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ɋɥɭɱɚɣ ɝ) ɞɨɫɬɚɬɨɱɧɨ ɫɬɚɧɞɚɪɬɟɧ (ɫɦ., ɧɚɩɪɢɦɟɪ, ɪɢɫ.5.2, ɝɞɟ ɫɬɟɪɠɟɧɶ ɢɦɟɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɟɪɟɦɟɳɚɬɶɫɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨ, ɢɥɢ ɪɢɫ.2.9, ɝɞɟ ɜɧɟɲɧɢɯ ɫɜɹɡɟɣ ɧɟɬ ɢ

	Ɋ		Ɋ	Ɋ	Ɋ
Ɋ		N1	Ɋ		Ɋ
	N1	N2	N1
		N2		Ɋ	Ɋ
	Ɋ
ɚ)			ɛ)		ɜ)

N1

Ɋɢɫ. 5.10

ɤɨɧɫɬɪɭɤɰɢɹ ɦɨɠɟɬ ɞɜɢɝɚɬɶɫɹ ɤɚɤ ɠɟɫɬɤɨɟ ɬɟɥɨ).

5.3. ɋɭɩɟɪɩɨɡɢɰɢɹ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥɨɜɵɯ ɮɚɤɬɨɪɨɜ

Ɋɟɲɢɜ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɜ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɨɣ ɡɚɞɚɱɟ (ɜ ɨɬɜɟɬ ɜɯɨɞɹɬ ɩɪɨɢɡɜɨɥɶɧɵɟ ɜɟɥɢɱɢɧɵ ɯ1, ɯ2 ,…,ɯk , k – ɫɬɟɩɟɧɶ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢ), ɦɨɠɧɨ ɫɬɪɨɢɬɶ ɷɩɸɪɵ Ɏ ɦɟɬɨɞɨɦ ɫɟɱɟɧɢɣ. ɍɞɨɛɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɭɩɟɪɩɨɡɢɰɢɸ:

Ɏ=Ɏɪ+ɏ1Ɏ1+ɏ2Ɏ2+…,

(5.3)

ɝɞɟ Ɏ – ɧɟɤɨɬɨɪɵɣ ɫɢɥɨɜɨɣ ɮɚɤɬɨɪ ɜ ɩɪɨɢɡɜɨɥɶɧɨɦ ɫɟɱɟɧɢɢ z ɤɨɧɫɬɪɭɤɰɢɢ, Ɏɪ– ɬɨɬ ɠɟ ɮɚɤɬɨɪ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɜɫɟ ɧɟɢɡɜɟɫɬɧɵɟ ɏi ɪɚɜɧɵ ɧɭɥɸ; Ɏ1 – ɩɪɢ ɧɭɥɟɜɨɣ ɜɧɟɲɧɟɣ ɧɚɝɪɭɡɤɟ ɢ ɧɭɥɟɜɵɯ ɏi, ɤɪɨɦɟ ɨɞɧɨɝɨ ɏ1=1; Ɏ2 – ɬɨɥɶɤɨ ɨɬ ɏ2=1 (ɜɧɟɲɧɢɟ ɫɢɥɵ ɢ ɨɫɬɚɥɶɧɵɟ ɏi ɪɚɜɧɵ ɧɭɥɸ) ɢ ɬ.ɞ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɜɫɟ ɟɞɢɧɢɱɧɵɟ ɷɩɸɪɵ Ɏi ɨɬɜɟɱɚɸɬ ɫɨɫɬɨɹɧɢɹɦ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɨɫɬɢ. ɗɬɨɬ ɬɟɪɦɢɧ ɨɡɧɚɱɚɟɬ ɧɚɥɢɱɢɟ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɢɯ.

5.4. ɍɫɥɨɜɢɹ ɫɨɜɦɟɫɬɧɨɫɬɢ ɞɟɮɨɪɦɚɰɢɣ

ɋɬɚɬɢɱɟɫɤɚɹ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ ɡɚɞɚɱɢ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɭɫɥɨɜɢɣ ɪɚɜɧɨɜɟɫɢɹ ɧɟɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɟɚɤɰɢɣ ɜ ɦɟɲɚɸɳɢɯ ɫɜɹɡɹɯ. ɇɟɨɛɯɨɞɢɦɨ ɩɪɢɜɥɟɤɚɬɶ ɞɜɟ ɞɪɭɝɢɟ ɫɬɨɪɨɧɵ ɦɟɯɚɧɢɤɢ – ɝɟɨɦɟɬɪɢɱɟɫɤɭɸ ɢ ɮɢɡɢɱɟɫɤɭɸ.

Ƚɟɨɦɟɬɪɢɱɟɫɤɢɟ ɭɫɥɨɜɢɹ – ɷɬɨ ɭɫɥɨɜɢɹ ɫɨɜɦɟɫɬɧɨɫɬɢ ɞɟɮɨɪɦɚɰɢɣ ɨɫɟɜɨɣ ɥɢɧɢɢ Ⱦ(z). ȼ ɨɬɥɢɱɢɟ ɨɬ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɡɚɞɚɱ, ɜ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɯ ɧɟ ɜɫɹɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɞɟɮɨɪɦɚɰɢɣ ɨɫɟɜɨɣ ɥɢɧɢɢ ɨɤɚɡɵɜɚɟɬɫɹ ɜɨɡɦɨɠɧɵɦ, ɬɨ ɟɫɬɶ ɫɨɜɦɟɫɬɧɵɦ (ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɧɚɥɨɠɟɧɧɵɦ ɧɚ ɤɨɧɫɬɪɭɤɰɢɸ ɫɜɹɡɹɦ). Ⱦɥɹ ɡɚɩɢɫɢ ɭɫɥɨɜɢɣ ɫɨɜɦɟɫɬɧɨɫɬɢ ɭɞɨɛɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɉȼɉ: ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ (ɝɥɚɜɚ 2), ɷɬɨɬ ɩɪɢɧɰɢɩ ɡɚɦɟɧɹɟɬ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɨɝɪɚɧɢɱɟɧɢɹ, ɟɫɥɢ ɧɚɦ ɢɡɜɟɫɬɧɵ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ. ȼɵɪɚɠɟɧɢɟ (5.3) ɫ ɨɬɜɟɱɚɸɳɢɦɢ ɭɫɥɨɜɢɹɦ ɪɚɜɧɨɜɟɫɢɹ ɷɩɸɪɚɦɢ Ɏɪ, Ɏi ɩɪɟɞɥɚɝɚɟɬ ɦɧɨɠɟɫɬɜɨ ɪɚɜɧɨɜɟɫɧɵɯ ɫɨɫɬɨɹɧɢɣ, ɫɪɟɞɢ ɤɨɬɨɪɵɯ ɷɩɸɪɵ Ɏi

ɭɞɨɛɧɵ ɬɟɦ, ɱɬɨ ɨɧɢ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɵ. ɉɨɫɤɨɥɶɤɭ W=Wc (ɫɦ. ɩɭɧɤɬ 2) ɢ ɞɥɹ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɪɚɛɨɬɚ ɜɧɟɲɧɢɯ ɫɢɥ ɪɚɜɧɚ ɧɭɥɸ, ɬɨ

³ȾɎi dz = 0.

(5.4)

ɗɬɨ ɢ ɟɫɬɶ ɭɫɥɨɜɢɹ ɫɨɜɦɟɫɬɧɨɫɬɢ – k ɭɪɚɜɧɟɧɢɣ (ɫɬɨɥɶɤɨ ɢɦɟɟɬɫɹ ɧɟɡɚɜɢɫɢɦɵɯ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɷɩɸɪ Ɏi ). Ʉɚɤ ɜɢɞɢɦ, ɱɢɫɥɨ ɭɪɚɜɧɟɧɢɣ (5.4) ɜ ɬɨɱɧɨɫɬɢ ɪɚɜɧɨ ɧɟɞɨɫɬɚɸɳɟɦɭ ɤɨɥɢɱɟɫɬɜɭ ɭɫɥɨɜɢɣ ɪɚɜɧɨɜɟɫɢɹ.

Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɬɚɤ ɢɡɹɳɧɨ ɜɵɝɥɹɞɹɬ ɭɫɥɨɜɢɹ ɫɨɜɦɟɫɬɧɨɫɬɢ ɞɟɮɨɪɦɚɰɢɣ ɨɫɟɜɨɣ ɥɢɧɢɢ (ɬɨ ɟɫɬɶ ɟɟ ɨɬɤɥɨɧɟɧɢɣ ɨɬ ɱɟɪɬɟɠɚ) ɥɢɲɶ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɜɫɟ ɨɩɨɪɵ ɜɵɩɨɥɧɟɧɵ ɢɞɟɚɥɶɧɨ ɩɨ ɱɟɪɬɟɠɭ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜ ɷɬɢ ɭɫɥɨɜɢɹ ɞɨɥɠɧɵ ɜɯɨɞɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɬɤɥɨɧɟɧɢɹ (ɢɯ ɧɚɡɵɜɚɸɬ ɫɦɟɳɟɧɢɹɦɢ ɨɩɨɪ).

Ⱦɥɹ ɡɚɩɢɫɢ ɬɚɤɢɯ ɤɨɪɪɟɤɬɢɪɨɜɚɧɧɵɯ ɭɫɥɨɜɢɣ ɫɨɜɦɟɫɬɧɨɫɬɢ ɞɟɮɨɪɦɚɰɢɣ ɫɥɟɞɭɟɬ, ɟɳɟ ɧɚ ɫɬɚɞɢɢ ɜɵɛɨɪɚ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɵ, ɫɱɢɬɚɬɶ ɦɟɲɚɸɳɢɦɢ (ɢ ɫɧɢɦɚɬɶ ɢɯ) ɜɫɟ ɫɦɟɳɚɸɳɢɟɫɹ ɫɜɹɡɢ. Ɍɨɝɞɚ ɜ i-ɦ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɩɪɢ Xi=1) ɪɟɚɤɰɢɢ ɷɬɢɯ ɫɜɹɡɟɣ Rim (m – ɧɨɦɟɪ ɫɜɹɡɢ) ɫɬɚɧɨɜɹɬɫɹ “ɜɧɟɲɧɢɦɢ ɫɢɥɚɦɢ” ɞɥɹ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɵ ɢ ɉȼɉ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɨɛɵɱɧɨɦ ɜɢɞɟ Wc=W, ɢɥɢ

³ȾɎidz = 6Rim'm	(5.5)
m

ɗɬɨ ɢ ɟɫɬɶ ɭɫɥɨɜɢɟ ɫɨɜɦɟɫɬɧɨɫɬɢ Ⱦ(z), ɫɨɝɥɚɫɨɜɚɧɧɨɟ ɫɨ ɫɦɟɳɟɧɢɹɦɢ ɨɩɨɪ 'm. ɉɪɢɦɟɪ 4. ȼ ɞɜɚɠɞɵ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɨɣ ɡɚɞɚɱɟ ɧɚ ɪɢɫ.5.11 ɫɦɟɳɚɸɬ-

ɫɹ ɜɫɟ ɬɪɢ ɫɜɹɡɢ ɜ ɩɪɚɜɨɣ ɡɚɞɟɥɤɟ. Ɂɚɩɢɫɚɬɶ ɭɫɥɨɜɢɹ ɫɨɜɦɟɫɬɧɨɫɬɢ ɞɥɹ Ⱦ(z) ɩɪɢ

3l	P	A
2l	2l
3P		3P	R 3
l			R 4
Ɋɢɫ.5.11			Ɋɢɫ.5.12

ɳɚɬɶɫɹ ɜɨɤɪɭɝ ɬɨɱɤɢ Ⱥ. ɍɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ:

Pɡɚɞɚɧɧɵɯ '1, '2, '3.

Ɋɟɲɟɧɢɟ. ȼɵɛɢɪɚɹ ɨɫɧɨɜɧɭɸ ɫɢɫɬɟɦɭ, ɨɬɛɪɨɫɢɦ ɷɬɢ ɬɪɢ ɫɜɹɡɢ ɢ ɨɞɧɭ ɢɡ ɞɜɭɯ ɨɫɬɚɜɲɢɯ- R 1 ɫɹ – ɞɨɩɭɫɬɢɦ, ɧɢɠɧɸɸ (ɪɢɫ.5.12). Ʉɢɧɟɦɚɬɢɱɟ-

R 2 ɫɤɢɣ ɚɧɚɥɢɡ ɞɚɟɬ ɞɜɟ ɩɪɨɫɬɟɣɲɢɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ: ɞɜɢɝɚɬɶɫɹ ɩɨ ɝɨɪɢɡɨɧɬɚɥɢ ɢɥɢ ɜɪɚ-

– R4 +3P – P +R1= R1 – R4+2P= 0;
– R4 3l+3P 2l – R2 3l+R1 2l – R3=0.	(5.6)

Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ Ri ɩɪɢɞɟɬɫɹ ɜɜɟɫɬɢ ɞɜɟ ɩɪɨɢɡɜɨɥɶɧɵɟ ɜɟɥɢɱɢɧɵ ɏ1 ɢ ɏ2. ɇɚɩɪɢɦɟɪ,

R4=3ɏ1, R1= 3ɏ1 –2P, R3=3ɏ2l, R2=2P/3 – ɏ1 – ɏ2

(ɩɪɨɜɟɪɹɟɬɫɹ ɩɨɞɫɬɚɧɨɜɤɨɣ ɜ ɭɫɥɨɜɢɹ (5.6)). Ⱦɜɚ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹ

– ɞɥɹ ɏ1=1 ɢ ɞɥɹ ɏ2=1 – ɢɥɥɸɫɬɪɢɪɭɸɬɫɹ ɪɢɫ.5.13 ɢ 5.14: ɩɨɤɚɡɚɧɵ ɪɟɚɤɰɢɢ

ɨɩɨɪ ɢ ɜɧɭɬɪɟɧɧɢɟ ɫɢɥɨɜɵɟ ɮɚɤɬɨɪɵ. ɍɫɥɨɜɢɹ ɫɨɜɦɟɫɬɧɨɫɬɢ (5.5) ɩɪɢɧɢɦɚɸɬ ɜɢɞ ('4 ɩɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɪɚɜɧɨ ɧɭɥɸ):

³	N(1)(z)H0(z)dz + ³	M(1)(z) F (z)dz=3'1	– '2,
8l	8l
³	N(2)(z)H0(z)dz + ³	M(2)(z)F(z)dz=3l'3	– '2.
8l	8l

3

1

9l

6l

R1i

ɗɆ1

ɗN 1

3

31

Ɋɢɫ.5.13

ȼ ɱɚɫɬɧɨɫɬɢ, ɧɭɥɟɜɵɟ ɤɪɢɜɢɡɧɚ ɨɫɟɜɨɣ ɥɢɧɢɢ F ɢ ɩɪɨɞɨɥɶɧɚɹ ɞɟɮɨɪɦɚɰɢɹ H0 ɫɨ-

2

ɗN

2

3l

Ri

ɗɆ

2

3l

1

3l

1

Ɋɢɫ.5.14

ɜɦɟɫɬɧɵ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ

3'1 –'2= 0,

3l'3 –'2= 0.

(5.7)

Ɋɟɲɟɧɢɟ ɷɬɨɣ ɩɨɫɥɟɞɧɟɣ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɢɦɟɟɬ ɜɢɞ

>'1,'2,'3@=ɏ3>1,3,1/l@,

(5.8)

ɝɞɟ ɏ3 – ɩɪɨɢɡɜɨɥɶɧɚɹ ɜɟɥɢɱɢɧɚ. ɉɪɢ ɬɚɤɢɯ ɫɦɟɳɟɧɢɹɯ ɨɩɨɪ ɜ ɫɥɭɱɚɟ ɨɬɫɭɬɫɬɜɢɹ ɧɚɝɪɭɡɤɢ ɢ ɧɚɝɪɟɜɚ ɧɚɩɪɹɠɟɧɢɹ ɜ ɪɚɦɟ, ɢɡɝɨɬɨɜɥɟɧɧɨɣ ɢɞɟɚɥɶɧɨ ɩɨ ɱɟɪɬɟɠɭ, ɨɬɫɭɬɫɬɜɭɸɬ.

5.5. Ɏɢɡɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ

Ɏɢɡɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ ɫɜɹɡɵɜɚɸɬ ɜ ɤɚɠɞɨɦ ɫɟɱɟɧɢɢ ɫɬɟɪɠɧɹ ɜɧɭɬɪɟɧɧɢɟ ɫɢɥɨɜɵɟ ɮɚɤɬɨɪɵ Ɏ ɫ ɞɟɮɨɪɦɚɰɢɹɦɢ ɨɫɟɜɨɣ ɥɢɧɢɢ Ⱦ. ȿɫɥɢ ɫɩɪɚɜɟɞɥɢɜ ɡɚɤɨɧ Ƚɭɤɚ, ɬɨ

Ⱦ=Ɏ/ɀ.

Ɂɞɟɫɶ ɀ – ccɠɟɫɬɤɨɫɬɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹcc ɫɬɟɪɠɧɹ, ɪɚɜɧɚɹ ES (ɟɫɥɢ Ɏ=N, ɚ Ⱦ=H0 – ɜɵɬɹɠɤɚ ɨɫɟɜɨɣ ɥɢɧɢɢ) ɢɥɢ EIx (ɟɫɥɢ Ɏ=Ɇɯ, ɚ Ⱦ=Fɯ – ɤɪɢɜɢɡɧɚ, ɢɥɢ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɜɨɤɪɭɝ ɨɫɢ ɯ) ɢɥɢ GIk (ɟɫɥɢ Ɏ=T – ɤɪɭɬɹɳɢɣ ɦɨɦɟɧɬ, ɚ Ⱦ=T – ɤɪɭɬɤɚ, ɬɨ ɟɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɭɝɨɥ ɡɚɤɪɭɱɢɜɚɧɢɹ – ɩɨɜɨɪɨɬɚ ɫɟɱɟɧɢɹ ɜɨɤɪɭɝ ɨɫɢ z). ɉɪɢ ɧɚɝɪɟɜɟ ɜɨɡɧɢɤɚɸɬ ɬɟɩɥɨɜɵɟ ɞɟɮɨɪɦɚɰɢɢ Ⱦ T. Ɉɛɵɱɧɨ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɞɜɚ ɜɢɞɚ ɬɟɩɥɨɜɨɣ ɞɟɮɨɪɦɚɰɢɢ ɨɫɟɜɨɣ ɥɢɧɢɢ ɫɬɟɪɠɧɹ:

H0T = DTɫɪ, FɯɌ = D'yT ,

ɝɞɟ Tɫɪ – ɫɪɟɞɧɹɹ ɩɨ ɫɟɱɟɧɢɸ ɫɬɟɪɠɧɹ ɬɟɦɩɟɪɚɬɭɪɚ, 'yT – ɫɪɟɞɧɢɣ ɝɪɚɞɢɟɧɬ ɬɟɦ-

ɩɟɪɚɬɭɪɵ ɩɨ ɨɫɢ y (dT/dy). Ɏɢɡɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ

Ⱦ = Ɏ/ɀ+ ȾT.

ɇɚɤɨɧɟɰ, ɟɫɥɢ ɢɦɟɸɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɞɟɮɨɪɦɚɰɢɢ Ⱦ0 (ɚ ɜ ɤɚɱɟɫɬɜɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɩɪɢɧɢɦɚɸɬɫɹ ɜɫɟ ɞɪɭɝɢɟ ɨɬɤɥɨɧɟɧɢɹ ɨɫɢ ɫɬɟɪɠɧɹ ɨɬ ɱɟɪɬɟɠɚ), ɬɨ ɜ ɩɨɫɥɟɞɧɟɦ ɜɵɪɚɠɟɧɢɢ ɞɨɛɚɜɥɹɟɬɫɹ Ⱦ0

Ⱦ = Ɏ/ɀ+ ȾT+ Ⱦ0.

(5.9)

5.6. Ʉɚɧɨɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ

Ɏɢɡɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ ɡɚɦɵɤɚɸɬ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ «ɪɚɫɤɪɵɬɢɹ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢ» ɨɩɪɟɞɟɥɟɧɢɹ ɧɟɢɡɜɟɫɬɧɵɯ Xi ɦɟɬɨɞɚ ɫɢɥ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɷɬɚ ɫɢɫɬɟɦɚ ɜɤɥɸɱɚɟɬ ɨɞɧɨ ɫɬɚɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ (5.3) – ɫɭɩɟɪɩɨɡɢɰɢɸ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥɨɜɵɯ ɮɚɤɬɨɪɨɜ; ɨ ɪɚɜɧɨɜɟɫɢɢ ɤɚɠɞɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɦɵ ɡɚɛɨɬɢɦɫɹ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɩɸɪ. ȼ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ ɜɯɨɞɹɬ ɬɚɤɠɟ k ɭɪɚɜɧɟɧɢɣ ɫɨɜɦɟɫɬɧɨɫɬɢ ɞɟɮɨɪɦɚɰɢɣ (5.5) ɢ ɮɢɡɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ (5.9). Ʌɟɝɤɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɷɬɨ ɩɨɥɧɚɹ ɫɢɫɬɟɦɚ: ɩɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (5.3) ɜ (5.9), ɚ ɩɨɫɥɟɞɧɟɟ

– ɜ ɭɪɚɜɧɟɧɢɹ (5.5), ɩɨɥɭɱɢɦ k ɪɚɡɪɟɲɚɸɳɢɯ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɨ k ɧɟɢɡɜɟɫɬɧɵɯ. Ɉɧɢ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɤɚɧɨɧɢɱɟɫɤɨɦ ɜɢɞɟ: ɧɚɩɪɢɦɟɪ, ɩɪɢ k=2

G11X1+G12X2+'1P+'1T +'10=¦R1m'm,
G21X1+G22X2+'2P+'2T +'20=¦R2m'.			(5.10)
Ɂɞɟɫɶ
Gij=³(ɎiɎj/ɀ)dz, 'iP=³(ɎiɎP/ɀ)dz, 'iT=³ɎiȾTdz, 'i0=³ɎiȾ0dz,
L	L	L	L

(L – ɫɭɦɦɚɪɧɚɹ ɞɥɢɧɚ ɫɬɟɪɠɧɟɣ ɤɨɧɫɬɪɭɤɰɢɢ). ɇɚɩɨɦɧɢɦ, ɱɬɨ ɩɪɢ ɜɵɛɨɪɟ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɵ ɜɫɟ ɫɦɟɳɚɸɳɢɟɫɹ ɨɩɨɪɵ ɫɱɢɬɚɸɬɫɹ ɦɟɲɚɸɳɢɦɢ ɢ ɫɧɢɦɚɸɬɫɹ, ɢ Rjm ɩɪɟɞɫɬɚɜɥɹɟɬ ɪɟɚɤɰɢɸ ɜ m-ɣ ɫɜɹɡɢ ɩɪɢ ɞɟɣɫɬɜɢɢ ɬɨɥɶɤɨ Xj=1.

ɉɪɢɦɟɪ 5. Ɍɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɫɢɥɨɜɵɟ ɮɚɤɬɨɪɵ ɜ ɤɨɧɫɬɪɭɤɰɢɢ ɧɚ ɪɢɫ.5.15. ɋɨɯɪɚɧɢɜ ɫɢɦɦɟɬɪɢɸ ɢ ɭɛɪɚɜ ɜɫɟ ɜɧɟɲɧɢɟ ɫɜɹɡɢ, ɩɨɥɭɱɢɦ ccɗcc (ɪɢɫ.5.15ɛ) ɫ ɞɜɭɦɹ ɧɟɢɡɜɟɫɬɧɵɦɢ Ⱥ, ȼ. ȿɞɢɧɫɬɜɟɧɧɨɟ ɫɢɦɦɟɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ –

ɫɭɦɦɚ ɦɨɦɟɧɬɨɜ ɫɢɥ 2Ⱥl+2Bl – 2M= 0 – ɦɨɠɧɨ ɪɟɲɢɬɶ, ɧɚɩɪɢɦɟɪ, ɬɚɤ:

Ⱥ= X1, B=M/l – X1.

		Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɤɨɫɨɫɢɦɦɟɬɪɢɱɧɨɣ ɧɚɝɪɭɡɤɟ (ɫɦ., ɧɚɩɪɢɦɟɪ, ɪɢɫ. 5.15ɜ) ɪɚɜ-
	ɧɨɜɟɫɢɹ ɜ ɞɚɧɧɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɧɟ ɛɭɞɟɬ ɧɢ ɩɪɢ ɤɚɤɢɯ ɡɧɚɱɟɧɢɹɯ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ
	– ɢɡ-ɡɚ ɲɚɪɧɢɪɚ ɧɚ ɨɫɢ ɫɢɦɦɟɬɪɢɢ; ɩɟɪɟɞ ɧɚɦɢ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɣ ɦɟɯɚ-
	ɧɢɡɦ. ȿɞɢɧɢɱɧɚɹ ɷɩɸɪɚ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ Ɇɢ1 (ɏ1=1, Ɇ=0) ɢ ccɝɪɭɡɨɜɚɹcc
	ɷɩɸɪɚ (ɏ1=0, Ɇ=Ɇ) ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 5.15ɝ, ɞ. Ⱦɥɹ ɪɚɦɵ ɩɨɫɬɨɹɧɧɨɣ ɠɟɫɬɤɨɫɬɢ
	ɧɚ ɢɡɝɢɛ EI ɧɚɣɞɟɦ: G11=4l3/(3EI), '1P=Ml2/(3EI),
							ȼ			ȼ
							Ⱥ			Ⱥ
			Ɇ	l	Ɇ				P
			l
		l	Ɇ	l			Ɇ
			ɚ)		ȼ	Ⱥ	ɛ)	Ⱥ	ɜ)
								ȼ
				Ɋɢɫ. 5.15					5M
				1			M
			1				l		4l
					Ɇ		Ɇ	Ɇ	Ɇ	M
		l		l						4l
			l							M
		l			Ɇ		Ɇ	Ɇ	Ɇ
										4
		1	ɗɆ u1		M	ɗɆup			ɗɆ u
		1	ɝ)		l		ɞ)		ɟ)
				Ɋɢɫ. 5.15
	X1= – '1P /G11= – M/(4l) ɢ, ɧɚɤɨɧɟɰ, ɩɨɥɭɱɢɦ ɗɆɢ (ɪɢɫ.5.15ɟ). ɋɬɨɢɬ ɭɩɨɦɹɧɭɬɶ,
	ɱɬɨ ɬɪɚɞɢɰɢɨɧɧɵɦ ɦɟɬɨɞɨɦ ɩɪɢ ɤɢɧɟɦɚɬɢɱɟɫɤɢ ɧɟɢɡɦɟɧɹɟɦɨɣ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɟ
	ɷɬɚ ɡɚɞɚɱɚ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɪɟɲɟɧɚ, ɬɚɤ ɤɚɤ ɤɨɧɫɬɪɭɤɰɢɹ ɢɡɧɚɱɚɥɶɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ
	ɫɨɛɨɣ ɦɟɯɚɧɢɡɦ.
		ɉɪɢɦɟɪ 6. ȼ ɡɚɞɚɱɟ, ɩɨɤɚɡɚɧɧɨɣ ɧɚ ɪɢɫ. 5.16, ɧɟɬ ɜɧɟɲɧɢɯ ɫɢɥ ɢ ɤɨɧɫɬɪɭɤɰɢɹ
	ɜɵɩɨɥɧɟɧɚ ɢɞɟɚɥɶɧɨ ( Ⱦ0(z)= 0), ɧɨ ɨɩɨɪɵ – ɫ ɨɬɤɥɨɧɟɧɢɟɦ ɨɬ ɱɟɪɬɟɠɚ: ɩɪɢ ɫɛɨɪ-
	ɤɟ ɨɛɧɚɪɭɠɢɥɨɫɶ, ɱɬɨ ɡɚɞɟɥɤɚ Ⱥ ɩɨɜɟɪɧɭɬɚ ɧɚ ɭɝɨɥ MȺ ɩɨ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɟ, ɚ ɨɩɨɪɚ
	ȼ ɫɦɟɳɟɧɚ ɜɥɟɜɨ ɧɚ ɜɟɥɢɱɢɧɭ 'ȼ. Ɍɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɹ ɜ ɪɚɦɟ, ɟɫɥɢ
		l	D	ɷɬɢ ɫɦɟɳɟɧɢɹ ɧɟɫɨɜɦɟɫɬɧɵ.
					ɉɪɢ ɜɵɛɨɪɟ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɵ ɫɧɢɦɚɟɦ ɫɦɟɳɚɸ-
	l	l		ɳɢɟɫɹ ɫɜɹɡɢ ( ɜ ɫɟɱɟɧɢɹɯ Ⱥ ɢ ȼ); ɭɛɟɪɟɦ ɬɚɤɠɟ ɫɜɹɡɶ ɋ,
				ɱɬɨɛɵ ɫɩɪɚɜɚ ɨɬ ɥɸɛɨɝɨ ɫɟɱɟɧɢɹ ɜɫɟ ɫɜɹɡɢ ɨɬɫɭɬɫɬɜɨɜɚ-
	Ⱥ		ɋ
				ɥɢ. Ɍɟɦ ɫɚɦɵɦ ɩɨɥɭɱɢɦ ɨɫɧɨɜɧɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. 5.17).
		ȼ	l	ȿɟ ɤɢɧɟɦɚɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɨɧɚ ɢɦɟɟɬ
		Ɋɢɫ.5.16		ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ: ɩɨɜɨɪɚɱɢɜɚɟɬɫɹ ɤɚɤ ɠɟɫɬɤɨɟ ɰɟ-

ɥɨɟ ɜɨɤɪɭɝ ɬɨɱɤɢ Ⱥ ɢ – ɩɪɢ ɧɟɩɨɞɜɢɠɧɨɣ ɱɚɫɬɢ ȺD – ɭɱɚɫɬɨɤ Dɋ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ,
ɦɨɠɟɬ ɩɨɜɨɪɚɱɢɜɚɬɶɫɹ ɜɨɤɪɭɝ ɬɨɱɤɢ D. ɉɨɤɚɠɟɦ ɪɟɚɤɰɢɢ ɨɬɛɪɨɲɟɧɧɵɯ ɫɜɹɡɟɣ R1,
R2, R3,	ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɡɚɞɚɱɭ (ɪɢɫ.5.18). ȼɧɟɲɧɢɯ ɧɚɝɪɭɡɨɤ ɜ
	D			l	D		ɷɬɨɣ ɡɚɞɚɱɟ ɧɟɬ. Ɋɟɚɤɰɢɢ R1 ɢ
							R2 ɧɚɩɪɚɜɥɹɟɦ ɧɟ ɩɪɨɢɡɜɨɥɶ-
"O"			l	"ɗ"	l		ɧɨ (ɜ ɨɬɥɢɱɢɟ ɨɬ R3): ɱɬɨɛɵ ɧɟ
							ɨɲɢɛɢɬɶɫɹ	ɩɪɢ		ɜɵɱɢɫɥɟɧɢɢ
		ɋ		R 2
Ⱥ			Ⱥ		l	ɋ	ɩɪɚɜɨɣ ɱɚɫɬɢ		ɤɚɧɨɧɢɱɟɫɤɨɝɨ
		R 1			ȼ	R 3	ɭɪɚɜɧɟɧɢɹ,	ɢɯ		ɧɚɩɪɚɜɥɟɧɢɟ
Ɋɢɫ.5.17				Ɋɢɫ.5.18			ɨɬɜɟɱɚɟɬ ɧɚɩɪɚɜɥɟɧɢɸ ɡɚɞɚɧ-
							ɧɵɯ ɫɦɟɳɟɧɢɣ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɨɜɟɞɟɧɧɵɦ ɤɢɧɟɦɚɬɢɱɟɫɤɢɦ ɚɧɚɥɢɡɨɦ ɡɚɩɢɫɵɜɚɟɦ ɞɜɚ
ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ:

				R3l – R2l= 0,		R3 2l+ R1= 0.
Ɋɟɲɚɟɦ ɷɬɭ ɫɢɫɬɟɦɭ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɢɡɜɟɫɬɧɵɯ R1, R2, R3:
				R3=X1, R2=X1, R1= – 2X1l.
ɉɪɢɧɹɜ X1 = 1, ɫɬɪɨɢɦ ɷɩɸɪɭ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ (ɪɢɫ.5.19ɚ,ɛ) ɢ ɜɵɱɢɫɥɹɟɦ
		l	D		l		G11=10l3/(3EI). ȼɥɢɹ-
							ɧɢɟɦ ɧɚ ɷɬɨɬ ɤɨɷɮɮɢ-
	l		l				ɰɢɟɧɬ ɧɨɪɦɚɥɶɧɨɣ ɢ
2l		1		ɋ		ɗɆ1	ɩɨɩɟɪɟɱɧɨɣ	ɫɢɥɵ
	Ⱥ		l			l	ɩɪɟɧɟɛɪɟɝɚɟɦ	ɜɜɢɞɭ
							ɟɝɨ ɦɚɥɨɫɬɢ ɩɨ ɫɪɚɜ-
				1	2l	l
		ɚ)					ɧɟɧɢɸ ɫ ɢɡɝɢɛɨɦ. Ʉɚ-
						ɛ)	ɧɨɧɢɱɟɫɤɨɟ	ɭɪɚɜɧɟ-
				Ɋɢɫ. 5.19
			3				ɧɢɟ ɞɥɹ ɷɬɨɣ	ɡɚɞɚɱɢ
ɢɦɟɟɬ ɜɢɞ G11X1=¦R1m'm, ɩɪɚɜɚɹ ɱɚɫɬɶ (ɩɪɢ X1 = 1) ɪɚɜɧɚ – 2l MA+1 'B. Ɍɚɤɢɦ

i 1

ɨɛɪɚɡɨɦ, ɟɫɥɢ, ɫɥɭɱɚɣɧɨ, 'B=2MAl, ɬɨ ɧɚɩɪɹɠɟɧɢɣ ɜ ɤɨɧɫɬɪɭɤɰɢɢ ɧɟ ɜɨɡɧɢɤɚɟɬ; ɢɧɚɱɟ – X1=('B – 2lMA)/G11. ɍɦɧɨɠɢɜ ɟɞɢɧɢɱɧɭɸ ɷɩɸɪɭ (ɪɢɫ.5.19ɛ) ɧɚ ɏ1, ɧɚɣɞɟɦ Ɇ, ɚ ɡɚɬɟɦ – ɧɚɩɪɹɠɟɧɢɹ.

5.7. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɟɪɟɦɟɳɟɧɢɣ

ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɨɣ ɡɚɞɚɱɟ, ɤɚɤ ɢ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ, ɪɚɰɢɨɧɚɥɶɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɟɬɨɞ Ɇɨɪɚ: ɮɨɪɦɭɥɢɪɨɜɚɬɶ ɜɫɩɨɦɨɝɚɬɟɥɶɧɭɸ ɡɚɞɚɱɭ, ɭɞɚɥɢɜ ɜɫɟ ɜɧɟɲɧɢɟ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɤɨɧɫɬɪɭɤɰɢɸ ɢ ɩɪɢɥɨɠɢɜ ɮɢɤɬɢɜɧɭɸ ɟɞɢɧɢɱɧɭɸ ɧɚɝɪɭɡɤɭ ɬɪɟɛɭɟɦɨɝɨ ɬɢɩɚ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɤɨɧɫɬɪɭɤɰɢɹ (ɜɦɟɫɬɟ ɫ ɨɩɨɪɚɦɢ) ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɟɠɧɟɣ, ɬɨ ɟɫɬɶ ɜɫɩɨɦɨɝɚɬɟɥɶɧɚɹ ɡɚɞɚɱɚ ɬɚɤɠɟ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɚ.

Ɉɞɧɚɤɨ ɚɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜɬɨɪɨɣ ɪɚɡ ɪɚɫɤɪɵɜɚɬɶ ɫɬɚɬɢɱɟɫɤɭɸ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ (ɩɪɢ ɮɢɤɬɢɜɧɨɣ ɧɚɝɪɭɡɤɟ) ɧɟ ɧɭɠɧɨ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɜɟɥɢɱɢɧɵ

Xi ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥ, ɚ ɞɟɮɨɪɦɚɰɢɢ ɜ ɤɨɧɫɬɪɭɤɰɢɢ ɜɫɟɝɞɚ ɫɨɜɦɟɫɬɧɵ (ɪɟɱɶ ɢɞɟɬ ɨ ɩɨɥɧɵɯ ɞɟɮɨɪɦɚɰɢɹɯ, ɚ ɧɟ ɨ ɦɨɧɬɚɠɧɵɯ, ɢɥɢ ɬɟɩɥɨɜɵɯ, ɢɥɢ ɫɢɥɨɜɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɞɟɮɨɪɦɚɰɢɢ). Ɋɚɛɨɬɚ ɠɟ ɫɚɦɨɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɫɢɥ ɧɚ ɫɨɜɦɟɫɬɧɵɯ ɞɟɮɨɪɦɚɰɢɹɯ ɜɫɟɝɞɚ ɪɚɜɧɚ ɧɭɥɸ – ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɜɟɥɢɱɢɧ Xi.

Ɋɚɫɫɦɨɬɪɢɦ, ɧɚɩɪɢɦɟɪ, ɫɥɭɱɚɣ ɨɞɢɧ ɪɚɡ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɨɣ ɤɨɧɫɬɪɭɤɰɢɢ. ȼɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ ɞɥɹ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥɨɜɵɯ ɮɚɤɬɨɪɨɜ ɢ ɞɥɹ ɪɟɚɤɰɢɣ ɨɩɨɪ (ɫɦɟɳɚɸɳɢɯɫɹ ɢɥɢ ɧɟ ɫɦɟɳɚɸɳɢɯɫɹ, ɧɨ ɦɟɲɚɸɳɢɯ) ɫɩɪɚɜɟɞɥɢɜɚ ɫɭɩɟɪɩɨɡɢɰɢɹ:

Ɏɜɫ=ɎPɜɫ +X1 ɜɫ Ɏ1ɜɫ,

Rmɜɫ= Rmɜɫ(P)+ Rmɜɫ(X1 ɜɫ).

ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɷɬɢɯ ɜɵɪɚɠɟɧɢɣ ɞɥɹ ɜɧɟɲɧɢɯ ɢ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥ ɜ ɨɩɪɟɞɟɥɟɧɢɟ Ɇɨɪɚ ɞɥɹ ɩɟɪɟɦɟɳɟɧɢɹ ɩɪɢ ɧɚɥɢɱɢɢ ɫɦɟɳɚɸɳɢɯɫɹ ɨɩɨɪ (2.5) ɩɨɥɭɱɢɦ

	n		n		n
' ³Ⱦ)ɜɫdz–¦ 'iRiɜɫ=³Ⱦ)pɜɫdz–¦'iRiɜɫ(P)+X1ɜɫ[³ȾɎ1ɜɫdz–¦'iRiɜɫ(X1ɜɫ=1)]
L	i 1	L	i 1	L	i 1

(ɭɱɬɟɧɨ, ɱɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɮɢɤɬɢɜɧɨɣ ɧɚɝɪɭɡɤɢ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ ɪɟɚɤɰɢɢ ɨɬɛɪɨɲɟɧɧɵɯ ɫɜɹɡɟɣ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɩɚɪɚɦɟɬɪɭ X1ɜɫ). Ɉɞɧɚɤɨ ɜɵɪɚɠɟɧɢɟ ɜ ɩɨɫɥɟɞɧɟɣ ɫɤɨɛɤɟ ɪɚɜɧɨ ɧɭɥɸ – ɜ ɫɜɹɡɢ ɫ ɬɪɟɛɨɜɚɧɢɟɦ ɫɨɜɦɟɫɬɧɨɫɬɢ (5.5) ɞɥɹ ɞɟɮɨɪɦɚɰɢɢ Ⱦ(z) ɜ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɹ ɨɩɪɟɞɟɥɹɬɶ ɡɧɚɱɟɧɢɟ X1ɜɫ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ, ɨɧɨ ɜɫɟ ɪɚɜɧɨ ɛɭɞɟɬ ɭɦɧɨɠɟɧɨ ɧɚ ɧɨɥɶ. Ɇɨɠɧɨ ɡɚɩɢɫɚɬɶ

'=³ȾɎpɜɫɩ dz –¦ Riɜɫɩ(P)'i,

(5.11)

(ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɪɢɪɚɜɧɢɜɚɧɢɸ X1ɜɫ ɧɭɥɸ), ɧɨ ɛɵɜɚɟɬ ɭɞɨɛɧɨ, ɧɟ ɪɚɫɤɪɵɜɚɹ ɜɬɨɪɨɣ ɪɚɡ ɫɬɚɬɢɱɟɫɤɭɸ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ, ɩɪɢɧɹɬɶ ɞɥɹ ɷɬɨɣ ɧɟɢɡɜɟɫɬɧɨɣ ɤɚɤɨɟɧɢɛɭɞɶ ɞɪɭɝɨɟ ɡɧɚɱɟɧɢɟ ɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɵɪɚɠɟɧɢɟ (2.5).

ɉɪɢɦɟɪ 7. Ɋɚɦɚ ɧɚ ɪɢɫ.5.20 ɜɵɩɨɥɧɟɧɚ ɢɞɟɚɥɶɧɨ (Ⱦ0=0), ɧɨ ɤɪɟɩɢɬɫɹ ɧɚ ɨɩɨɪɵ, ɢɡɝɨɬɨɜɥɟɧɧɵɟ ɧɟɬɨɱɧɨ. ɇɚɫɤɨɥɶɤɨ ɫɦɟɫɬɢɬɫɹ ɬɨɱɤɚ Ⱥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɟɪɬɟɠɨɦ?

Ɋɟɲɟɧɢɟ. ɉɟɪɜɚɹ ɱɚɫɬɶ ɡɚɞɚɱɢ – ɨɩɪɟɞɟɥɟɧɢɟ ɭɩɪɭɝɢɯ ɞɟɮɨɪɦɚɰɢɣ (ɩɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ) ɪɟɲɚɟɬɫɹ ɫɬɚɧɞɚɪɬɧɨ. ɉɨɫɤɨɥɶɤɭ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɫɦɟɳɚɸɬɫɹ ɜɫɟ ɨɩɨɪɵ, ɜ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɟ ɩɪɢɞɟɬɫɹ ɫɧɹɬɶ ɜɫɟ ɜɧɟɲɧɢɟ ɫɜɹɡɢ. ɉɨɹɜɹɬɫɹ ɬɪɢ ɨɛɵɱɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ (ɪɢɫ.5.21, ɧɟɢɡɜɟɫɬɧɵɯ ɱɟɬɵɪɟ, ɫɬɟɩɟɧɶ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢ ɪɚɜɧɚ ɟɞɢɧɢɰɟ). Ʉɚɧɨɧɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɜɢɞ G11ɏ1=¦ Ri(1)'i (ɫɦɟɳɟɧɢɹ ɫɱɢɬɚɸɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ, ɟɫɥɢ ɢɯ ɧɚɩɪɚɜɥɟɧɢɹ ɨɬɜɟɱɚɸɬ ɫɬɪɟɥɤɚɦ ɧɚ ɪɢɫ.5.21). ɉɨɥɭɱɟɧɧɚɹ ɩɨɫɥɟ ɪɚɫɤɪɵɬɢɹ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢ ɷɩɸɪɚ ɤɪɢɜɢɡɧ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ.5.22, ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ ɚ = 0.6('1 – '2+'3 – '4)/l2. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɥɨɠɟɧɢɹ ɬɨɱɤɢ Ⱥ ɫɥɟɞɭɟɬ ɧɚɣɬɢ ɟɟ ɝɨɪɢɡɨɧɬɚɥɶɧɨɟ ɢ ɜɟɪɬɢɤɚɥɶɧɨɟ ɫɦɟɳɟɧɢɟ, ɜɵɡɜɚɧɧɨɟ ɫɦɟɳɟɧɢɹɦɢ ɨɩɨɪ 'i. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɟ ɫɦɟɳɟɧɢɟ ɪɚɜɧɨ '4 (ɩɪɨɞɨɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ɫɬɟɪɠɧɹ, ɤɚɤ ɨɛɵɱɧɨ, ɩɪɟɧɟɛɪɟɝɚɟɦ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɡɝɢɛɧɨɣ).

l

R1

R

A l

R 2

a

l

R 3

a

Ɋɢɫ.5.20

Ɋɢɫ.5.21

Ɋɢɫ.5.22

ɑɬɨɛɵ ɧɚɣɬɢ ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ X, ɫɥɟɞɭɟɬ ɪɟɲɢɬɶ ɜɫɩɨɦɨɝɚɬɟɥɶɧɭɸ ɡɚɞɚɱɭ: ɩɪɢɥɨɠɢɬɶ ɜ ɬɨɱɤɟ Ⱥ ɜɟɪɬɢɤɚɥɶɧɭɸ ɟɞɢɧɢɱɧɭɸ ɫɢɥɭ (ɪɢɫ.5.23, ɢɳɟɦ ɩɟɪɟɦɟɳɟɧɢɟ ɜɜɟɪɯ). Ⱦɥɹ ɪɟɲɟɧɢɹ ɧɚɦ ɩɨɧɚɞɨɛɹɬɫɹ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɢ ɜɫɟ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ (ɪɢɫɭɧɨɤ 5.24 – ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɫɢɫɬɟɦɚ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ). ɉɨɫɤɨɥɶɤɭ ɡɧɚɱɟɧɢɟ ɧɟɢɡɜɟɫɬɧɨɣ X1ɜɫ ɧɚɦ ɧɟ ɜɚɠɧɨ, ɦɨɠɧɨ ɜɵɛɪɚɬɶ ɥɸɛɨɟ ɢɡ ɛɟɫɤɨɧɟɱɧɨɝɨ ɦɧɨɠɟɫɬɜɚ ɪɟɲɟɧɢɣ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ, ɬɨ ɟɫɬɶ ɨɧɚ ɤɚɤ ɛɵ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɭɸ. ɉɨɤɚɠɟɦ ɷɬɨ, ɜɵɛɪɚɜ ɞɜɚ ɜɚɪɢɚɧɬɚ ɪɟɲɟɧɢɹ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɢ.

Ɋɟɲɟɧɢɟ ɚ. ɉɪɢɦɟɦ ɡɧɚɱɟɧɢɟ R1ɜɫ ɧɚ ɪɢɫ.5.24 ɪɚɜɧɵɦ ɧɭɥɸ, ɬɨɝɞɚ R2ɜɫ= – 2, R3ɜɫ=1, R4ɜɫ=0. ɗɩɸɪɚ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ.5.25;

R1ɜɫ

l

R4ɜɫ

l

1 l

l

1

R 2ɜɫ

R 3ɜɫ

Ɋɢɫ.5.23

Ɋɢɫ.5.24

Ɋɢɫ.5.25

X = 5/6l2a – (– 2·'2 +1·'3) = ('1+3'2 – '3 – '4)/2.

Ʉɚɤ ɜɢɞɢɦ, ɪɟɡɭɥɶɬɚɬ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɠɟɫɬɤɨɫɬɢ ɪɚɦɵ, ɟɫɥɢ ɩɨɫɥɟɞɧɹɹ ɩɨɫɬɨɹɧɧɚ. Ɋɟɲɟɧɢɟ ɛ. ȿɫɥɢ ɩɪɢɪɚɜɧɹɬɶ ɧɭɥɸ ɧɟ R1ɜɫ, ɚ R3ɜɫ, ɬɨ ɩɨɥɭɱɢɦ R1ɜɫ= – 1, R2ɜɫ=

– 1, R3ɜɫ= 0, R4ɜɫ= 1. ɗɩɸɪɚ Mɜɫ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ.5.26, ɢɡ ɜɵɪɚɠɟɧɢɹ (2.5) ɩɨɥɭɱɚɟɦ

X = – 5/6l2a – (–1·'1 – 1·'2+ 1·'4) = ('1+3'2 – '3 – '4)/2.

Ɉɬɜɟɬ ɬɨɬ ɠɟ.

ȼ ɩɪɢɜɟɞɟɧɧɵɯ ɜɚɪɢɚɧɬɚɯ «ɪɟɲɟɧɢɹ» ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɢ ɦɵ ɩɪɢɪɚɜɧɢɜɚɥɢ ɨɞɧɭ ɢɡ ɪɟɚɤɰɢɣ ɧɭɥɸ – ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɩɨɩɪɨɳɟ ɷɩɸɪɭ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ. Ɇɨɠɟɬɟ ɞɥɹ ɭɩɪɚɠɧɟɧɢɹ ɩɪɢɪɚɜɧɹɬɶ ɨɞɧɭ ɢɡ ɪɟɚɤɰɢɣ, ɧɚɩɪɢɦɟɪ, 13,5. ȿɫɥɢ ɩɪɚɜɢɥɶɧɨ ɧɚɣɞɟɬɟ ɨɫɬɚɥɶɧɵɟ ɢ

ɧɟ ɨɲɢɛɟɬɟɫɶ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɷɩɸɪɵ Mɜɫ, ɩɨɥɭɱɢɬɟ ɩɪɟɠɧɢɣ ɨɬɜɟɬ.

ɉɪɢɦɟɪ 8. ȼ ɮɟɪɦɟ, ɩɨɤɚɡɚɧɧɨɣ ɧɚ ɪɢɫ.5.27, ɩɚɪɵ ɨɛɨ- l

	ɡɧɚɱɟɧɧɵɯ ɫɬɟɪɠɧɟɣ ɨɞɢɧɚɤɨɜɵ, ɢɯ ɞɥɢɧɵ ɪɚɜɧɵ l ɢ 2 l).	Ɋɢɫ.5.26
	Ɍɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɫɬɟɪɠɧɹ 1.

Ɋɟɲɟɧɢɟ. Ɂɚɞɚɱɚ ɤɨɫɨɫɢɦɦɟɬɪɢɱɧɚ; ɷɬɨ ɧɟɬɪɭɞɧɨ ɭɜɢɞɟɬɶ, ɫɦɟɫɬɢɜ ɬɨɱɤɭ ɩɪɢɥɨɠɟɧɢɹ ɫɢɥɵ P ɤ ɰɟɧɬɪɭ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɨɝɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɫɬɟɪɠɧɹ (ɪɢɫ.5.28). ɉɨ ɪɟɤɨɦɟɧɞɚɰɢɢ ɞɥɹ ɮɟɪɦ, ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɢɫɬɟɦɵ ɪɚɡɪɟɡɚɟɦ ɜɫɟ ɫɬɟɪɠɧɢ ɢ ɨɛɨɡɧɚɱɚɟɦ ɧɟɢɡɜɟɫɬɧɵɟ ɪɟɚɤɰɢɢ ɫɧɹɬɵɯ ɫɜɹɡɟɣ ɫ ɭɱɟɬɨɦ ɤɨɫɨɣ ɫɢɦɦɟɬɪɢɢ (ɪɢɫ.5.28). ɂɡ ɭɫɥɨɜɢɣ ɪɚɜɧɨɜɟɫɢɹ ɧɚɣɞɟɦ B= P 2 /2, A= P/2; ɬɟɦ ɫɚɦɵɦ ɧɚɣɞɟɧɵ ɧɨɪɦɚɥɶɧɵɟ ɫɢɥɵ.

Ɋ		Ɋ		Ⱦɥɹ ɩɨɢɫɤɚ ɭɝɥɚ
				ɩɨɜɨɪɨɬɚ	M	ɜɨɡɜɪɚ-
2	1			ɳɚɟɦɫɹ	ɤ	ɢɫɯɨɞɧɨɣ
1		ȼ Ⱥ 1		ɡɚɞɚɱɟ	(ɪɢɫ.5.27),
2	ȼ			ɫɧɢɦɚɟɦ	ɧɚɝɪɭɡɤɭ		P
	Ⱥ			ɢ ɩɪɢɤɥɚɞɵɜɚɟɦ ɩɚɪɭ
				ɫɢɥ ɦɨɦɟɧɬɨɦ			1
Ɋɢɫ. 5.27	Ɋɢɫ.5.28		Ɋɢɫ. 5.29	(ɪɢɫ.5.29).ɑɬɨɛɵ ɜɨɫ-
				ɩɨɥɶɡɨɜɚɬɶɫɹ ɢɧɬɟ-

ɝɪɚɥɨɦ Ɇɨɪɚ, ɧɭɠɧɨ ɩɨɫɬɪɨɢɬɶ ɷɩɸɪɭ ɧɨɪɦɚɥɶɧɵɯ ɫɢɥ ɜ ɷɬɨɣ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ

				ɡɚɞɚɱɟ. Ɂɞɟɫɶ ɫɢɦɦɟɬɪɢɢ ɧɟɬ ("ɗ" ɩɨɤɚɡɚɧɚ ɧɚ
ȼ Ⱥ				ɪɢɫ.5.30). ɇɟɬɪɢɜɢɚɥɶɧɵɯ ɭɫɥɨɜɢɣ	ɪɚɜɧɨɜɟɫɢɹ –
				ɱɟɬɵɪɟ, ɧɟɢɡɜɟɫɬɧɵɯ – ɩɹɬɶ; ɡɚɞɚɱɚ ɫɬɚɬɢɱɟɫɤɢ ɧɟ-
Ⱥ
ȼ	N2	N3	N4	ɨɩɪɟɞɟɥɢɦɚ.
				ɉɨɥɶɡɭɹɫɶ ɪɚɡɪɟɲɟɧɢɟɦ ɩɪɢɧɹɬɶ ɜɨ ɜɫɩɨɦɨɝɚ-
1	N2	N4		ɬɟɥɶɧɨɣ ɡɚɞɚɱɟ ɧɟɢɡɜɟɫɬɧɭɸ ɦɟɬɨɞɚ ɫɢɥ ɩɪɨɢɡ-
				ɜɨɥɶɧɨ (ɱɬɨ ɛɵ ɨɧɚ ɫɨɛɨɣ ɧɢ ɩɪɟɞɫɬɚɜɥɹɥɚ), ɩɪɢ-
N3
				ɦɟɦ, ɧɚɩɪɢɦɟɪ, ɱɬɨ N4ɜɫ=0. ɂɡ ɪɚɜɧɨɜɟɫɢɹ ɠɟɫɬɤɨ-
Ɋɢɫ. 5.30				ɝɨ ɫɬɟɪɠɧɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɢ N3= 0. Ɋɚɜɧɨɜɟɫɢɟ ɥɟɜɨ-
				ɝɨ ɫɬɟɪɠɧɹ ɬɪɟɛɭɟɬ ɡɧɚɱɟɧɢɹ A= – 1/l ɢ, ɜɨɡɜɪɚɳɚ-
ɹɫɶ ɤ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦɭ, ɧɚɣɞɟɦ ɨɫɬɚɥɶɧɵɟ ɧɟɢɡɜɟɫɬɧɵɟ: N2ɜɫ = –					2 /l, B=1/l. ȼɫɟ

ɧɨɪɦɚɥɶɧɵɟ ɫɢɥɵ ɧɚɣɞɟɧɵ (N1ɜɫ=B=1/l), ɢɡ ɢɧɬɟɝɪɚɥɚ Ɇɨɪɚ ɧɚɯɨɞɢɦ M:

M =¦ Ni Niɜɫli /(ES)i= ( 2 /(ES)2+1/(2ES)1)P.

ɑɭɬɶ ɦɟɧɟɟ ɝɪɨɦɨɡɞɤɨ ɷɬɭ ɡɚɞɚɱɭ ɦɨɠɧɨ ɛɵɥɨ ɪɟɲɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɫɢɦɦɟɬɪɢɸ (ɤɨɫɭɸ) ɢɫɯɨɞɧɨɣ ɡɚɞɚɱɢ: ɩɨɜɨɪɨɬ ɨɛɨɢɯ ɫɬɟɪɠɧɟɣ 1 ɨɞɢɧɚɤɨɜ. ɇɚɣɞɟɦ ɫɭɦɦɭ ɭɝɥɨɜ ɩɨɜɨɪɨɬɚ ɷɬɢɯ ɫɬɟɪɠɧɟɣ, ɩɪɢɥɨɠɢɜ, ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɜɟ ɟɞɢɧɢɱɧɵɟ ɨɞɢɧɚɤɨɜɨ ɧɚɩɪɚɜɥɟɧɧɵɟ ɩɚɪɵ ɫɢɥ (ɪɢɫ.5.31, 5.32). Ɋɚɜɧɨɜɟɫɢɟ ɜɟɪɬɢɤɚɥɶɧɵɯ ɫɬɟɪɠɧɟɣ ɬɪɟɛɭɟɬ Aɜɫ=1/l; ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ – Cɜɫ= 2 /l, Bɜɫ=

– 1/l. ɂɧɬɟɝɪɚɥ Ɇɨɪɚ:

2M =¦Ni Niɜɫli /(ES)i=2(P/2 1/l l/(ES)1)+2 ( 2 P/2 2 /l l 2 /(ES)2),

Ⱥɜɫ Ⱥɜɫ

	ȼɜɫ ȼɜɫ
1	Ⱥɜɫ

1	1

	ɋ	ɜɫ	ɜɫ
		ȼ
	ɋ	ɜɫ

Ⱥɜɫ

1

Ɋɢɫ. 5.31

Ɋɢɫ.5.32

ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫ ɩɪɟɞɵɞɭɳɢɦ ɨɬɜɟɬɨɦ.

5.8. Ɍɟɦɩɟɪɚɬɭɪɧɵɟ ɫɦɟɳɟɧɢɹ

ȼ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ ɛɵɥ ɪɚɫɫɦɨɬɪɟɧ ɨɛɳɢɣ ɫɥɭɱɚɣ ɨɩɪɟɞɟɥɟɧɢɹ ɫɦɟɳɟɧɢɣ ɫ ɩɨɦɨɳɶɸ ɢɧɬɟɝɪɚɥɚ Ɇɨɪɚ. ɇɚ ɩɪɚɤɬɢɤɟ ɱɚɫɬɨ ɩɪɢɯɨɞɢɬɫɹ ɢɦɟɬɶ ɞɟɥɨ ɫ ɬɟɩɥɨɜɵɦɢ ɫɦɟɳɟɧɢɹɦɢ. ɇɢɠɟ ɩɨɤɚɡɚɧɵ ɞɜɚ ɩɪɢɟɦɚ, ɨɛɥɟɝɱɚɸɳɢɯ ɷɬɨ ɞɟɥɨ.

ɉɭɫɬɶ ɜɧɟɲɧɢɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɧɚ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɭɸ ɤɨɧɫɬɪɭɤɰɢɸ ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɧɚɝɪɟɜ (ɧɟɬ ɫɢɥɨɜɵɯ ɜɨɡɞɟɣɫɬɜɢɣ), ɚ ɥɢɦɢɬɢɪɭɟɬ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɶ ɧɟ ɩɪɨɱɧɨɫɬɶ, ɚ ɠɟɫɬɤɨɫɬɶ ɤɨɧɫɬɪɭɤɰɢɢ. Ɍɟɦɩɟɪɚɬɭɪɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɧɟ ɨɩɪɟɞɟɥɹɬɶ ɢ, ɨɤɚɡɵɜɚɟɬɫɹ, ɫɬɚɬɢɱɟɫɤɭɸ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ ɜ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟ ɦɨɠɧɨ ɧɟ ɪɚɫɤɪɵɜɚɬɶ, ɧɨ ɫɥɟɞɭɟɬ ɩɨɥɧɨɫɬɶɸ ɪɟɲɢɬɶ ɜɫɩɨɦɨɝɚɬɟɥɶɧɭɸ (ɢɡɨɬɟɪɦɢɱɟɫɤɭɸ) ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɭɸ ɡɚɞɚɱɭ. ɉɨɤɚɠɟɦ ɷɬɨ.

ɂɧɬɟɝɪɚɥ Ɇɨɪɚ (ɟɫɥɢ ɨɩɨɪɵ ɧɚ ɦɟɫɬɟ)

'=³ȾɎɜɫdz	(5.12)
L

ɬɪɟɛɭɟɬ, ɤɚɡɚɥɨɫɶ ɛɵ, ɡɧɚɧɢɹ ɩɨɥɧɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟ:

Ⱦ=Ⱦɟ + ȾɌ, Ⱦɟ=Ɏ/ɀ,

ɝɞɟ, ɜɜɢɞɭ ɨɬɫɭɬɫɬɜɢɹ ɜɧɟɲɧɢɯ ɫɢɥ, Ɏ=¦ɎmXm (ɫɦ. ɜɵɪɚɠɟɧɢɟ (5.3)). ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɵɪɚɠɟɧɢɟ (5.12) ɩɪɢɧɢɦɚɟɬ ɜɢɞ

'=ɏm³ɎmɎɜɫdz/ɀ+³ȾTɎɜɫdz.		(5.13)
L	L

ǻȟȚȍȔ, ȟȚȖǼȊș/Ǯ=ǬȊș (ȊșȗȖȔȖȋȈȚȍȓȤȕȈȧ ȏȈȌȈȟȈ țȗȘțȋȈ) Ȑ

³Ⱦɜɫ Ɏmdz=0

(5.14)

(ɞɟɮɨɪɦɚɰɢɢ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ ɫɨɜɦɟɫɬɧɵ: ɩɪɢ ɟɟ ɪɟɲɟɧɢɢ ɦɵ ɞɨɛɪɨɫɨɜɟɫɬɧɨ ɪɚɫɤɪɵɥɢ ɫɬɚɬɢɱɟɫɤɭɸ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ, ɢɝɧɨɪɢɪɭɹ ɪɟɤɨɦɟɧɞɚɰɢɢ ɩɪɟɞɵɞɭɳɟɝɨ ɩɚɪɚɝɪɚɮɚ). ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ

'=³ȾTɎɜɫdz

(5.15)

L