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1,5

1,4

1,3

1,2

1,1

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

Ɋɢɫ. 5.13. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɟɡɟɪɜɢɪɨɜɚɧɢɹ ɨɬ ɱɢɫɥɚ ɫɟɤɰɢɣ ɦɚɝɢ-

ɫɬɪɚɥɶɧɨɣ ɫɟɬɢ

Ʉɚɤ ɜɢɞɧɨ ɢɡ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɨɝɨ ɝɪɚɮɢɤɚ, ɩɪɢ ɚɜɚɪɢɣɧɨɦ ɜɵɤɥɸ-

ɱɟɧɢɢ ɭɱɚɫɬɤɚ

IIȺ ɜ ɤɨɧɟɱɧɵɯ ɬɨɱɤɚɯ ɦɚɝɢɫɬɪɚɥɢ ɩɨɞɞɟɪɠɢɜɚɸɬɫɹ ɪɚɫ-

ɩɨɥɚɝɚɟɦɵɟ ɧɚɩɨɪɵ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɧɨɪɦɚɥɶɧɨɣ ɪɚɛɨɬɵ ɚɛɨɧɟɧɬɨɜ.

Ȼɟɡ ɭɱɟɬɚ ɪɟɡɟɪɜɢɪɨɜɚɧɢɹ ɬɚɤɢɟ ɪɟɠɢɦɵ ɪɟɚɥɢɡɨɜɚɬɶ ɧɟɜɨɡɦɨɠɧɨ. ɉɪɢ

ɭɱɟɬɟ ɪɟɡɟɪɜɢɪɨɜɚɧɢɹ ɩɨɜɵɲɚɟɬɫɹ ɝɢɞɪɚɜɥɢɱɟɫɤɚɹ ɭɫɬɨɣɱɢɜɨɫɬɶ ɫɢɫɬɟ-

ɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ, ɬɚɤ ɤɚɤ ɫɭɳɟɫɬɜɟɧɧɨ ɜɨɡɪɚɫɬɚɟɬ ɪɚɫɩɨɥɚɝɚɟɦɵɣ

ɧɚɩɨɪ ɜ ɤɨɧɟɱɧɵɯ ɬɨɱɤɚɯ ɦɚɝɢɫɬɪɚɥɶɧɨɣ ɫɟɬɢ ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɪɟɠɢɦɟ.

5.10. Ɋɚɫɱɟɬ ɞɥɢɧɧɵɯ ɬɪɚɧɡɢɬɧɵɯ ɩɚɪɨ- ɢ ɝɚɡɨɩɪɨɜɨɞɨɜ

ɉɪɢ ɬɪɚɧɫɩɨɪɬɟ ɭɩɪɭɝɨɣ ɫɪɟɞɵ (ɝɚɡɚ ɢɥɢ ɩɚɪɚ) ɩɨ ɞɥɢɧɧɵɦ ɬɪɭɛɨ-

ɩɪɨɜɨɞɚɦ ɩɪɨɢɫɯɨɞɢɬ ɡɚɦɟɬɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜɞɨɥɶ ɬɪɭɛɨɩɪɨɜɨɞɚ.

ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɭɞɟɥɶɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɩɚɪɚ ɩɟɪɟɦɟɧɧɨ, ɬɚɤ

ɤɚɤ ɩɥɨɬɧɨɫɬɶ ɫɪɟɞɵ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɟɟ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɹɸɬɫɹ ɩɨ

ɞɥɢɧɟ ɬɪɭɛɨɩɪɨɜɨɞɚ.

l

Ɋɢɫ.5.14. ɋɯɟɦɚ ɥɢɧɢɢ ɩɟɪɟɝɪɟɬɨɝɨ ɩɚɪɚ

Ɋɚɫɫɦɨɬɪɢɦ, ɤɚɤ ɢɡɦɟɧɹɟɬɫɹ ɞɚɜɥɟɧɢɟ ɫɪɟɞɵ ɩɨ ɞɥɢɧɟ ɬɪɭɛɨɩɪɨ-

ɜɨɞɚ. ɉɭɫɬɶ ɝɚɡ ɢɥɢ ɩɚɪ ɞɜɢɠɟɬɫɹ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ ɞɥɢɧɨɣ

L ɨɬ ɬɨɱɤɢ 1

ɬɨɱɤɟ 2 (ɪɢɫ. 5.14). ɋɨɫɬɨɹɧɢɟ ɫɪɟɞɵ ɜ ɬɨɱɤɟ 1 ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɚɜɥɟɧɢ-

ɟɦ

, ɚɛɫɨɥɸɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍ

ɢ ɩɥɨɬɧɨɫɬɶɸ ȡ

Ɉɛɨɡɧɚɱɢɦ ɭɞɟɥɶɧɭɸ ɥɢɧɟɣɧɭɸ ɩɨɬɟɪɸ ɞɚɜɥɟɧɢɹ ɜ ɧɚɱɚɥɟ ɬɪɭ-

ɛɨɩɪɨɜɨɞɚ ɱɟɪɟɡ

ɢ ɞɨɥɸ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ ɞɚɜɥɟɧɢɹ ɱɟɪɟɡ ɚ. ȼɵɞɟɥɢɦ

ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɭɱɚɫɬɨɤ ɞɥɢɧɨɣ

ɞl. Ɉɛɨɡɧɚɱɢɦ ɫɪɟɞ-

ɧɟɟ ɞɚɜɥɟɧɢɟ ɫɪɟɞɵ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɱɟɪɟɡ

ɪ, ɬɟɦɩɟɪɚɬɭɪɭ ɱɟɪɟɡ Ɍ, ɩɥɨɬ-

ɧɨɫɬɶ ɱɟɪɟɡ ȡ ɢ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɱɟɪɟɡ

ɞɪ.

Ɍɚɤ ɤɚɤ ɭɞɟɥɶɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ

ɩɥɨɬɧɨɫɬɢ ɫɪɟɞɵ, ɬɨ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɚ ɭɱɚɫɬɤɟ

ɞl ɫɨɫɬɚɜɢɬ

lRp w

D w

)1(

(5.22)

Ɂɧɚɤ ɦɢɧɭɫ ɜ ɥɟɜɨɣ ɱɚɫɬɢ (5.22) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɚɞɟɧɢɸ ɞɚɜɥɟɧɢɹ.

ɉɪɢɧɢɦɚɹ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɩɥɨɬɧɨɫɬɶ ɫɪɟɞɵ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨ-

ɧɚɥɶɧɨɣ ɞɚɜɥɟɧɢɸ ɢ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɚɛɫɨɥɸɬɧɨɣ ɬɟɦɩɟɪɚ-

ɬɭɪɟ, ɩɨɥɭɱɚɟɦ



(5.23)

ɨɬɤɭɞɚ

Rp wD w

)1(

ɢɥɢ

pRpp

wD w

)1(

(5.24)

ɉɪɨɢɧɬɟɝɪɢɪɭɟɦ (5.24) ɜ ɩɪɟɞɟɥɚɯ ɢɡɦɟɧɟɧɢɹ ɞɚɜɥɟɧɢɹ ɨɬ ɪ

ɞɨ ɪ

ɢ ɞɥɢɧɵ ɬɪɭɛɨɩɪɨɜɨɞɚ ɨɬ L ɞɨ 0

³³

wD w

)1(

pRpp

ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ

ɫɪ

)1(

D 

(5.25ɚ)

ɉɨɫɥɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɧɟɱ-

ɧɨɝɨ ɞɚɜɥɟɧɢɹ ɫɪɟɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ

ɫɪ

)1(2

D



(5.26ɚ)

ɉɨ (5.26ɚ) ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɞɚɜɥɟɧɢɟ ɜ ɤɨɧɰɟ ɩɚɪɨɩɪɨɜɨɞɚ ɞɥɢ-

ɧɨɣ L ɩɨ ɡɚɞɚɧɧɵɦ ɩɚɪɚɦɟɬɪɚɦ ɩɚɪɚ ɪ

, Ɍ

ɢ ɭɞɟɥɶɧɨɦɭ ɥɢɧɟɣɧɨɦɭ ɩɚ-

ɞɟɧɢɸ ɞɚɜɥɟɧɢɹ R

ɜ ɧɚɱɚɥɟ ɩɚɪɨɩɪɨɜɨɞɚ. ɉɨɫɤɨɥɶɤɭ

ɬɨ ɜɵɪɚɠɟɧɢɟ (5.25ɚ) ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɫɥɟɞɭɸɳɟɣ ɦɨɞɢɮɢ-

ɤɚɰɢɢ:

ɫɪ

)1(

D 

(5.25ɛ)

ɝɞɟ R

– ɭɞɟɥɶɧɨɟ ɥɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɤɨɧɰɟ ɩɚɪɨɩɪɨɜɨɞɚ.

ɇɚ ɨɫɧɨɜɟ (5.25ɛ) ɜɵɜɨɞɢɬɫɹ ɮɨɪɦɭɥɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɞɚɜɥɟɧɢɹ

ɩɚɪɚ ɜ ɧɚɱɚɥɟ ɩɚɪɨɩɪɨɜɨɞɚ ɪ

ɩɨ ɡɚɞɚɧɧɵɦ ɩɚɪɚɦɟɬɪɚɦ ɪ

, Ɍ

ɢ ɭɞɟɥɶ-

ɧɨɦɭ ɥɢɧɟɣɧɨɦɭ ɩɚɞɟɧɢɸ ɞɚɜɥɟɧɢɹ R

ɜ ɤɨɧɰɟ ɩɚɪɨɩɪɨɜɨɞɚ:

ɫɪ

)1(2

D



(5.26ɛ)

Ɉɬɧɨɲɟɧɢɟ Ɍ

ɫɪ

/ Ɍ

ɜɵɛɢɪɚɟɬɫɹ ɧɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ ɬɟɩɥɨɜɨɝɨ

ɪɚɫɱɟɬɚ ɬɪɭɛɨɩɪɨɜɨɞɚ. ɉɪɢ ɪɚɫɱɟɬɟ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ

ɦɨɠɧɨ ɨɬɧɨɲɟɧɢɟ Ɍ

ɫɪ

/ Ɍ

ɩɪɢɧɢɦɚɬɶ ɪɚɜɧɵɦ ɟɞɢɧɢɰɟ.

ɍɪɚɜɧɟɧɢɟ (5.25ɛ) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɬɚɤɠɟ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ:

ɫɪ

1ɭɩ

)1( D G

(5.27)

ɝɞɟ

21ɭɩ

ppp  G

– ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɭɩɪɭɝɨɣ ɫɪɟɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ;

2/)(

21ɫɪ

ppp 

– ɫɪɟɞɧɟɟ ɞɚɜɥɟɧɢɟ ɫɪɟɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ,

2/)(

21ɫɪ

TTT 

– ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɫɪɟɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ.

ɉɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɟɭɩɪɭɝɨɣ ɫɪɟɞɵ ɩɪɢ ɬɟɯ ɠɟ ɡɧɚɱɟɧɢɹɯ R

, ɚ, L

LRp )1(

1ɧ

D G

(5.28)

Ɉɬɧɨɲɟɧɢɟ ɩɚɞɟɧɢɹ ɞɚɜɥɟɧɢɹ ɭɩɪɭɝɨɣ ɫɪɟɞɵ ɤ ɩɚɞɟɧɢɸ ɞɚɜɥɟɧɢɹ ɧɟ-

ɭɩɪɭɝɨɣ ɫɪɟɞɵ ɩɪɢ ɨɞɧɢɯ ɢ ɬɟɯ ɠɟ ɡɧɚɱɟɧɢɹɯ R

, ɚ, L

ɫɪ

ɭɩ

(5.29)

ɇɚ ɪɢɫ. 5.15 ɩɨɤɚɡɚɧ ɯɚɪɚɤɬɟɪ

ɢɡɦɟɧɟɧɢɹ ɞɚɜɥɟɧɢɹ ɧɟɭɩɪɭɝɨɣ ɇ ɢ

ɭɩɪɭɝɨɣ ɍɉ ɫɪɟɞɵ ɜɞɨɥɶ ɬɪɭɛɨɩɪɨ-

ɜɨɞɚ. ɉɪɢ ɞɜɢɠɟɧɢɢ ɧɟɭɩɪɭɝɨɣ ɫɪɟ-

ɞɵ

const/ G lp

, ɭɩɪɭɝɨɣ

var/ G lp

ȿɫɥɢ ɡɚɞɚɧɵ ɩɚɪɚɦɟɬɪɵ

ɬɪɚɧɫɩɨɪɬɢɪɭɟɦɨɣ ɫɪɟɞɵ p

ɢ T

ɧɚɱɚɥɟ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢ ɞɚɜɥɟɧɢɟ ɪ

ɤɨɧɰɟ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɬɨ ɧɚ ɨɫɧɨɜɟ

(5.26) ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɭɞɟɥɶɧɨɟ

ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɧɚɱɚɥɟ ɬɪɭɛɨ-

ɩɪɨɜɨɞɚ R

, ɩɨ ɤɨɬɨɪɨɦɭ ɞɨɥɠɟɧ

ɜɵɛɢɪɚɬɶɫɹ ɟɝɨ ɞɢɚɦɟɬɪ

ɍɉ

Ɋɢɫ. 5.15. ɏɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ

ɞɚɜɥɟɧɢɹ ɜɞɨɥɶ ɬɪɭɛɨɩɪɨɜɨɞɚ ɫ

ɧɟɭɩɪɭɝɨɣ ɇ ɢ ɭɩɪɭɝɨɣ ɍɉ ɫɪɟɞɨɣ

ɂɡ ɫɨɜɦɟɫɬɧɨɝɨ ɪɟɲɟɧɢɹ (5.10) ɢ (5.23) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟ-

ɧɢɟ ɞɥɹ ɪɚɫɱɟɬɚ ɞɨɥɢ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ ɞɚɜɥɟɧɢɹ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ,

ɬɪɚɧɫɩɨɪɬɢɪɭɸɳɢɯ ɭɩɪɭɝɢɟ ɫɪɟɞɵ,

ɫɪ

15,1

(5.31)

ɝɞɟ G – ɪɚɫɯɨɞ ɫɪɟɞɵ, ɤɝ/ɫ;

– ɩɥɨɬɧɨɫɬɶ ɫɪɟɞɵ ɜ ɧɚɱɚɥɟ ɩɚɪɨɩɪɨɜɨɞɚ,

ɤɝ/ɦ ', ɪ

– ɞɚɜɥɟɧɢɟ ɜ ɧɚɱɚɥɟ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢ ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɣ ɜ

ɬɪɭɛɨɩɪɨɜɨɞɟ, ɉɚ.

Ⱦɢɚɦɟɬɪ ɬɪɭɛɨɩɪɨɜɨɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ (5.8) ɩɨ ɡɚɞɚɧɧɨɦɭ ɪɚɫɯɨ-

ɞɭ G, ɭɞɟɥɶɧɨɦɭ ɥɢɧɟɣɧɨɦɭ ɩɚɞɟɧɢɸ ɞɚɜɥɟɧɢɹ ɜ ɧɚɱɚɥɟ ɬɪɭɛɨɩɪɨɜɨɞɚ

, ɩɥɨɬɧɨɫɬɢ ɫɪɟɞɵ ɜ ɧɚɱɚɥɟ ɬɪɭɛɨɩɪɨɜɨɞɚ

Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ɢ ɡɚɞɚɧɢɹ

ɂɡ ɤɚɤɨɝɨ ɭɫɥɨɜɢɹ ɜɵɛɢɪɚɟɬɫɹ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɫɟɤɰɢɨɧɢɪɭɸ-

ɳɢɦɢ ɡɚɞɜɢɠɤɚɦɢ ɦɚɝɢɫɬɪɚɥɶɧɵɯ ɜɨɞɹɧɵɯ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ?

Ʉɚɤɨɜɚ ɨɫɧɨɜɧɚɹ ɰɟɥɶ ɛɥɨɤɢɪɨɜɤɢ ɫɦɟɠɧɵɯ ɦɚɝɢɫɬɪɚɥɟɣ ɜɨɞɹɧɵɯ

ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ? ɂɡɨɛɪɚɡɢɬɟ ɩɪɢɧɰɢɩɢɚɥɶɧɭɸ ɫɯɟɦɭ ɬɚɤɨɣ ɛɥɨɤɢ-

ɪɨɜɤɢ. ɉɨɱɟɦɭ ɛɥɨɤɢɪɭɸɬɫɹ ɬɪɭɛɨɩɪɨɜɨɞɵ ɬɨɥɶɤɨ ɛɨɥɶɲɢɯ ɞɢɚ-

ɦɟɬɪɨɜ?

ɇɚɩɢɲɢɬɟ ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɞɥɹ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɞɜɢɠɟɧɢɹ ɧɟ-

ɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɩɨ ɭɱɚɫɬɤɭ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɇɚɡɨɜɢɬɟ ɡɧɚɱɟɧɢɹ

ɢ ɪɚɡɦɟɪɧɨɫɬɢ ɱɥɟɧɨɜ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ.

Ʉɚɤɚɹ ɫɜɹɡɶ ɦɟɠɞɭ ɧɚɩɨɪɨɦ ɢ ɞɚɜɥɟɧɢɟɦ? Ʉɚɤɢɟ ɪɚɡɦɟɪɧɨɫɬɢ

ɢɦɟɸɬ ɷɬɢ ɩɚɪɚɦɟɬɪɵ? Ʉɚɤ ɨɧɢ ɜɡɚɢɦɧɨ ɩɟɪɟɫɱɢɬɵɜɚɸɬɫɹ?

ɇɚɩɢɲɢɬɟ ɮɨɪɦɭɥɭ Ⱦɚɪɫɢ ɞɥɹ ɪɚɫɱɟɬɚ ɭɞɟɥɶɧɨɝɨ ɥɢɧɟɣɧɨɝɨ ɩɚɞɟ-

ɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ. ɇɚɡɨɜɢɬɟ ɡɧɚɱɟɧɢɹ ɢ ɪɚɡɦɟɪɧɨɫɬɢ

ɱɥɟɧɨɜ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ.

ɑɬɨ ɬɚɤɨɟ ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɫɬɟɧɤɢ

ɬɪɭɛɨɩɪɨɜɨɞɚ?

)1(

ɫɪ

D

(5.30)

7. Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɟɫɬɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ? ɉɨ-

ɱɟɦɭ ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɞɥɢɧɚ ɦɟɫɬɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ

ɞɢɚɦɟɬɪɚ ɬɪɭɛɨɩɪɨɜɨɞɚ? ɂɡ ɤɚɤɢɯ ɭɪɚɜɧɟɧɢɣ ɷɬɨ ɫɥɟɞɭɟɬ?

ɂɡɥɨɠɢɬɟ ɨɫɧɨɜɧɵɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɪɟɠɢɦɭ ɞɚɜɥɟɧɢɣ ɜɨɞɹɧɵɯ ɬɟɩ-

ɥɨɜɵɯ ɫɟɬɟɣ ɢɡ ɭɫɥɨɜɢɹ ɧɚɞɟɠɧɨɫɬɢ ɪɚɛɨɬɵ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟ-

ɧɢɹ.

Ʉɚɤɨɟ ɩɪɟɢɦɭɳɟɫɬɜɨ ɢɦɟɟɬ ɭɫɬɚɧɨɜɥɟɧɢɟ ɨɛɲɟɣ ɫɬɚɬɢɱɟɫɤɨɣ ɡɨɧɵ

ɞɥɹ ɜɫɟɣ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ? ȼɫɟɝɞɚ ɥɢ ɜɨɡɦɨɠɧɨ ɬɚɤɨɟ ɪɟ-

ɲɟɧɢɟ? ɑɟɦ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɬɚɤɚɹ ɜɨɡɦɨɠɧɨɫɬɶ?

10.

ɇɚ ɨɫɧɨɜɟ ɤɚɤɢɯ ɭɫɥɨɜɢɣ ɧɚ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɝɪɚɮɢɤ ɧɚɧɨɫɹɬɫɹ

ɭɪɨɜɧɢ ɞɨɩɭɫɬɢɦɵɯ ɦɚɤɫɢɦɚɥɶɧɵɯ ɢ ɦɢɧɢɦɚɥɶɧɵɯ ɩɶɟɡɨɦɟɬɪɢɱɟ-

ɫɤɢɯ ɧɚɩɨɪɨɜ ɞɥɹ ɩɨɞɚɸɳɟɣ ɢ ɨɛɪɚɬɧɨɣ ɥɢɧɢɣ ɫɢɫɬɟɦɵ ɬɟɩɥɨ-

ɫɧɚɛɠɟɧɢɹ?

11.

ɂɡ ɤɚɤɢɯ ɭɫɥɨɜɢɣ ɜɵɛɢɪɚɸɬɫɹ ɫɯɟɦɵ ɩɪɢɫɨɟɞɢɧɟɧɢɹ ɭɫɬɚɧɨɜɨɤ ɤ

ɜɨɞɹɧɵɦ ɬɟɩɥɨɜɵɦ ɫɟɬɹɦ?

12.

ɉɪɢɜɟɞɢɬɟ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɪɚɡ-

ɜɟɬɜɥɟɧɧɨɣ ɜɨɞɹɧɨɣ ɬɟɩɥɨɜɨɣ ɫɟɬɢ. Ʉɚɤɨɜɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ

ɨɬ- ɞɟɥɶɧɵɯ ɪɚɫɱɟɬɧɵɯ ɨɩɟɪɚɰɢɣ?

13.

ɉɪɢɜɟɞɢɬɟ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɪɚɡ-

ɜɟɬɜɥɟɧɧɨɣ ɩɚɪɨɜɨɣ ɫɟɬɢ. ȼ ɱɟɦ ɫɨɫɬɨɢɬ ɦɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ?

14.

ɉo ɤɚɤɨɦɭ ɪɚɫɯɨɞɭ ɜɨɞɵ ɜɵɛɢɪɚɸɬɫɹ ɞɢɚɦɟɬɪɵ ɬɟɩɥɨɜɨɣ ɫɟɬɢ

ɜ ɨɬɤɪɵɬɵɯ ɫɢɫɬɟɦɚɯ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ?

15.

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɛɨɱɢɣ ɧɚɩɨɪ ɫɟɬɟɜɵɯ ɧɚɫɨɫɨɜ ɜɨɞɹɧɨɣ ɬɟɩɥɨ-

ɜɨɣ ɫɟɬɢ? ɂɡ ɤɚɤɢɯ ɫɥɚɝɚɟɦɵɯ ɨɧ ɫɨɫɬɨɢɬ?

16.

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɛɨɱɢɣ ɧɚɩɨɪ ɩɨɞɩɢɬɨɱɧɵɯ ɧɚɫɨɫɨɜ ɜ ɨɬɤɪɵɬɵɯ

ɫɢɫɬɟɦɚɯ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ?

17.

ɉɨ ɤɚɤɨɦɭ ɪɚɫɯɨɞɭ ɫɟɬɟɜɨɣ ɜɨɞɵ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɪɨɟɤɬɧɚɹ ɩɨɞɚ-

ɱɚ ɫɟɬɟɜɵɯ ɧɚɫɨɫɨɜ? Ʉɚɤɨɟ ɞɨɩɭɫɤɚɟɬɫɹ ɦɢɧɢɦɚɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ

ɫɟɬɟɜɵɯ ɧɚɫɨɫɨɜ ɧɚ ɫɬɚɧɰɢɢ?

18.

ȼ ɱɟɦ ɫɨɫɬɨɢɬ ɦɟɬɨɞ ɨɩɪɟɞɟɥɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɤɨɧɰɟ ɞɥɢɧɧɨɝɨ ɬɪɚɧ-

ɡɢɬɧɨɝɨ ɩɚɪɨɩɪɨɜɨɞɚ?

6. Ƚɢɞɪɚɜɥɢɱɟɫɤɢɣ ɪɟɠɢɦ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ

6.1. Ƚɢɞɪɚɜɥɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɢɫɬɟɦɵ

ȼɨɞɹɧɵɟ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɫɥɨɠɧɵɟ

ɝɢɞɪɚɜɥɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɵɯ ɪɚɛɨɬɚ ɨɬɞɟɥɶɧɵɯ ɡɜɟɧɶɟɜ ɧɚɯɨ-

ɞɢɬɫɹ ɜɨ ɜɡɚɢɦɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ. Ⱦɥɹ ɩɪɚɜɢɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɢ ɪɟɝɭɥɢ-

ɪɨɜɚɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɝɢɞɪɚɜɥɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɚɛɨɬɚɸɳɟ-

ɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ – ɰɢɪɤɭɥɹɰɢɨɧɧɵɯ ɧɚɫɨɫɨɜ ɢ ɫɟɬɢ.

Ƚɢɞɪɚɜɥɢɱɟɫɤɢɣ ɪɟɠɢɦ, ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɱɤɨɣ ɩɟɪɟɫɟɱɟ-

ɧɢɹ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɧɚɫɨɫɚ ɢ ɫɟɬɢ. ɇɚ ɪɢɫ. 6.1 ɤɪɢɜɚɹ 1 –

ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɫɨɫɚ; ɤɪɢɜɚɹ 2 – ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɟɩɥɨɜɨɣ ɫɟɬɢ; ɬɨɱɤɚ

Ⱥ – ɩɟɪɟɫɟɱɟɧɢɟ ɷɬɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɨɩɪɟɞɟɥɹɟɬ ɝɢɞɪɚɜɥɢɱɟɫɤɢɣ ɪɟɠɢɦ

ɫɢɫɬɟɦɵ; ɇ – ɧɚɩɨɪ, ɪɚɡɜɢɜɚɟɦɵɣ ɧɚɫɨɫɨɦ, ɪɚɜɧɵɣ ɩɨɬɟɪɟ ɧɚɩɨɪɚ ɜ

ɡɚɦɤɧɭɬɨɣ ɫɢɫɬɟɦɟ; V – ɨɛɴɟɦɧɚɹ ɩɨɞɚɱɚ ɧɚɫɨɫɚ, ɪɚɜɧɚɹ ɪɚɫɯɨɞɭ ɜɨɞɵ ɜ

ɫɢɫɬɟɦɟ.

Ɋɚɫɯɨɞ ɜɨɞɵ

Ɋɢɫ. 6.1. Ƚɢɞɪɚɜɥɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɫɨɫɚ ɢ ɬɟɩɥɨɜɨɣ ɫɟɬɢ

Ƚɢɞɪɚɜɥɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɧɚɫɨɫɚ ɧɚɡɵɜɚɟɬɫɹ ɡɚɜɢɫɢ-

ɦɨɫɬɶ ɧɚɩɨɪɚ ɇ ɢɥɢ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɣ ¨ɪ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɧɚɫɨɫɨɦ, ɨɬ

ɨɛɴɟɦɧɨɣ ɩɨɞɚɱɢ ɧɚɫɨɫɚ V. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɫɨɫɨɜ ɨɛɵɱɧɨ ɨɩɪɟɞɟ-

ɥɹɸɬɫɹ ɡɚɜɨɞɚɦɢ-ɢɡɝɨɬɨɜɢɬɟɥɹɦɢ ɢɥɢ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɵ ɩɨ ɞɚɧ-

ɧɵɦ ɢɫɩɵɬɚɧɢɹ.

ɉɪɢ ɩɨɫɬɨɹɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ ɪɚɛɨɱɢɣ ɭɱɚ-

ɫɬɨɤ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɛɥɢɠɟɧɧɨ

ɨɩɢɫɚɧ

ɭɪɚɜɧɟɧɢɟɦ

VsHH 

(6.1)

ɝɞɟ H

– ɭɫɥɨɜɧɵɣ ɧɚɩɨɪ ɧɚɫɨɫɚ ɩɪɢ ɪɚɫɯɨɞɟ V = 0; s

– ɭɫɥɨɜɧɨɟ

ɜɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɧɚɫɨɫɚ, ɦ · ɫ

/ɦ

ȼ ɩɪɢɥɨɠɟɧɢɹɯ 12–13 ɩɪɢɜɟɞɟɧɵ ɬɟɯɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

ɪɹɞɚ ɫɟɬɟɜɵɯ ɧɚɫɨɫɨɜ, ɩɪɢɦɟɧɹɟɦɵɯ ɜ ɫɨɜɪɟɦɟɧɧɵɯ ɬɟɩɥɨɮɢɤɚɰɢɨɧɧɵɯ

ɫɢɫɬɟɦɚɯ.

ɉɪɢ ɩɨɫɬɨɹɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɧɚɫɨ-

ɫɨɦ,

,)1(

 x

xNN

(6.2)

ɝɞɟ V

, N

– ɩɨɞɚɱɚ ɢ ɦɨɳɧɨɫɬɶ ɧɚɫɨɫɚ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ (ɩɪɢ

ɦɚɤɫɢɦɚɥɶɧɨɦ ɄɉȾ); N – ɦɨɳɧɨɫɬɶ ɧɚɫɨɫɚ ɩɪɢ ɩɨɞɚɱɟ V, ɯ = N

/ N

–

ɤɨɷɮɮɢɰɢɟɧɬ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ; N

– ɦɨɳɧɨɫɬɶ ɧɚɫɨɫɚ ɩɪɢ ɯɨɥɨɫɬɨɦ

ɯɨɞɟ (V = 0). Ʉɨɷɮɮɢɰɢɟɧɬ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɰɟɧɬɪɨɛɟɠɧɵɯ ɧɚɫɨɫɨɜ ɧɚɯɨ-

ɞɢɬɫɹ ɜ ɩɪɟɞɟɥɚɯ 0,2 < ɯ < 0,5.

Ɇɨɳɧɨɫɬɶ, ȼɬ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɧɚɫɨɫɨɦ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ,

ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

ɧɧɧɧ.ɭ

/,NVp

(6.2 ɚ)

ɝɞɟ ¨p

– ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɣ, ɪɚɡɜɢɜɚɟɦɵɣ ɧɚɫɨɫɨɦ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ

ɪɟɠɢɦɟ, ɉɚ; V

– ɩɨɞɚɱɚ ɧɚɫɨɫɚ, ɦ

/ɫ;

ɧ.ɭ

– ɄɉȾ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ

(ɩɪɨɢɡɜɟɞɟɧɢɟ ɄɉȾ ɧɚɫɨɫɚ

ɧɚ ɄɉȾ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ

ɉɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɜ ɫɪɟɞɧɟɦ

ɧ.ɭ

= 0,7 – 0,8. Ɍɚɤ ɤɚɤ ɩɨ-

ɬɟɪɹ ɧɚɩɨɪɚ ɜ ɬɟɩɥɨɜɵɯ ɫɟɬɹɯ, ɤɚɤ ɩɪɚɜɢɥɨ, ɩɨɞɱɢɧɹɟɬɫɹ ɤɜɚɞɪɚɬɢɱɧɨɦɭ

ɡɚɤɨɧɭ, ɬɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɤɜɚɞɪɚ-

ɬɢɱɧɭɸ ɩɚɪɚɛɨɥɭ, ɨɩɢɫɵɜɚɟɦɭɸ ɭɪɚɜɧɟɧɢɟɦ

VsH '

ɢɥɢ

sVp '

(6.3)

(6.4)

ɝɞɟ ¨ɇ – ɩɨɬɟɪɹ ɧɚɩɨɪɚ, ɦ; ¨ɪ – ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ, ɉɚ; V – ɪɚɫɯɨɞ ɜɨɞɵ,

/ɫ; s

ɧ –

ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɟɬɢ, ɜɵɪɚɠɟɧɧɨɟ ɱɟɪɟɡ ɟɞɢɧɢɰɵ ɧɚɩɨɪɚ (ɩɨɬɟ-

ɪɹ ɧɚɩɨɪɚ ɩɪɢ V = 1), ɉɚ·ɫ

/ ɦ

;

s = s

= s

Ȗ – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɟɬɢ, ɜɵɪɚɠɟɧɧɨɟ ɱɟɪɟɡ ɟɞɢɧɢɰɵ ɞɚɜɥɟ-

ɧɢɹ (ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɩɪɢ V = 1), ɉɚ·ɫ

/ ɦ

; ȡ – ɩɥɨɬɧɨɫɬɶ ɜɨɞɵ, ɤɝ/ɦ

;

g = 9,81 ɦ/ɫ

– ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ; Ȗ – ɭɞɟɥɶɧɵɣ ɜɟɫ ɜɨɞɵ,

ɇ/ɦ

ɂɡ ɫɨɜɦɟɫɬɧɨɝɨ ɪɟɲɟɧɢɹ (5.7), (5.8), (5.9), (6.3) ɢ (6.4) ɧɚɯɨɞɢɦ

25,5

/)( dllAs

U

(6.5ɚ)

25,5

ɷɧ

/)( gdllAs



(6.5ɛ)

ɝɞɟ Ⱥ

= 0,0894

0,25

k ɦ

0,25

Ʉɚɤ ɜɢɞɧɨ ɢɡ (6.5), ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɟɬɢ

s ɡɚɜɢɫɢɬ ɨɬ ɟɟ ɝɟɨɦɟɬɪɢ-

ɱɟɫɤɢɯ ɪɚɡɦɟɪɨɜ, ɚɛɫɨɥɸɬɧɨɣ ɲɟɪɨɯɨɜɚɬɨɫɬɢ ɜɧɭɬɪɟɧɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ

ɬɪɭɛɨɩɪɨɜɨɞɨɜ, ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɞɥɢɧɵ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɢ ɩɥɨɬ-

ɧɨɫɬɢ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɧɨ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɯɨɞɚ ɬɟɩɥɨɧɨɫɢɬɟɥɹ. Ⱦɥɹ

ɞɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɟɬɢ ɟɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɩɨ

ɨɞɧɨɦɭ ɢɡɜɟɫɬɧɨɦɭ ɪɟɠɢɦɭ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ s ɞɨɫɬɚ-

ɬɨɱɧɨ ɡɧɚɬɶ ɞɥɹ ɨɞɧɨɝɨ ɤɚɤɨɝɨ-ɧɢɛɭɞɶ ɪɟɠɢɦɚ

ɪɚɫɯɨɞ ɜɨɞɵ V ɢ ɫɨɨɬ-

ɜɟɬɫɬɜɭɸɳɟɟ ɷɬɨɦɭ ɪɚɫɯɨɞɭ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ¨ɪ.

ɇɚɣɞɟɧɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɬɧɨɫɢɬɫɹ ɤ ɬɟɦɩɟɪɚɬɭɪɟ ɬɟɩɥɨɧɨɫɢɬɟ-

ɥɹ, ɢɦɟɜɲɟɣ ɦɟɫɬɨ ɩɪɢ ɞɚɧɧɨɦ ɪɟɠɢɦɟ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ

ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɟɬɢ, ɫɬɪɨɝɨ ɝɨɜɨɪɹ, ɞɨɥɠɧɨ ɢɡɦɟɧɹɬɶɫɹ

ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɟɝɨ ɩɥɨɬɧɨɫɬɢ: s

= Ȗ

/Ȗ

= ȡ

/ȡ

Ɉɞɧɚɤɨ ɟɫɥɢ ɧɚ ɨɫɧɨɜɟ ɪɟɠɢɦɧɵɯ ɞɚɧɧɵɯ ɧɚɯɨɞɢɬɶ ɫɨɩɪɨɬɢɜɥɟ-

ɧɢɟ ɩɪɢ ɫɪɟɞɧɟɣ ɬɟɦɩɟɪɚɬɭɪɟ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɬɨ ɜ ɭɫɥɨɜɢɹɯ ɪɚɛɨɬɵ ɜɨ-

ɞɹɧɵɯ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ ɦɨɠɧɨ ɧɟ ɭɱɢɬɵɜɚɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɞɵ, ɬɚɤ ɤɚɤ ɫɬɟɩɟɧɶ ɢɡɦɟɧɟɧɢɹ ɩɥɨɬɧɨɫɬɢ ɜɨɞɵ ɜ

ɩɪɟɞɟɥɚɯ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ, ɢɦɟɸɳɢɯ ɦɟɫɬɨ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ, ɧɟ-

ɡɧɚɱɢɬɟɥɶɧɚ.

ɋɨɩɪɨɬɢɜɥɟɧɢɟ s

ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɩɶɟɡɨ-

ɦɟɬɪɢɱɟɫɤɢɯ ɝɪɚɮɢɤɨɜ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ s ɫɨɩɪɨɬɢɜɥɟɧɢɟ s

ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɩɥɨɬɧɨɫɬɢ ɬɟɩɥɨɧɨɫɢɬɟɥɹ.

ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ ɢɡɦɟɧɹ-

ɟɬɫɹ ɢ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ. Ɉɛɴɟɦɧɵɣ ɪɚɫɯɨɞ (ɩɨɞɚɱɚ), ɧɚɩɨɪ ɢ ɬɪɟɛɭɟ-

ɦɚɹ ɦɨɳɧɨɫɬɶ ɧɚɫɨɫɚ ɫɜɹɡɚɧɵ ɫɥɟɞɭɸɳɟɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫ ɱɚɫɬɨɬɨɣ ɟɝɨ

ɜɪɚɳɟɧɢɹ:

21212121

// NNHHVVnn

(6.6)

ɝɞɟ V

, H

, N

– ɩɨɞɚɱɚ, ɧɚɩɨɪ ɢ ɦɨɳɧɨɫɬɶ ɩɪɢ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ n

;

, H

, N

–

ɬɟ ɠɟ ɩɨɤɚɡɚɬɟɥɢ ɩɪɢ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ n

/ɫ

Ɋɢɫ. 6.2. Ƚɢɞɪɚɜɥɢɱɟɫɤɢɣ ɪɟɠɢɦ ɫɢɫɬɟɦɵ ɩɪɢ ɪɚɡɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɧɚɫɨ-

ɫɨɜ

ɇɚ ɪɢɫ. 6.2 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɫɨɫɚ ɩɪɢ ɞɜɭɯ ɡɧɚɱɟɧɢɹɯ

ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ n

ɢ ɩ

ɍɪɚɜɧɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɫɨɫɚ ɩɪɢ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ n

(ɤɪɢɜɚɹ 1)

ɉɪɢ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɫɟɬɢ s

, ɪɚɛɨɱɚɹ ɬɨɱɤɚ ɧɚɫɨɫɚ Ⱥ ɧɚɯɨɞɢɬɫɹ ɢɡ

ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɧɚɩɨɪɚ, ɪɚɡɜɢɜɚɟɦɨɝɨ ɧɚɫɨɫɨɦ, ɩɨɬɟɪɟ ɧɚɩɨɪɚ ɜ ɬɟɩ-

ɥɨɜɨɣ ɫɟɬɢ:

ɨɬɤɭɞɚ

11 01.

;

HsV H



(6.8)

ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɫ ɩ

ɞɨ n

ɪɚɛɨɱɚɹ ɬɨɱɤɚ ɧɚɫɨɫɚ

ɩɟɪɟɦɟɳɚɟɬɫɹ ɢɡ ɬɨɱɤɢ Ⱥ ɜ ɬɨɱɤɭ ȼ. ɉɪɢ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ n

ɭɫɥɨɜɧɵɣ

ɧɚɩɨɪ, ɪɚɡɜɢɜɚɟɦɵɣ ɧɚɫɨɫɨɦ ɩɪɢ ɧɭɥɟɜɨɣ ɩɨɞɚɱɟ (V=0),

001

VsHH 

10011

VsVsHH



(6.7)