EP / Теория ЭП Драчев

ɐɟɥɶɸ ɨɛɭɱɟɧɢɹ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ «ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɚɜɬɨɦɚɬɢɤɚ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɤɨɦɩɥɟɤɫɨɜ» ɹɜɥɹɟɬɫɹ ɩɨɞɝɨɬɨɜɤɚ ɢɧɠɟɧɟɪɨɜ ɲɢɪɨɤɨɝɨ ɩɪɨɮɢɥɹ, ɫɩɨɫɨɛɧɵɯ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɢ ɬɜɨɪɱɟɫɤɢ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ, ɢɫɫɥɟɞɨɜɚɧɢɹ, ɧɚɥɚɞɤɢ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɜ ɥɸɛɵɯ ɨɬɪɚɫɥɹɯ ɧɚɪɨɞɧɨɝɨ ɯɨɡɹɣɫɬɜɚ.

Ƚɥɚɜɚ ɜɬɨɪɚɹ

ɆȿɏȺɇɂɑȿɋɄȺə ɑȺɋɌɖ ɗɅȿɄɌɊɈɉɊɂȼɈȾȺ

2.1. Ʉɢɧɟɦɚɬɢɱɟɫɤɢɟ ɫɯɟɦɵ ɪɚɛɨɱɢɯ ɨɪɝɚɧɨɜ

Ɉɫɧɨɜɧɚɹ ɡɚɞɚɱɚ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ – ɩɪɢɜɟɞɟɧɢɟ ɜ ɞɜɢɠɟɧɢɟ ɢɫɩɨɥɧɢɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɨɜ ɢ ɭɩɪɚɜɥɟɧɢɟ ɢɯ ɞɜɢɠɟɧɢɟɦ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɜɫɟ ɦɟɯɚɧɢɱɟɫɤɢ ɫɜɹɡɚɧɧɵɟ ɦɟɠɞɭ ɫɨɛɨɣ ɞɜɢɠɭɳɢɟɫɹ ɢɧɟɪɰɢɨɧɧɵɟ ɦɚɫɫɵ ɞɜɢɝɚɬɟɥɹ, ɩɟɪɟɞɚɱɢ ɢ ɪɚɛɨɱɟɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɞɜɢɠɭɳɢɯɫɹ ɦɚɫɫɚɯ ɭɫɬɚɧɨɜɤɢ ɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɹɡɹɯ ɦɟɠɞɭ ɧɢɦɢ ɞɚɟɬ ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ.

Ʉɢɧɟɦɚɬɢɱɟɫɤɢɟ ɫɯɟɦɵ ɤɨɧɤɪɟɬɧɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɛɟɫɤɨɧɟɱɧɨ ɦɧɨɝɨɨɛɪɚɡɧɵ, ɨɞɧɚɤɨ ɨɛɥɚɞɚɸɬ ɨɛɳɢɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ, ɪɚɫɫɦɨɬɪɟɜ ɪɹɞ ɤɨɧɤɪɟɬɧɵɯ ɩɪɢɦɟɪɨɜ.

1. ɉɪɨɫɬɟɣɲɢɦ ɩɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɜɟɧɬɢɥɹɬɨɪɚ, ɢɡɨɛɪɚɠɟɧɧɚɹ ɧɚ ɪɢɫ. 2.1. Ɋɨɬɨɪ ɞɜɢɝɚɬɟɥɹ Ⱦ ɱɟɪɟɡ ɫɨɟɞɢɧɢɬɟɥɶɧɭɸ ɦɭɮɬɭ ɋɆ ɜɪɚɳɚɟɬ ɜɚɥ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ ɜɟɧɬɢɥɹɬɨɪɚ ȼ. ȼɫɟ ɷɥɟɦɟɧɬɵ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɞɜɢɠɭɬɫɹ ɫ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɫɤɨɪɨɫɬɶɸ.

Ȧ

	ɋɆ
		ȦɊɈ
Ⱦ		ȼ

Ɇ

ǻɆɊɈ ɆɊɈ

Ɋɢɫ. 2.1. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜɟɧɬɢɥɹɬɨɪɚ

Ɇɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɆɊɈ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɤɨɪɨɫɬɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ȦɊɈ , ɫɨɡɞɚɟɬɫɹ ɧɚ ɪɚɛɨɱɟɦ ɤɨɥɟɫɟ ɜɟɧɬɢɥɹɬɨɪɚ

n

ɆɊɈ ǻɆɊɈ Ɇȼɇ §¨¨ȦɊɈ ·¸¸ , (2.1)

© Ȧȼɇ ¹

ɝɞɟ ǻɆɊɈ – ɦɨɦɟɧɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɬɟɪɶ ɧɚ ɬɪɟɧɢɟ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ ɜɟɧɬɢɥɹɬɨɪɚ;

Ȧȼɇ – ɧɨɦɢɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɜɟɧɬɢɥɹɬɨɪɚ; Ɇȼɇ– ɧɨɦɢɧɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɟɧɬɢɥɹɬɨɪɚ ɩɪɢ ɟɝɨ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ;

11

n – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɦɚɝɢɫɬɪɚɥɢ, ɧɚ ɤɨɬɨɪɭɸ ɪɚɛɨɬɚɟɬ ɜɟɧɬɢɥɹɬɨɪ (n = 2 – ɦɚɝɢɫɬɪɚɥɶ ɛɟɡ ɩɪɨɬɢɜɨɞɚɜɥɟɧɢɹ).

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜɟɧɬɢɥɹɬɨɪɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɤɜɚɞɪɚɬɢɱɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɦɟɧɬɚ ɨɬ ɫɤɨɪɨɫɬɢ (ɫɦ. ɪɢɫ. 2.1). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɜɟɧɬɢɥɹɬɨɪɚ ɹɜɥɹɟɬɫɹ ɛɟɡɪɟɞɭɤɬɨɪɧɵɦ, ɧɟɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫɤɨɪɨɫɬɢ ɨɬ ɦɨɦɟɧɬɚ.

ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɩɪɚɤɬɢɱɟɫɤɢɯ ɫɥɭɱɚɟɜ ɩɨ ɪɚɡɥɢɱɧɵɦ ɫɨɨɛɪɚɠɟɧɢɹɦ ɰɟɥɟɫɨɨɛɪɚɡɧɚɹ ɧɨɦɢɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɧɟ ɫɨɜɩɚɞɚɟɬ ɫ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɉɪɢ ɷɬɨɦ ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɫɨɝɥɚɫɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ ɩɭɬɟɦ ɜɜɟɞɟɧɢɹ ɜ ɤɢɧɟɦɚɬɢɱɟɫɤɭɸ ɰɟɩɶ ɪɚɡɥɢɱɧɵɯ ɩɟɪɟɞɚɱ: ɡɭɛɱɚɬɵɯ, ɮɪɢɤɰɢɨɧɧɵɯ, ɰɟɩɧɵɯ, ɤɥɢɧɨɪɟɦɟɧɧɵɯ ɢ ɬ.ɩ. Ⱦɥɹ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɫɬɭɩɟɧɱɚɬɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɢɫɩɨɥɶɡɭɸɬ ɤɨɪɨɛɤɢ ɩɟɪɟɞɚɱ, ɞɥɹ ɩɥɚɜɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ – ɮɪɢɤɰɢɨɧɧɵɟ ɜɚɪɢɚɬɨɪɵ.

2. ȼ ɤɢɧɟɦɚɬɢɱɟɫɤɭɸ ɫɯɟɦɭ ɩɪɢɜɨɞɚ ɲɩɢɧɞɟɥɹ ɬɨɤɚɪɧɨɝɨ ɫɬɚɧɤɚ (ɪɢɫ. 2.2) ɜɜɟɞɟɧɚ ɤɥɢɧɨɪɟɦɟɧɧɚɹ ɩɟɪɟɞɚɱɚ ɄɊɉ ɢ ɤɨɪɨɛɤɚ ɩɟɪɟɞɚɱ Ʉɉ ɞɥɹ ɫɬɭɩɟɧɱɚɬɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ. ȼɵɯɨɞɧɨɣ ɜɚɥ ɤɨɪɨɛɤɢ ɩɟɪɟɞɚɱ ɫɜɹɡɚɧ ɫɨ ɲɩɢɧɞɟɥɟɦ ɫɬɚɧɤɚ ɒ, ɜ ɤɨɬɨɪɨɦ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɡɚɝɨɬɨɜɤɚ Ɂ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɜɪɚɳɚɸɳɟɣɫɹ ɞɟɬɚɥɢ ɫ ɧɟɩɨɞɜɢɠɧɵɦ ɪɟɡɰɨɦ Ɋ ɜɨɡɧɢɤɚɸɬ ɭɫɢɥɢɟ ɪɟɡɚɧɢɹ ɢ ɦɨɦɟɧɬ ɪɟɡɚɧɢɹ

ɆZ FZ rɁ,

(2.2)

ɝɞɟ ɆZ – ɦɨɦɟɧɬ ɪɟɡɚɧɢɹ;

FZ – ɭɫɢɥɢɟ ɪɟɡɚɧɢɹ; rɁ – ɪɚɞɢɭɫ ɡɚɝɨɬɨɜɤɢ.

ɉɨ ɬɪɟɛɨɜɚɧɢɹɦ ɬɟɯɧɨɥɨɝɢɢ ɨɛɪɚɛɨɬɤɚ ɞɟɬɚɥɟɣ ɜɟɞɟɬɫɹ ɜ ɪɟɠɢɦɟ ɩɨɫɬɨ-

ɹɧɫɬɜɚ ɦɨɳɧɨɫɬɢ
PZ MZ ȦPO const ,	(2.3)

ɩɨɷɬɨɦɭ ɦɨɦɟɧɬ ɪɟɡɚɧɢɹ ɛɭɞɟɬ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɫɤɨɪɨɫɬɢ ȦɊɈ ɩɪɢ ɟɟ ɢɡɦɟɧɟɧɢɢ, ɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɢɧɢɦɚɟɬ ɜɢɞ ɝɢɩɟɪɛɨɥɵ (ɫɦ. ɪɢɫ. 2.2). Ʉɪɨɦɟ ɩɨɥɟɡɧɨɝɨ ɦɨɦɟɧɬɚ MɊɈ MZ , ɜɨ ɜɫɟɯ ɷɥɟɦɟɧɬɚɯ ɤɢɧɟɦɚɬɢɱɟ-

ɫɤɨɣ ɰɟɩɢ ɞɟɣɫɬɜɭɸɬ ɫɢɥɵ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɜ ɡɭɛɱɚɬɵɯ ɡɚɰɟɩɥɟɧɢɹɯ, ɜ ɬɪɭɳɢɯɫɹ ɩɨɜɟɪɯɧɨɫɬɹɯ ɤɥɢɧɨɪɟɦɟɧɧɨɣ ɩɟɪɟɞɚɱɢ.

ɋɆ
	Ʉɉ
Ⱦ

ɄɊɉ

ɒ

Ȧ

ȦɊɈ

ȦɊɈ

Ɋ

Ɇ

ɆɊɈ

Ɋɢɫ. 2.2. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɲɩɢɧɞɟɥɹ ɬɨɤɚɪɧɨɝɨ ɫɬɚɧɤɚ

12

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɒ ɹɜɥɹɟɬɫɹ ɧɟɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫɤɨɪɨɫɬɢ ɨɬ ɦɨɦɟɧɬɚ, ɞɥɹ ɫɨɝɥɚɫɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ ɞɜɢɝɚɬɟɥɹ ɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɪɢɦɟɧɟɧɵ ɪɟɞɭɤɬɨɪ Ʉɉ ɢ ɤɥɢɧɨɪɟɦɟɧɧɚɹ ɩɟɪɟɞɚɱɚ ɄɊɉ.

ȼ ɦɟɯɚɧɢɡɦɟ ɩɟɪɟɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ ɦɨɫɬɨɜɨɝɨ ɤɪɚɧɚ (ɪɢɫ. 2.3) ɦɨɦɟɧɬ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɩɪɟɨɞɨɥɟɜɚɟɬ ɬɨɥɶɤɨ ɫɢɥɵ ɬɪɟɧɢɹ. Ⱦɜɢɝɚɬɟɥɶ Ⱦ ɱɟɪɟɡ ɪɟɞɭɤɬɨɪ Ɋ ɜɪɚɳɚɟɬ ɜɟɞɭɳɭɸ ɩɚɪɭ ɤɨɥɟɫ ɬɟɥɟɠɤɢ, ɩɪɟɨɞɨɥɟɜɚɹ ɫɢɥɭ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɬɟɥɟɠɤɢ

FPO	kɁ m g f μ rɲ ,	(2.4)
	RK

ɨɛɭɫɥɨɜɥɟɧɧɭɸ ɬɪɟɧɢɟɦ ɫɤɨɥɶɠɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɢ ɬɪɟɧɢɟɦ ɤɚɱɟɧɢɹ ɤɨɥɟɫ ɩɨ ɪɟɥɶɫɚɦ, ɝɞɟ kɁ – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ; m – ɦɚɫɫɚ ɬɟɥɟɠɤɢ ɫ ɝɪɭɡɨɦ; g –

ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ; f MTPK – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɤɚɱɟɧɢɹ;

		N
μ	FTPC	– ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ; M	– ɦɨɦɟɧɬ ɬɪɟɧɢɹ ɤɚɱɟɧɢɹ;
	N	TPK

FTPC – ɫɢɥɚ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ; RK , rɲ– ɪɚɞɢɭɫɵ ɤɨɥɟɫɚ ɢ ɲɟɣɤɢ ɨɫɢ ɤɨɥɟɫɚ.

ɋɢɥɚ ɬɪɟɧɢɹ FPO ɜɫɟɝɞɚ ɧɚɩɪɚɜɥɟɧɚ ɧɚɜɫɬɪɟɱɭ ɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ. ɉɨɞ ɪɟɚɤɬɢɜɧɵɦɢ ɫɢɥɚɦɢ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɬɚɤɢɟ ɫɢɥɵ, ɤɨɬɨɪɵɟ ɩɪɢ ɫɦɟɧɟ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɦɟɧɹɸɬ ɫɜɨɣ ɡɧɚɤ. Ɂɧɚɱɢɬ, FPO – ɪɟɚɤɬɢɜɧɚɹ

ɫɢɥɚ. ɂɡ ɮɨɪɦɭɥɵ (2.4) ɫɥɟɞɭɟɬ, ɱɬɨ ɦɨɞɭɥɶ ɫɢɥɵ ɬɪɟɧɢɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɉɪɢɜɟɞɟɧɧɚɹ ɮɨɪɦɭɥɚ (2.4) ɢ ɜɢɞ ɦɟɯɚɧɢɱɟ-

Ɋ		ȦɊɈ
		dɄ
	Ⱦ
		DɄ
		ɆɊɈ

Ɋɢɫ. 2.3. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɟɯɚɧɢɡɦɚ ɩɟɪɟɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ (ɫ ɪɟɚɤɬɢɜɧɵɦ ɯɚɪɚɤɬɟɪɨɦ ɧɚɝɪɭɡɤɢ)

ɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɟ ɭɱɢɬɵɜɚɸɬ ɫɭɯɨɟ ɬɪɟɧɢɟ (ɩɨɤɨɹ), ɧɟɫɤɨɥɶɤɨ ɭɜɟɥɢɱɢɜɚɸɳɢɟ ɫɢɥɵ ɬɪɟɧɢɹ ɩɪɢ ɩɭɫɤɟ ɦɟɯɚɧɢɡɦɚ.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɬɟɥɟɠɤɢ ɹɜɥɹɟɬɫɹ ɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɩɨɫɬɨɹɧɧɵɦ, ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɫɤɨɪɨɫɬɢ, ɦɨɦɟɧɬɨɦ, ɡɧɚɤ ɤɨɬɨɪɨɝɨ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ, ɬ.ɟ. ɧɨɫɹɳɢɦ ɪɟɚɤɬɢɜɧɵɣ ɯɚɪɚɤɬɟɪ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɦɟɯɚɧɢɡɦɚ ɩɟɪɟɞɜɢɠɟɧɢɹ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɺɦɚ ɫɨɡɞɚɟɬɫɹ ɫɢɥɨɣ ɬɹɠɟɫɬɢ ɩɨɞɜɟɲɟɧɧɨɝɨ ɝɪɭɡɚ, ɩɪɢɱɟɦ ɟɺ ɧɚɩɪɚɜɥɟɧɢɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɝɪɭɡɚ. ɉɨɞ ɚɤɬɢɜɧɵɦɢ ɫɢɥɚɦɢ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɬɚɤɢɟ ɫɢɥɵ, ɤɨɬɨɪɵɟ ɩɪɢ ɫɦɟɧɟ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪ-

ɝɚɧɚ ɧɟ ɦɟɧɹɸɬ ɫɜɨɣ ɡɧɚɤ. Ɂɧɚɱɢɬ, ɫɢɥɚ ɬɹɠɟɫɬɢ – ɚɤɬɢɜɧɚɹ ɫɢɥɚ:
FPO m g.	(2.5)

13

4. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 2.4. Ⱦɜɢɝɚɬɟɥɶ Ⱦ ɱɟɪɟɡ ɪɟɞɭɤɬɨɪ Ɋ ɜɪɚɳɚɟɬ ɛɚɪɚɛɚɧ Ȼ, ɧɚ ɤɨɬɨɪɨɦ ɧɚɦɨɬɚɧ ɬɪɨɫ ɫ ɝɪɭɡɨɦ. ɇɚ ɝɪɭɡ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ ɬɹɠɟɫɬɢ, ɧɟ ɡɚɜɢɫɹɳɚɹ ɨɬ ɫɤɨɪɨɫɬɢ.

Ɍɒ	Ɋ
ɋɆ
	1
Ⱦ
Mȼ
Ȧ	2

		Ȼ
	ɋɆ
4
		DȻ
3		ɆɊɈ

m	Ƚɪɭɡ	v
ȦɊɈ

ȦɊɈ

ɆɊɈ

Ɋɢɫ. 2.4. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɺɦɚ (ɫ ɚɤɬɢɜɧɵɦ ɯɚɪɚɤɬɟɪɨɦ ɧɚɝɪɭɡɤɢ)

Ʉɪɨɦɟ ɫɢɥɵ ɬɹɠɟɫɬɢ ɞɜɢɝɚɬɟɥɶ ɩɪɟɨɞɨɥɟɜɚɟɬ ɫɢɥɵ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɢ ɡɭɛɱɚɬɵɯ ɡɚɰɟɩɥɟɧɢɹɯ ɪɟɞɭɤɬɨɪɚ (ɩɭɧɤɬɢɪɧɵɟ ɥɢɧɢɢ ɧɚ ɪɢɫ. 2.4 – ɫ ɭɱɟɬɨɦ

FPO ).

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɺɦɚ ɜ ɰɟɥɨɦ ɹɜɥɹɟɬɫɹ ɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɩɨɫɬɨɹɧɧɵɦ, ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɫɤɨɪɨɫɬɢ, ɦɨɦɟɧɬɨɦ, ɡɧɚɤ ɤɨɬɨɪɨɝɨ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ, ɬ.ɟ. ɧɨɫɹɳɢɦ ɚɤɬɢɜɧɵɣ ɯɚɪɚɤɬɟɪ.

Ɇɨɦɟɧɬ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɧɨɫɢɬ ɚɤɬɢɜɧɵɣ ɯɚɪɚɤɬɟɪ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɥɢɮɬɚ – ɪɟɜɟɪɫɢɜɧɵɣ, ɜ ɩɪɢɜɟɞɟɧɧɨɣ ɫɯɟɦɟ – ɪɟɞɭɤɬɨɪɧɵɣ.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɦɧɨɝɨɨɛɪɚɡɢɢ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɫɯɟɦ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɨɧɢ ɨɛɥɚɞɚɸɬ ɫɥɟɞɭɸɳɢɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ:

–ɪɟɜɟɪɫɢɜɧɵɟ ɢɥɢ ɧɟɪɟɜɟɪɫɢɜɧɵɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ;

–ɪɟɞɭɤɬɨɪɧɵɟ ɢɥɢ ɛɟɡɪɟɞɭɤɬɨɪɧɵɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ;

–ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɞɟɣɫɬɜɭɸɬ ɞɜɢɠɭɳɢɟ ɦɨɦɟɧɬɵ ɢ ɫɢɥɵ, ɦɨɦɟɧɬɵ ɢ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɚ ɬɚɤɠɟ ɦɨɦɟɧɬɵ ɢ ɫɢɥɵ ɬɪɟɧɢɹ;

–ɦɨɦɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɨɹɧɧɵ ɢɥɢ ɦɨɝɭɬ ɡɚɜɢɫɟɬɶ ɨɬ ɫɤɨɪɨɫɬɢ, ɭɝɥɚ ɩɨɜɨɪɨɬɚ, ɜɪɟɦɟɧɢ;

–ɦɨɦɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɨɝɭɬ ɢɦɟɬɶ ɯɚɪɚɤɬɟɪ ɚɤɬɢɜɧɵɣ (ɷɧɟɪɝɢɹ ɩɨɫɬɭɩɚɟɬ ɨɬ ɞɪɭɝɨɝɨ ɢɫɬɨɱɧɢɤɚ ɢɥɢ ɢɦɟɟɬɫɹ ɡɚɩɚɫ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ) ɢɥɢ ɪɟɚɤɬɢɜɧɵɣ (ɨɛɭɫɥɨɜɥɟɧ ɫɢɥɚɦɢ ɬɪɟɧɢɹ);

–ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɪɟɚɤɬɢɜɧɵɟ ɦɨɦɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɫɤɚɱɤɨɦ ɢɡɦɟɧɹɸɬ ɡɧɚɤ, ɚ ɚɤɬɢɜɧɵɟ ɦɨɦɟɧɬɵ – ɡɧɚɤ ɧɟ ɢɡɦɟɧɹɸɬ.

2.2. Ɋɚɫɱɟɬɧɵɟ ɫɯɟɦɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɞɚɟɬ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨɛ ɢɞɟɚɥɶɧɵɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɫɜɹɡɹɯ ɦɟɠɞɭ ɞɜɢɠɭɳɢɦɢɫɹ ɦɚɫɫɚɦɢ ɤɨɧɤɪɟɬɧɨɣ ɭɫɬɚɧɨɜɤɢ, ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ ɞɟɮɨɪɦɚɰɢɢ ɷɥɟɦɟɧɬɨɜ ɩɪɢ ɢɯ ɧɚɝɪɭɠɟɧɢɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɧɟɪɰɢɨɧɧɵɟ ɦɚɫɫɵ ɫɢɫɬɟɦɵ ɞɜɢɠɭɬɫɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ, ɩɨɷɬɨɦɭ ɧɟɥɶɡɹ ɫɪɚɜɧɢɜɚɬɶ ɫɢ-

14

ɥɵ ɢɥɢ ɦɨɦɟɧɬɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɜ ɞɜɢɠɭɳɢɯɫɹ ɫ ɪɚɡɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ ɷɥɟɦɟɧɬɚɯ.

ɋ ɩɨɦɨɳɶɸ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɧɟɨɛɯɨɞɢɦɨ ɫɨɫɬɚɜɢɬɶ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɜ ɤɨɬɨɪɨɣ ɜɫɟ ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ, ɦɨɦɟɧɬɵ ɧɚɝɪɭɡɤɢ ɜɪɚɳɚɸɳɢɯɫɹ ɷɥɟɦɟɧɬɨɜ, ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɢɯɫɹ ɷɥɟɦɟɧɬɨɜ, ɚ ɬɚɤɠɟ ɪɟɚɥɶɧɵɟ ɠɟɫɬɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɹɡɟɣ ɡɚɦɟɧɹɸɬɫɹ ɷɤɜɢɜɚɥɟɧɬɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ, ɩɪɢɜɟɞɟɧɧɵɦɢ ɤ ɨɞɧɨɣ ɫɤɨɪɨɫɬɢ, ɱɚɳɟ ɜɫɟɝɨ – ɤ ɫɤɨɪɨɫɬɢ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ.

ɉɪɢɜɟɞɟɧɢɟ ɦɨɦɟɧɬɨɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ.

Ʉɪɢɬɟɪɢɟɦ ɩɪɢɜɟɞɟɧɢɹ ɦɨɦɟɧɬɨɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɹɜɥɹɟɬɫɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɛɚɥɚɧɫ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦ, ɡɚɤɥɸɱɚɸɳɢɣɫɹ ɜ ɪɚɜɟɧɫɬɜɟ ɷɧɟɪɝɢɣ, ɡɚɬɪɚɱɟɧɧɵɯ ɧɚ ɜɵɩɨɥɧɟɧɢɟ ɨɩɪɟɞɟɥɟɧɧɨɣ ɪɚɛɨɬɵ ɜ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɚɯ.

ȼ ɢɞɟɚɥɶɧɨɦ ɫɥɭɱɚɟ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜ ɩɟɪɟɞɚɱɟ ɦɨɳɧɨɫɬɶ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ PPO ɪɚɜɧɚ ɦɨɳɧɨɫɬɢ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ PB :

PPO PB .

(2.6)

Ɋɚɫɫɦɨɬɪɢɦ ɞɥɹ ɩɪɢɦɟɪɚ ɦɟɯɚɧɢɡɦ ɩɨɞɴɟɦɚ (ɫɦ. ɪɢɫ. 2.4).

Ⱦɥɹ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɛɚɪɚɛɚɧɚ:

– ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ

PPO

MPO ȦPO ,

(2.7)

– ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ

PB

MB Ȧ,

(2.8)

ɉɨɞɫɬɚɜɢɜ ɭɪɚɜɧɟɧɢɹ (2.7) ɢ (2.8) ɜ (2.6), ɩɨɥɭɱɢɦ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

ɞɜɢɠɟɧɢɸ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ:

MB

MPO ȦPO

MPO

,

(2.9)

Ȧ

iP

ɝɞɟ ip

Ȧ

– ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ.

ȦPO

Ⱦɥɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ

P

M

Ȧ

m g

Dɛ

ȦɊɈ

m g v G v ,

(2.10)

PO

PO

PO

2

ɬɨɝɞɚ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ,

MB

G

v

G

,

(2.11)

Ȧ

ȡ

v

– ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ, ɦ.

ɝɞɟ ȡ

Ȧ

ɉɪɢɜɟɞɟɧɢɟ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ. Ʉɪɢɬɟɪɢɟɦ ɩɪɢɜɟɞɟ-

ɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ ɡɚɩɚɫɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɪɟɚɥɶɧɨɣ ɫɯɟɦɵ ɪɚɜɧɚ ɫɭɦɦɟ ɤɢɧɟɬɢɱɟɫɤɢɯ ɷɧɟɪɝɢɣ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ ɞɜɢɠɟɧɢɹ.

15

Ⱦɥɹ ɫɯɟɦɵ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ (ɫɦ. ɪɢɫ. 2.4) ɜɵɪɚɠɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ WɄɂɇ ɞɥɹ ɪɚɫɱɟɬɧɨɣ ɢ ɪɟɚɥɶɧɨɣ ɫɯɟɦ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ

WɄɂɇ J

Ȧ2

JȾȼ

Ȧ2

JɌɒ

Ȧ2

J1

Ȧ2

J2

Ȧ2

J3

Ȧ2

2

2

2

2

2

2

ȦɊɈ2

ȦɊɈ2

v2

(2.12)

J

J

m

,

4

2

Ȼ

2

2

ɝɞɟ J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ; JȾȼ, JɌɒ, J1, J2, J3, J4, JȻ – ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɜɢɝɚɬɟɥɹ, ɬɨɪ-

ɦɨɡɧɨɝɨ ɲɤɢɜɚ, ɲɟɫɬɟɪɟɧ ɪɟɞɭɤɬɨɪɚ, ɛɚɪɚɛɚɧɚ; m – ɦɚɫɫɚ ɝɪɭɡɚ;

Ȧ1 – ɫɤɨɪɨɫɬɶ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɜɚɥɚ ɪɟɞɭɤɬɨɪɚ.

ɉɨɞɟɥɢɜ ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (2.12) ɧɚ Ȧ2/2, ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ J ɪɚɫɱɺɬɧɨɣ ɫɯɟɦɵ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ,

J J		J J J		1		J	1		J			1		J	1		m ȡ2 .	(2.13)
					2			2		4			2			2
	Ⱦȼ	Ɍɒ	1 2	i		3	i					i		Ȼ	i
				1			1					P			P

ȼ ɩɨɥɭɱɟɧɧɨɦ ɜɵɪɚɠɟɧɢɢ:

i1 – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɞɨ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɜɚɥɚ ɪɟɞɭɤɬɨɪɚ; iɊ – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ;

ȡ v – ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ɨɬ ɥɢɧɟɣɧɨɣ ɫɤɨɪɨɫɬɢ ɝɪɭɡɚ ɞɨ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ.

Ȧ

ȼ ɫɜɹɡɢ ɫɨ ɫɥɨɠɧɨɫɬɶɸ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɷɥɟɦɟɧɬɨɜ ɩɟɪɟɞɚɱɢ, ɪɚɫɱɟɬ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, ɜɵɩɨɥɧɹɸɬ ɩɨ ɮɨɪɦɭɥɟ

								J į JȾȼ JɉɊɊɈ,			(2.14)
									JȾȼ JɉȿɊ	1,1...1,3,	(2.15)
						į
									JȾȼ
ɝɞɟ J	J	J		J2			J3		– ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɟɪɟɞɚɱɢ;
				i 2			i
ɉȿɊ	Ɍɒ		1
				1		12
J		JȻ	m ȡ2			– ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɜɪɚɳɚɸɳɟɝɨɫɹ ɷɥɟ-
		i 2
ɉɊ.ɊɈ
		P

ɦɟɧɬɚ (ɛɚɪɚɛɚɧɚ) ɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɟɝɨɫɹ ɷɥɟɦɟɧɬɚ (ɦɚɫɫɵ ɝɪɭɡɚ) ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ.

Ɋɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ȡ ɢ ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ Jɩɪ ɦɨɝɭɬ ɛɵɬɶ ɩɟɪɟɦɟɧɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ.

ȼ ɤɭɥɚɱɤɨɜɨɦ ɦɟɯɚɧɢɡɦɟ (ɪɢɫ.2.5) ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɡɚɤɪɟɩɥɟɧ ɪɵɱɚɝ ɪɚɞɢɭɫɚ R, ɧɚ ɤɨɧɰɟ ɤɨɬɨɪɨɝɨ ɭɫɬɚɧɨɜɥɟɧ ɪɨɥɢɤ. Ɋɨɥɢɤ ɜɨɡɞɟɣɫɬɜɭɟɬ ɧɚ ɬɚɪɟɥɤɭ ɬɨɥɤɚɬɟɥɹ, ɤɨɬɨɪɵɣ ɩɟɪɟɦɟɳɚɟɬ ɞɟɬɚɥɶ ɦɚɫɫɨɣ m. ɋɢɥɨɜɨɟ ɡɚɦɵɤɚɧɢɟ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɩɪɭɠɢɧɨɣ, ɧɚɞɟɬɨɣ ɧɚ ɬɨɥɤɚɬɟɥɶ. ɉɪɢ ɪɚɜɧɨɦɟɪɧɨɦ ɜɪɚɳɟɧɢɢ ɜɚɥɚ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Ȧ ɦɚɫɫɚ m ɩɟɪɟɦɟɳɚɟɬɫɹ ɩɨ ɡɚɤɨɧɭ Į= R·sin ij=R·sin(Ȧt) ɫɨ ɫɤɨɪɨɫɬɶɸ v=dD/dt=Ȧ·R·cos ij.

ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ɫɬɚɧɨɜɢɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ ȡ= v/Ȧ=R·cosij.

16

Ɋɢɫ. 2.5. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɤɭɥɚɱɤɨɜɨɝɨ ɦɟɯɚɧɢɡɦɚ

	m	v
R		ij=Ȧt

ɉɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɩɨɜɨɪɨɬɚ

Ɇɫ = F·ȡ= (mg – Fɩɪ) R·cosij.

ɉɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɚɤɠɟ ɦɟɧɹɟɬ ɫɜɨɸ ɜɟɥɢɱɢɧɭ ɜ ɮɭɧɤɰɢɢ ɭɝɥɚ ɩɨɜɨɪɨɬɚ

Jɩɪ= mR2·cos2ij.

ɉɪɢɜɟɞɟɧɧɵɦ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ ɪɚɫ-

ɱɺɬɧɨɣ ɫɯɟɦɵ ɧɚɡɵɜɚɸɬ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɪɨɫɬɟɣɲɟɣ ɫɢɫɬɟɦɵ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɷɥɟɦɟɧɬɨɜ, ɜɪɚɳɚɸɳɢɯɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ ɜɚɥɚ, ɤ ɤɨɬɨɪɨɦɭ ɨɫɭɳɟɫɬɜɥɟɧɨ ɩɪɢɜɟɞɟɧɢɟ, ɢ ɤɨɬɨɪɚɹ ɨɛɥɚɞɚɟɬ ɩɪɢ ɷɬɨɦ ɡɚɩɚɫɨɦ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɪɚɜɧɵɦ ɡɚɩɚɫɭ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ.

2.3. ɍɱɟɬ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɚɯ

ȼ ɩɪɨɰɟɫɫɟ ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɜɨɡɧɢɤɚɸɬ ɩɨɬɟɪɢ ɜ ɷɥɟɦɟɧɬɚɯ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ (ɜ ɪɟɞɭɤɬɨɪɚɯ, ɤɥɢɧɨɪɟɦɟɧɧɵɯ ɩɟɪɟɞɚɱɢ, ɲɤɢɜɚɯ, ɩɨɬɟɪɢ ɧɚ ɬɪɟɧɢɟ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɨɩɨɪɚɯ ɢ ɬ.ɩ.).

Ɇɟɬɨɞ ɄɉȾ. ȼɟɥɢɱɢɧɚ ɩɨɬɟɪɶ ɬɪɚɞɢɰɢɨɧɧɨ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ (ɄɉȾ). ɉɪɢ ɷɬɨɦ ɭɱɢɬɵɜɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɷɧɟɪɝɢɢ: ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɤ ɦɟɯɚɧɢɡɦɭ ɩɪɢ ɪɚɛɨɬɟ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɢɥɢ ɨɬ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ – ɜ ɬɨɪɦɨɡɧɨɦ ɪɟɠɢɦɟ. ȿɫɥɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨɞɴɺɦ ɝɪɭɡɚ, ɬɨ ɞɜɢɝɚɬɟɥɶ ɫɨɜɟɪɲɚɟɬ ɩɨɥɟɡɧɭɸ ɪɚɛɨɬɭ ɩɨ ɩɨɞɴɺɦɭ ɝɪɭɡɚ PPO ɢ ɩɨɤɪɵɜɚɟɬ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɧɚ ɬɪɟɧɢɟ ɜ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ǻɊ

(ɪɢɫ. 2.6). ɄɉȾ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

Ɋȼ ɊɊɈ

ǻɊ

Ɋɢɫ. 2.6. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɦɟɯɚɧɢɡɦɚ ɩɪɢ ɩɨɞɴɺɦɟ ɝɪɭɡɚ

Ɋȼ ɊɊɈ

ǻɊ

Ɋɢɫ. 2.7. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɦɟɯɚɧɢɡɦɚ ɩɪɢ ɫɩɭɫɤɟ ɝɪɭɡɚ

. Ș	PPO		MPO ȦPO		MPO	(2.16)
	PB		MB Ȧ MB iP

ɉɪɢ ɨɩɭɫɤɚɧɢɢ ɝɪɭɡɚ ɬɟɪɹɟɦɚɹ ɢɦ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɩɟɪɟɞɚɺɬɫɹ ɞɜɢɝɚɬɟɥɸ (ɪɢɫ. 2.7). ɉɨɷɬɨɦɭ ɩɨɬɟɪɢ ɧɚ ɬɪɟɧɢɟ ǻɊ ɜ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɩɨɤɪɵɜɚɸɬɫɹ ɭɠɟ ɡɚ ɫɱɺɬ ɷɬɨɣ ɷɧɟɪɝɢɢ, ɢ ɄɉȾ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

Ș	PB		MB Ȧ		MB iP	.	(2.17)
	PPO		MPO ȦPO
					MPO

Ɉɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɪɶ ɱɟɪɟɡ ɄɉȾ ɧɨɫɢɬ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ. ɉɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɟ ɢ ɧɨɦɢɧɚɥɶɧɨɦ ɄɉȾ ɩɟɪɟɞɚɱɢ ɩɨɬɟɪɢ ɜ ɩɟɪɟɞɚɱɟ ɪɚɜɧɵ ɧɨɦɢɧɚɥɶɧɵɦ. ɋɧɢɠɟɧɢɟ ɧɚɝɪɭɡɤɢ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɄɉȾ, ɚ ɩɪɢ ɦɚɥɵɯ ɧɚɝɪɭɡɤɚɯ ɄɉȾ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɪɶ ǻɊ ɜ

17

ɩɟɪɟɞɚɱɟ ɱɟɪɟɡ ɄɉȾ ɫɬɚɧɨɜɢɬɫɹ ɧɟɞɨɫɬɨɜɟɪɧɵɦ.

Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɚɯ ɄɉȾ ɩɟɪɟɞɚɱɢ ɢɡɦɟɧɹɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨ, ɬɚɤ ɤɚɤ ɢɡɦɟɧɹɟɬɫɹ ɫɤɨɪɨɫɬɶ, ɢ ɱɟɪɟɡ ɩɟɪɟɞɚɱɭ ɩɪɨɯɨɞɹɬ ɫɬɚɬɢɱɟɫɤɢɟ ɢ ɞɢɧɚɦɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ. ɉɪɢɧɹɬɨ ɩɪɢɦɟɧɹɬɶ ɞɥɹ ɪɚɫɱɟɬɚ ɩɨɬɟɪɶ ɜ ɷɥɟɦɟɧɬɚɯ ɢɯ ɧɨɦɢɧɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ KH (ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ ɪɟɞɭɤɬɨɪɚ, ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ ɤɥɢɧɨɪɟɦɟɧɧɨɣ ɩɟɪɟɞɚɱɢ ɢ ɬ.ɩ.), ɱɬɨ ɞɚɟɬ ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɨɱɧɨɫɬɶ.

Ɇɟɬɨɞ ɪɚɡɞɟɥɟɧɢɹ ɩɨɬɟɪɶ. ɂɧɨɝɞɚ ɞɥɹ ɬɨɱɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɹɬɶ ɄɉȾ ɩɪɢ ɱɚɫɬɢɱɧɨɣ ɡɚɝɪɭɡɤɟ. Ɂɚɜɢɫɢɦɨɫɬɢ K f PPO,Z ɜ

ɫɩɪɚɜɨɱɧɢɤɚɯ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɩɪɢɜɨɞɹɬɫɹ. Ɍɨɝɞɚ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞ ɪɚɡɞɟɥɟɧɢɹ ɩɨɬɟɪɶ.

ȼɫɟ ɩɨɬɟɪɢ ɜ ɩɟɪɟɞɚɱɟ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɩɨɫɬɨɹɧɧɵɟ ǻPɉɈɋɌ	ɢ ɩɟɪɟ-
ɦɟɧɧɵɟ ǻPɉȿɊ . Ɍɨɝɞɚ ɨɛɳɢɟ ɩɨɬɟɪɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɤɚɤ ɫɭɦɦɭ ɩɨɫɬɨɹɧɧɵɯ ɢ
ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ:
ǻɊ ǻPɉɈɋɌ ǻɊɉȿɊ ,	(2.18)

ɉɨɫɬɨɹɧɧɵɟ ɩɨɬɟɪɢ ǻPɉɈɋɌ ɡɚɜɢɫɹɬ:

–ɨɬ ɤɨɧɫɬɪɭɤɰɢɢ ɨɩɨɪ ɡɚɰɟɩɥɟɧɢɣ;

–ɨɬ ɜɹɡɤɨɫɬɢ ɫɦɚɡɤɢ;

–ɨɬ ɤɚɱɟɫɬɜɚ ɨɛɪɚɛɨɬɤɢ ɡɭɛɰɨɜ;

–ɨɬ ɬɨɱɧɨɫɬɢ ɫɛɨɪɤɢ ɩɟɪɟɞɚɱɢ;

–ɨɬ ɫɬɟɩɟɧɢ ɢɡɧɨɲɟɧɧɨɫɬɢ ɡɚɰɟɩɥɟɧɢɹ ɢ ɬ.ɩ.

ɉɟɪɟɦɟɧɧɵɟ ɩɨɬɟɪɢ ǻPɉȿɊ ɡɚɜɢɫɹɬ ɨɬ ɡɚɝɪɭɡɤɢ ɦɟɯɚɧɢɡɦɚ. Ɇɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫ ɭɱɟɬɨɦ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɟ ɪɚɜɧɚ

Ɋȼ ɊɊɈ ǻɊ,

(2.19)

ɬɨɝɞɚ ɄɉȾ ɩɟɪɟɞɚɱɢ ɩɪɢ ɱɚɫɬɢɱɧɨ ɡɚɝɪɭɡɤɟ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ

ɊɊɈ

ɊɊɈ

Ɇ

1

,

Ș

ɊɊɈ ǻɊ ɊɊɈ ǻɊɉɈɋɌ

ǻɊɉȿɊ Ɇ ǻɆɉɈɋɌ

ǻɆɉȿɊ

1

b

a

(2.20)

kɁ

ɝɞɟ ǻɆɉɈɋɌ

ɚ Ɇɇ.ɊȿȾ – ɦɨɦɟɧɬ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ;

ǻɆɉȿɊ

b MC – ɦɨɦɟɧɬ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ;

kɁ

Ɇɋ

– ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɝɪɭɡɤɢ ɦɟɯɚɧɢɡɦɚ.

Ɇɇ

Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ a ɢ b ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɡɭɛɱɚɬɵɯ ɡɚɰɟɩɥɟɧɢɣ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɄɉȾ Șɇ ɩɪɢɜɨɞɹɬɫɹ ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ ɩɨ ɦɚɲɢɧɨɫɬɪɨɟɧɢɸ.

ɉɪɢɦɟɪ 2.1. Ɋɚɫɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɹ ɫɤɨɪɨɫɬɟɣ, ɫɬɚɬɢɱɟɫɤɢɯ ɦɨɦɟɧɬɨɜ ɢ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ, ɦɨɳɧɨɫɬɟɣ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɢ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɩɨ ɡɚɞɚɧɧɵɦ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦ ɩɚɪɚɦɟɬɪɚɦ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ.

Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ ɫɬɚɧɤɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.2.8. ȼɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɨɬ ɞɜɢɝɚɬɟɥɹ 1 ɱɟɪɟɡ ɪɟɞɭɤɬɨɪ 2 ɩɟɪɟɞɚɟɬɫɹ ɯɨɞɨɜɨɦɭ ɜɢɧɬɭ 3 ɢ ɱɟɪɟɡ ɝɚɣɤɭ 4, ɡɚɤɪɟɩɥɟɧɧɭɸ ɧɚ ɫɭɩɩɨɪɬɟ, ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɩɨɞɚɱɢ ɫɭɩɩɨɪɬɚ 5 ɩɨ ɧɚɩɪɚɜɥɹɸɳɢɦ 6. Ⱦɜɢɝɚɬɟɥɶ ɩɨɞɚɱɢ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɟɪɟɞɜɢɠɟɧɢɟ ɫɭɩɩɨɪɬɚ ɫɨ ɫɤɨɪɨɫɬɶɸ v ɢ ɩɪɟɨɞɨɥɟɧɢɟ

18

ɫɭɦɦɚɪɧɨɝɨ ɭɫɢɥɢɹ ɩɨɞɚɱɢ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɥɢɧɟɣɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɫɭɩɩɨɪɬɚ

Fɉ 1,2 FX FZ FY 9,81 m μC ,

(2.21)

ɤɨɬɨɪɨɟ ɡɚɜɢɫɢɬ ɨɬ ɫɨɫɬɚɜɥɹɸɳɢɯ ɩɪɨɰɟɫɫɚ ɪɟɡɚɧɢɹ: ɭɫɢɥɢɹ ɩɨɞɚɱɢ FX , ɪɚɞɢɚɥɶɧɨɝɨ ɭɫɢɥɢɹ FY # 0,8 FX , ɭɫɢɥɢɹ ɪɟɡɚɧɢɹ FZ # 2,5 FX , ɨɬ ɦɚɫɫɵ ɫɭɩɩɨɪɬɚ m ɢ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɫɭɩɩɨɪɬɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨ ɧɚɩɪɚɜɥɹɸɳɢɦ μC . Ʉɨ-

ɷɮɮɢɰɢɟɧɬ 1,2 ɭɱɢɬɵɜɚɟɬ ɩɟɪɟɤɨɫɵ ɩɪɢ ɞɜɢɠɟɧɢɢ ɫɭɩɩɨɪɬɚ. ɇɚ ɨɛɪɚɬɧɨɦ ɯɨɞɟ ɫɭɩɩɨɪɬɚ ɪɟɡɚɧɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ.

	5
	6
	4
1
2	3

Ɋɢɫ. 2.8. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ ɫɬɚɧɤɚ: 1– ɞɜɢɝɚɬɟɥɶ; 2– ɪɟɞɭɤɬɨɪ; 3 – ɯɨɞɨɜɨɣ ɜɢɧɬ; 4 – ɝɚɣɤɚ; 5 – ɫɭɩɩɨɪɬ; 6 – ɧɚɩɪɚɜɥɹɸɳɢɟ

Ɍɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɞɚɧɧɵɟ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ ɫɬɚɧɤɚ:

m2,4 ɬ – ɦɚɫɫɚ ɩɟɪɟɦɟɳɚɟɦɨɝɨ ɝɪɭɡɚ;

v = 42 ɦɦ/ɫ– ɫɤɨɪɨɫɬɶ ɩɟɪɟɦɟɳɟɧɢɹ ɝɪɭɡɚ;

FX	6 ɤɇ – ɭɫɢɥɢɟ ɩɨɞɚɱɢ;
DXB	44 ɦɦ – ɞɢɚɦɟɬɪ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ;
mɏȼ	100 ɤɝ– ɦɚɫɫɚ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ;
μɋ	0,08 – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɫɭɩɩɨɪɬɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨ
ɧɚɩɪɚɜɥɹɸɳɢɦ;
i12	5 – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɲɟɫɬɟɪɟɧɧɨɣ ɩɚɪɵ;
Ș12	0,9 – ɄɉȾ ɩɟɪɟɞɚɱɢ;
J	0,03 ɤɝ ɦ2 , J	2	0,6 ɤɝ ɦ2 – ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ɲɟɫɬɟɪɟɧ;
1
JȾȼ	0,2 ɤɝ ɦ2 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɨɬɨɪɚ ɞɜɢɝɚɬɟɥɹ;

Į= 5,5q – ɭɝɨɥ ɧɚɪɟɡɤɢ ɪɟɡɶɛɵ; ij = 4q – ɭɝɨɥ ɬɪɟɧɢɹ ɜ ɪɟɡɶɛɟ.

ɉɨɫɥɟ ɢɡɭɱɟɧɢɹ ɩɪɢɧɰɢɩɚ ɪɚɛɨɬɵ ɦɟɯɚɧɢɡɦɚ ɢ ɟɝɨ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɨɩɪɟɞɟɥɹɟɦ ɭɱɚɫɬɤɢ ɜɵɞɟɥɟɧɢɹ ɩɨɬɟɪɶ:

–ɜ ɪɟɞɭɤɬɨɪɟ (ɩɨɬɟɪɢ ɭɱɢɬɵɜɚɸɬɫɹ ɤɩɞ Ș12 );

–ɜ ɩɟɪɟɞɚɱɟ «ɜɢɧɬ – ɝɚɣɤɚ» (ɩɨɬɟɪɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɱɟɪɟɡ ɭɝɨɥ ɬɪɟɧɢɹ ij);

–ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ (ɩɨɬɟɪɢ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɱɟɪɟɡ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɨɞɧɚɤɨ ɷɬɢ ɩɨɬɟɪɢ ɦɚɥɵ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɭɱɢɬɵɜɚɸɬɫɹ).

19

ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ (ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ)

v 42

ȦɊɈ ȡ 2,12 19,8 ɪɚɞ ɫ,

ɝɞɟ ȡ – ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ɩɟɪɟɞɚɱɢ «ɜɢɧɬ – ɝɚɣɤɚ» ɫ ɲɚɝɨɦ h ʌ dXB tgĮ, ɞɢɚɦɟɬɪɨɦ dXB ɢ ɭɝɥɨɦ ɧɚɪɟɡɤɢ ɪɟɡɶɛɵ Į

ȡ	v		h		ʌ dXB tgĮ		dXB	tgĮ	44	tg 5,5q 2,12 ɦɦ,
	ȦPO		2 ʌ		2 ʌ	2			2

Ɇɨɦɟɧɬ ɧɚ ɜɚɥɭ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ (ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ) ɫ ɭɱɟɬɨɦ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɟ «ɜɢɧɬ – ɝɚɣɤɚ» ɭɝɥɨɦ ɬɪɟɧɢɹ ij:

		Fɉ	dCP	tg Į ij 10,67		0,044	tg 5,5q 4q 39,27 H ɦ,
ɆɊɈ
		2			2
ɝɞɟ Fɉ – ɫɭɦɦɚɪɧɨɟ ɭɫɢɥɢɟ ɩɨɞɚɱɢ
Fɉ 1,2	FX FZ FY 9,81 m μC				1,2 FX 2,5 FX 0,8 FX 9,81 m μC
1,2	6 2,5 6 0,8 6 9,81 2,4 0,08 10,67 ɤɇ.

Ɇɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɨɥɟɡɧɚɹ:

– ɛɟɡ ɭɱɟɬɚ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɟ «ɜɢɧɬ – ɝɚɣɤɚ»

ɊɊɈ	Fɉ v 10,67 103 42 10 3	448,14 Bɬ;
– ɫ ɭɱɟɬɨɦ ɩɨɬɟɪɶ
ɊɊɈ	ɆɊɈ ȦɊɈ 39,27 19,8	777,5 ȼɬ.

ɋɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ

		ɆɊɈ				39,27		8,73 ɇ ɦ.
Ɇȼ		i	Ș		5 0,9
	12		12
ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ
ȦȾȼ	ȦɊɈ i12				19,8 5			99,1ɪɚɞ ɫ.
Ɇɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ
ɊȾȼ	Ɇȼ ȦȾȼ				8,73 99,1 864,3 ȼɬ .

ɇɚɯɨɞɢɦ ɷɥɟɦɟɧɬɵ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ, ɡɚɩɚɫɚɸɳɢɟ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ: ɫɭɩɩɨɪɬ ɦɚɫɫɨɣ m, ɯɨɞɨɜɨɣ ɜɢɧɬ ɦɚɫɫɨɣ mXB , ɲɟɫɬɟɪɧɢ ɪɟɞɭɤɬɨɪɚ J1

ɢ J2 , ɪɨɬɨɪ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ – JȾȼ .

Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɫɫɨɣ m ɫɭɩɩɨɪɬɚ, ɩɟɪɟɦɟɳɚɸɳɟɣɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v, ɢ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ Jɏȼ .

Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɟɝɨɫɹ ɫɭɩɩɨɪɬɚ

J	m v2	m ȡ2	2400 0,002122 0,0106 ɤɝ ɦ2 .
C	ȦPO2

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