫɬɨɱɧɢɤ ɬɟɩɥɚ ɢ

ɤɚɠɞɵɣ ɩɨɬɪɟɛɢɬɟɥɶ ɨɫɬɚɸɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ ɩɨ ɬɟɩɥɨɧɨɫɢɬɟɥɸ, ɬɚɤ ɠɟ

ɤɚɤ ɢ ɦɚɝɢɫɬɪɚɥɶɧɵɟ ɬɟɩɥɨɜɵɟ ɫɟɬɢ. ȼ ɬɚɤɢɯ ɫɢɫɬɟɦɚɯ ɨɛɦɟɧ ɬɟɩɥɨɬɨɣ

ɦɟɠɞɭ ɢɫɬɨɱɧɢɤɚɦɢ ɢ ɬɪɚɧɡɢɬɧɨɣ ɬɟɩɥɨɦɚɝɢɫɬɪɚɥɶɸ, ɚ ɬɚɤɠɟ ɩɟɪɟɞɚɱɚ

ɬɟɩɥɨɬɵ ɢɡ ɦɚɝɢɫɬɪɚɥɢ ɩɨɬɪɟɛɢɬɟɥɸ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɬɟɩɥɨɨɛɦɟɧ-

ɧɢɤɢ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɬɢɩɚ.

ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ

ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɩɪɢɜɟɞɟɧɚ

ɧɚ ɪɢɫɭɧɤɟ 6.18. Ɍɚɤɚɹ ɫɯɟɦɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɤɚɠɞɨɦɭ ɭɱɚɫɬɧɢɤɭ ɩɪɨɰɟɫɫɚ

ɷɧɟɪɝɨɨɛɦɟɧɚ ɛɵɬɶ ɧɟɡɚɜɢɫɢɦɵɦ ɨɬ ɞɪɭɝɢɯ ɩɨ ɬɟɩɥɨɧɨɫɢɬɟɥɸ. ɗɬɨ ɨɡ-

ɧɚɱɚɟɬ, ɱɬɨ ɤɚɱɟɫɬɜɨ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɤɨɥɢɱɟɫɬɜɨ ɞɥɹ ɩɨɞɩɢɬɤɢ, ɚ ɡɧɚɱɢɬ

ɢ ɧɚɞɟɠɧɨɫɬɶ ɪɚɛɨɬɵ ɩɪɢɧɚɞɥɟɠɚɳɟɝɨ ɜɥɚɞɟɥɶɰɭ ɨɛɨɪɭɞɨɜɚɧɢɹ, ɨɩɪɟ-

ɞɟɥɹɟɬɫɹ ɢɦ ɫɚɦɢɦ.

Ɇɚɝɢɫɬɪɚɥɶɧɚɹ ɬɟɩɥɨɜɚɹ ɫɟɬɶ, ɹɜɥɹɹɫɶ ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɨɤɭɩɚɬɟɥɟɦ

ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɢ

ɩɪɨɞɚɜɰɨɦ ɟɟ ɩɨɬɪɟɛɢɬɟɥɹɦ, ɨɛɟɫɩɟ-

ɱɢɜɚɟɬ ɧɚɞɟɠɧɨɫɬɶ ɪɚɛɨɬɵ ɫɜɨɟɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɦɢɧɢɦɢɡɚɰɢɟɣ ɩɨɬɟɪɶ

ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɢ ɩɨɜɵɲɟɧɢɟɦ ɤɚɱɟɫɬɜɚ ɩɨɞɩɢɬɨɱɧɨɣ ɜɨɞɵ.

ɉɨɬɪɟɛɢɬɟɥɢ ɬɟɩɥɚ ɩɨɥɭɱɚɸɬ ɟɝɨ ɱɟɪɟɡ ɬɟɩɥɨɨɛɦɟɧɧɨɟ ɨɛɨɪɭɞɨ-

ɜɚɧɢɟ, ɱɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɝɢɞɪɚɜɥɢɱɟɫɤɭɸ ɧɟɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɦɚɝɢɫɬɪɚɥɶ-

ɧɵɯ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ. Ʉɪɨɦɟ ɬɨɝɨ ɩɨɬɪɟɛɢɬɟɥɶ ɬɚɤɠɟ ɡɚɢɧɬɟɪɟɫɨɜɚɧ ɜ

ɦɚɤɫɢɦɚɥɶɧɨɦ ɫɧɢɠɟɧɢɢ ɜɟɥɢɱɢɧɵ ɩɨɞɩɢɬɤɢ ɫɜɨɟɝɨ ɤɨɧɬɭɪɚ. ɗɬɨ ɨɡɧɚ-

ɱɚɟɬ, ɱɬɨ

ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɞɨɥɠɧɨ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɩɨ ɡɚɤɪɵɬɨɣ

ɫɯɟɦɟ. Ⱦɥɹ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɞɨɥɠɧɚ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɜɨɞɚ ɢɡ ɝɨ-

ɪɨɞɫɤɨɝɨ ɜɨɞɨɩɪɨɜɨɞɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɤɚɱɟɫɬɜɚ.

Ɋɢɫ. 6.18. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɩɟɪɫɩɟɤɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ.

ɍɫɥɨɜɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ: ɉ – ɩɨɬɪɟɛɢɬɟɥɶ ɬɟɩɥɚ; ɂ – ɢɫɬɨɱɧɢɤ ɬɟɩɥɚ; ɉɆ – ɩɨɞɚɸ-

ɳɚɹ ɦɚɝɢɫɬɪɚɥɶ; ɈɆ – ɨɛɪɚɬɧɚɹ ɦɚɝɢɫɬɪɚɥɶ; ɋɇ – ɫɟɬɟɜɵɟ ɧɚɫɨɫɵ; ɌɈ – ɬɟɩɥɨɨɛ-

ɦɟɧɧɢɤɢ; ɋɁ – ɫɟɤɰɢɨɧɢɪɭɸɳɢɟ (ɪɚɡɞɟɥɢɬɟɥɶɧɵɟ) ɡɚɞɜɢɠɤɢ

Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɟɞɥɚɝɚɟɦɚɹ ɫɯɟɦɚ ɩɨɡɜɨɥɹɟɬ ɜ ɩɨɥɧɨɣ ɦɟɪɟ ɪɟɚɥɢ-

ɡɨɜɚɬɶ ɩɪɢɧɰɢɩɵ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɱɟɪɟɡ ɞɨɝɨɜɨɪɧɵɟ ɨɬɧɨɲɟɧɢɹ,

ɩɨɜɵɫɢɬɶ ɧɚɞɟɠɧɨɫɬɶ ɷɧɟɪɝɨɫɧɚɛɠɟɧɢɹ ɩɨɬɪɟɛɢɬɟɥɟɣ ɱɟɪɟɡ ɩɨɜɵɲɟɧɢɟ

ɧɚɞɟɠɧɨɫɬɢ ɪɚɛɨɬɵ ɷɥɟɦɟɧɬɨɜ ɫɢɫɬɟɦɵ. Ɉɞɧɚɤɨ ɞɥɹ ɪɟɚɥɢɡɚɰɢɢ ɬɚɤɨɣ

ɫɯɟɦɵ ɧɟɨɛɯɨɞɢɦɵ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɡɚɬɪɚɬɵ ɧɚ ɬɟɩɥɨɨɛɦɟɧɧɨɟ ɢ ɧɚɫɨɫ-

ɧɨɟ ɨɛɨɪɭɞɨɜɚɧɢɟ, ɤɨɬɨɪɵɟ ɱɚɫɬɢɱɧɨ ɤɨɦɩɟɧɫɢɪɭɸɬɫɹ ɫɧɢɠɟɧɢɟɦ ɡɚ-

ɬɪɚɬ ɧɚ ɩɨɞɝɨɬɨɜɤɭ ɩɨɞɩɢɬɨɱɧɨɣ ɜɨɞɵ ɞɥɹ ɜɫɟɯ ɤɨɧɬɭɪɨɜ ɫɢɫɬɟɦɵ. Ɂɧɚ-

ɱɢɬɟɥɶɧɨɟ ɫɨɤɪɚɳɟɧɢɟ ɢɡɞɟɪɠɟɤ ɜɨɡɦɨɠɧɨ ɡɚ ɫɱɟɬ ɫɧɢɠɟɧɢɹ ɡɚɬɪɚɬ ɧɚ

ɪɟɦɨɧɬ.

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɛɳɟɩɪɢɡɧɚɧɧɨɣ ɤɨɧɰɟɩɰɢɟɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɬɟ-

ɩɥɨɮɢɤɚɰɢɢ ɧɢɱɬɨ ɧɟ ɩɪɟɩɹɬɫɬɜɭɟɬ ɢɫɬɨɱɧɢɤɚɦ ɬɟɩɥɚ ɪɟɚɥɢɡɨɜɵɜɚɬɶ

ɤɨɦɛɢɧɢɪɨɜɚɧɧɵɣ ɰɢɤɥ

ɩɪɨɢɡɜɨɞɫɬɜɚ ɬɟɩɥɨɜɨɣ ɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪ-

ɝɢɢ. Ⱦɥɹ ɷɬɨɝɨ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɰɢɤɥɵ: ɩɚɪɨɬɭɪɛɢɧɧɵɣ, ɝɚɡɨ-

ɬɭɪɛɢɧɧɵɣ, ɩɚɪɨɝɚɡɨɜɵɣ, ɢ ɞɪɭɝɢɟ.

ȼ ɫɜɹɡɢ ɫ ɨɠɢɞɚɟɦɵɦ ɪɟɡɤɢɦ ɫɧɢɠɟɧɢɟɦ ɩɨɬɪɟɛɥɹɟɦɨɣ ɞɥɹ ɩɨɞ-

ɩɢɬɤɢ ɨɬɞɟɥɶɧɵɯ ɤɨɧɬɭɪɨɜ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɢɫɱɟɡɚɟɬ ɧɟ-

ɨɛɯɨɞɢɦɨɫɬɶ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɤɪɭɩɧɵɯ ɜɨɞɨɩɨɞɝɨɬɨɜɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ.

Ⱦɥɹ ɤɚɠɞɨɝɨ ɯɨɡɹɢɧɚ ɡɚɬɪɚɬɵ ɧɚ ɩɨɞɝɨɬɨɜɤɭ ɞɨɛɚɜɨɱɧɨɣ ɜɨɞɵ ɛɭɞɭɬ ɨɩ-

ɪɟɞɟɥɹɬɶɫɹ ɬɨɥɶɤɨ ɬɟɯɧɢɱɟɫɤɨɣ ɤɭɥɶɬɭɪɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɨɛɨɪɭɞɨɜɚɧɢɹ.

ɗɬɨ ɭɬɜɟɪɠɞɟɧɢɟ ɨɞɢɧɚɤɨɜɨ ɨɬɧɨɫɢɬɫɹ ɤɚɤ ɤ ɢɫɬɨɱɧɢɤɚɦ ɷɧɟɪɝɢɢ, ɬɚɤ ɢ

ɤ ɬɪɚɧɡɢɬɧɨɣ ɦɚɝɢɫɬɪɚɥɢ ɢ ɩɨɬɪɟɛɢɬɟɥɹɦ.

Ⱦɪɭɝɨɟ ɞɟɥɨ, ɱɬɨ ɧɚɥɢɱɢɟ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɬɪɟɛɭɟɬ ɪɟɲɟ-

ɧɢɹ ɩɪɨɛɥɟɦɵ ɨɬɥɨɠɟɧɢɹ ɫɨɥɟɣ ɧɚ ɩɨɜɟɪɯɧɨɫɬɹɯ ɧɚɝɪɟɜɚ ɜ ɩɨɞɨɝɪɟɜɚɬɟ-

ɥɹɯ. ȿɫɥɢ ɫɨ ɫɬɨɪɨɧɵ ɩɨɫɬɚɜɳɢɤɚ ɬɟɩɥɚ (ɬɪɚɧɡɢɬɧɨɣ ɦɚɝɢɫɬɪɚɥɢ) ɷɬɨɬ

ɜɨɩɪɨɫ ɪɟɲɚɟɬɫɹ ɡɚ ɫɱɟɬ

ɜɵɫɨɤɨɝɨ ɤɚɱɟɫɬɜɚ ɫɟɬɟɜɨɣ ɜɨɞɵ, ɬɨ ɫɨ ɫɬɨɪɨɧɵ

ɫɵɪɨɣ ɩɢɬɶɟɜɨɣ ɜɨɞɵ ɩɪɨɛɥɟɦɚ ɨɫɬɚɟɬɫɹ. ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ

ɞɥɹ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɩɢɬɶɟɜɭɸ ɜɨɞɭ ɬɪɟɛɭɟɬ ɫɨɯɪɚɧɟɧɢɹ ɟɟ ɯɢ-

ɦɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ. ɗɬɨ ɢɫɤɥɸɱɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɯɢɦɢɱɟ-

ɫɤɢɯ ɦɟɬɨɞɨɜ ɨɛɪɚɛɨɬɤɢ ɜɨɞɵ ɞɥɹ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ. ɉɪɟɞɩɨɱɬɟ-

ɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɨɬɞɚɧɨ ɛɟɡɪɟɚɝɟɧɬɧɵɦ ɦɟɬɨɞɚɦ ɨɛɪɚɛɨɬɤɢ ɜɨɞɵ, ɤɨɬɨ-

ɪɵɟ ɢɫɤɥɸɱɚɥɢ ɛɵ

ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɪɚɡɨɜɚɧɢɹ ɨɬɥɨɠɟɧɢɣ ɫɨɥɟɣ ɠɟɫɬɤɨ-

ɫɬɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɹɯ ɧɚɝɪɟɜɚ. Ɉɞɧɨ ɢɡ ɩɟɪɫɩɟɤɬɢɜɧɵɯ ɧɚɩɪɚɜɥɟɧɢɣ –

ɦɚɝɧɢɬɧɚɹ ɨɛɪɚɛɨɬɤɚ ɜɨɞɵ

Ɇɚɝɧɢɬɧɚɹ ɨɛɪɚɛɨɬɤɚ ɜɨɞɵ ɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɚɩɩɚɪɚɬɚɯ ɧɚ

Ɍɗɋ ɢ Ⱥɗɋ ɭ ɧɚɫ ɢ ɡɚ ɪɭɛɟɠɨɦ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɨɜɨɥɶɧɨ ɞɚɜɧɨ, ɧɨ ɲɢɪɨ-

ɤɨɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɧɟ ɩɨɥɭɱɢɥɚ ɢɡ-ɡɚ ɫɥɨɠɧɨɫɬɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɧɢɡ-

ɤɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ. ɋ ɩɨɹɜɥɟɧɢɟɦ

ɦɚɝɧɢɬɧɵɯ ɭɫɬɚɧɨɜɨɤ ɫ ɩɨɫɬɨɹɧɧɵɦɢ

ɦɚɝɧɢɬɧɵɦɢ ɩɨɥɹɦɢ ɢɧɬɟɪɟɫ ɤ ɷɬɢɦ ɭɫɬɚɧɨɜɤɚɦ ɜɨɡɪɨɫ.

Ɋɚɡɪɚɛɨɬɚɧɧɵɟ ɜ Ɍɉɍ ɭɫɬɪɨɣɫɬɜɚ ɞɥɹ ɦɚɝɧɢɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɜɨɞɵ

ɆȺȽɇɍɋɌ» (ɪɢɫ.6.19) ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɬɟɯɧɢɱɟɫɤɨɣ ɜɨɞɵ ɜ

ɬɟɩɥɨɜɵɯ ɫɢɫɬɟɦɚɯ ɞɥɹ ɜɨɞɨɝɪɟɣɧɵɯ ɤɨɬɥɨɜ, ɜɨɞɹɧɵɯ ɬɟɩɥɨɨɛɦɟɧɧɢɤɨɜ

ɢ ɨɯɥɚɞɢɬɟɥɟɣ, ɨɛɨɪɨɬɧɵɯ ɫɢɫɬɟɦ ɬɟɯɧɢɱɟɫɤɨɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ Ɍɗɋ [1].

S NN S

ȼɨɞɚ

Ɋɢɫ. 6.19. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ

ɫɯɟɦɚ ɚɩɩɚɪɚɬɚ ɞɥɹ ɦɚɝɧɢɬ-

ɧɨɣ ɨɛɪɚɛɨɬɤɢ ɜɨɞɵ ɫ ɩɨɫɬɨ-

ɹɧɧɵɦɢ ɦɚɝɧɢɬɚɦɢ:

1 – ɡɚɡɨɪ; 2 – ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɨ-

ɜɵɯ ɥɢɧɢɣ; 3

– ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɢ-

ɠɟɧɢɹ ɜɨɞɵ; 4

– ɩɨɫɬɨɹɧɧɵɣ

ɦɚɝɧɢɬ;

– ɤɨɪɩɭɫ

ɉɨɞɥɟɠɚɳɚɹ ɨɛɪɚɛɨɬɤɟ ɜɨɞɚ ɩɪɨɯɨɞɢɬ ɜ ɡɚɡɨɪɟ 1 ɚɩɩɚɪɚɬɚ, ɩɟɪɟɫɟ-

ɤɚɟɬ ɫɢɥɨɜɵɟ ɥɢɧɢɢ 2, ɝɞɟ ɩɨɞɜɟɪɝɚɟɬɫɹ ɜɨɡɞɟɣɫɬɜɢɸ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝ-

ɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɜ ɧɟɪɚɜɧɨɜɟɫɧɨɣ ɜɨɞɧɨɣ

ɫɪɟɞɟ (ɤɨɧɰɟɧɬɪɚɰɢɹ ɫɜɨɛɨɞɧɨɝɨ ɞɢɨɤɫɢɞɚ ɭɝɥɟɪɨɞɚ ɦɟɧɶɲɟ ɪɚɜɧɨɜɟɫɧɨɣ

ɪɚɜɧ

ɫɜɨɛ

CaCOCaCO 

) ɨɛɪɚɡɭɸɬɫɹ ɰɟɧɬɪɵ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɫɨɥɟɣ

CaCO

. ɗɬɨɬ ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ ɥɢɲɶ ɜ ɦɨɦɟɧɬ ɜɨɡɞɟɣɫɬɜɢɹ ɦɚɝɧɢɬɧɨ-

ɝɨ ɩɨɥɹ. ɉɪɢ ɩɨɫɥɟɞɭɸɳɟɦ ɧɚɝɪɟɜɚɧɢɢ ɩɨ ɜɵɯɨɞɟ ɢɡ ɚɩɩɚɪɚɬɚ ɬɜɟɪɞɚɹ

ɮɚɡɚ ɜɵɞɟɥɹɟɬɫɹ ɜ ɦɚɫɫɟ ɜɨɞɵ ɜ ɜɢɞɟ ɲɥɚɦɚ. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɨɛɪɚɛɨɬɤɢ

ɜɨɞɵ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɧɚɩɪɹɠɟɧ-

ɧɨɫɬɶɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɡɚɡɨɪɟ, ɫɤɨɪɨɫɬɶɸ ɞɜɢɠɟɧɢɹ ɜɨɞɵ, ɭɝɥɨɦ ɦɟɠ-

ɞɭ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɞɜɢɠɟɧɢɹ ɜɨɞɵ

ɢ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɱɢɫɥɨɦ

ɩɟɪɟɫɟɱɟɧɢɣ ɢ ɜɪɟɦɟɧɟɦ ɤɨɧɬɚɤɬɚ ɜɨɞɵ ɫ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ.

ɗɬɚ ɭɫɬɚɧɨɜɤɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɚɝɧɢɬɧɵɣ ɞɢɧɚɦɢɱɟɫɤɢɣ ɪɟ-

ɚɤɬɨɪ ɢ ɢɦɟɟɬ ɨɪɢɝɢɧɚɥɶɧɨɟ ɬɟɯɧɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ, ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɩɪɢɧ-

ɰɢɩɢɚɥɶɧɨ ɧɨɜɵɯ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɹɯ ɨ ɫɜɨɣɫɬɜɚɯ ɦɚɝ-

ɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɨɞɬɜɟɪɠɞɟɧɧɵɦɢ ɦɧɨɝɨɱɢɫɥɟɧɧɵɦɢ ɢɫɫɥɟɞɨɜɚɧɢɹɦɢ.

Ɉɬɥɢɱɢɟ ɭɫɬɪɨɣɫɬɜ «

ɆȺȽɇɍɋɌ» ɨɬ ɤɥɚɫɫɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɨɤ – ɜ

ɫɬɪɭɤɬɭɪɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɦɟɠɞɭ ɫɨɛɨɣ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɱɬɨ ɩɨɞ-

ɬɜɟɪɠɞɟɧɨ ɩɚɬɟɧɬɨɦ ɊɎ ʋ 2092446. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɭɫɬɚɧɨɜɤɢ

ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 6.2. Ɍɢɩɨɪɚɡɦɟɪɵ ɜɵɩɭɫɤɚɟɦɵɯ ɚɩɩɚɪɚɬɨɜ ɩɪɟɞɫɬɚɜɥɟ-

ɧɵ ɜ ɬɚɛɥ. 6.1. ȼɵɛɨɪ ɦɚɝɧɢɬɧɨɣ ɭɫɬɚɧɨɜɤɢ (Ɇɍ) ɩɪɨɜɨɞɢɬɫɹ ɩɨ ɬɚɛɥɢɰɟ

ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɢɚɦɟɬɪɚ ɩɪɨɯɨɞɧɨɝɨ ɫɟɱɟɧɢɹ ɩɪɢɦɟɧɹɟɦɵɯ ɬɪɭɛ.

Ɇɨɞɟɥɢ

ɆȺȽɇɍɋɌ 100/ɏ, 120/ɏ 273/ɏ, 427/ɏ ɨɬɥɢɱɚɸɬɫɹ ɞɢɚɦɟɬɪɚɦɢ

ɤɨɪɩɭɫɨɜ ɢ ɬɢɩɚɦɢ ɦɚɝɧɢɬɧɵɯ ɫɢɫɬɟɦ. Ɇɚɝɧɢɬɧɵɟ ɫɢɫɬɟɦɵ ɢɦɟɸɬ ɢɧ-

ɞɢɜɢɞɭɚɥɶɧɵɟ ɨɬɥɢɱɢɹ, ɫɜɹɡɚɧɧɵɟ ɫ ɨɫɨɛɟɧɧɨɫɬɹɦɢ ɨɛɪɚɛɚɬɵɜɚɟɦɨɣ ɜɨ-

ɞɵ ɢ ɩɚɪɚɦɟɬɪɚɦɢ ɷɤɫɩɥɭɚɬɢɪɭɟɦɨɣ ɝɢɞɪɚɜɥɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ. Ɇɚɤɫɢ-

ɦɚɥɶɧɨɟ ɪɚɛɨɱɟɟ ɞɚɜɥɟɧɢɟ ɞɥɹ ɷɤɫɩɥɭɚɬɚɰɢɢ

– 16 ɚɬɦ.