Теоретическая механика_в_Вопросах_и_Ответах

Ɇɨɞɭɥɢ ɫɤɨɪɨɫɬɟɣ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɪɚɫɫɬɨɹɧɢɹɦ ɨɬ ɷɬɢɯ ɬɨɱɟɤ ɞɨ ɦɝɧɨɜɟɧɧɨɝɨ ɰɟɧɬɪɚ ɫɤɨɪɨɫɬɟɣ:

vM PM . vA PA

ɋɮɨɪɦɭɥɢɪɭɣɬɟ ɬɟɨɪɟɦɭ ɒɚɥɹ.

ɉɥɨɫɤɭɸ ɮɢɝɭɪɭ ɦɨɠɧɨ ɩɟɪɟɦɟɫɬɢɬɶ ɢɡ ɨɞɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɜ ɥɸɛɨɟ ɞɪɭ-

ɝɨɟ ɩɨɥɨɠɟɧɢɟ ɧɚ ɩɥɨɫɤɨɫɬɢ ɨɞɧɢɦ ɩɨɜɨɪɨɬɨɦ ɷɬɨɣ ɮɢɝɭɪɵ ɜɨɤɪɭɝ ɧɟɤɨ-

ɬɨɪɨɝɨ ɧɟɩɨɞɜɢɠɧɨɝɨ ɰɟɧɬɪɚ.

ɉɪɟɞɟɥɶɧɵɦ ɩɨɥɨɠɟɧɢɟɦ ɰɟɧɬɪɚ ɩɨɜɨɪɨɬɚ ɹɜɥɹɟɬɫɹ ɬɨɱɤɚ ɧɟɩɨɞɜɢɠɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɫ ɤɨɬɨɪɨɣ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɫɨɜɩɚɞɚɟɬ ɦɝɧɨɜɟɧɧɵɣ ɰɟɧɬɪ ɫɤɨ-

ɪɨɫɬɟɣ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ. ɗɬɚ ɬɨɱɤɚ ɧɚɡɵɜɚɟɬɫɹ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧɬɪɨɦ ɜɪɚ-

ɳɟɧɢɹ ɮɢɝɭɪɵ.

ɑɬɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɧɟɩɨɞɜɢɠɧɚɹ ɢ ɩɨɞɜɢɠɧɚɹ ɰɟɧɬɪɨɢɞɵ ɢ ɱɬɨ

ɩɪɨɢɫɯɨɞɢɬ ɫ ɰɟɧɬɪɚɦɢ ɩɪɢ ɞɟɣɫɬɜɢɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ?

Ʉɪɢɜɚɹ, ɩɪɟɞɫɬɚɜɥɹɸɳɚɹ ɝɟɨɦɟɬɪɢɱɟɫɤɨɟ ɦɟɫɬɨ ɦɝɧɨɜɟɧɧɵɯ ɰɟɧɬɪɨɜ ɜɪɚɳɟɧɢɹ ɧɚ ɧɟɩɨɞɜɢɠɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɧɚɡɵɜɚɟɬɫɹ ɧɟɩɨɞɜɢɠɧɨɣ ɰɟɧ-

ɬɪɨɢɞɨɣ.

Ʉɪɢɜɚɹ, ɩɪɟɞɫɬɚɜɥɹɸɳɚɹ ɝɟɨɦɟɬɪɢɱɟɫɤɨɟ ɦɟɫɬɨ ɦɝɧɨɜɟɧɧɵɯ ɰɟɧɬɪɨɜ ɫɤɨɪɨɫɬɟɣ, ɧɟɢɡɦɟɧɧɨ ɫɜɹɡɚɧɧɚɹ ɫ ɩɨɞɜɢɠɧɨɣ ɩɥɨɫɤɨɣ ɮɢɝɭɪɨɣ, ɧɚɡɵɜɚ-

ɟɬɫɹ ɩɨɞɜɢɠɧɨɣ ɰɟɧɬɪɨɢɞɨɣ.

ɉɪɢ ɞɟɣɫɬɜɢɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɩɨɞɜɢɠɧɚɹ ɰɟɧɬɪɨɢɞɚ ɤɚɬɢɬɫɹ ɛɟɡ ɫɤɨɥɶɠɟɧɢɹ ɩɨ ɧɟɩɨɞɜɢɠɧɨɣ ɰɟɧɬɪɨɢɞɟ (ɬɟɨɪɟɦɚ ɉɭɚɧɫɨ).

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɤɨɪɟɧɢɟ ɥɸɛɨɣ ɬɨɱɤɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ?

ɍɫɤɨɪɟɧɢɟ ɥɸɛɨɣ ɬɨɱɤɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɪɚɜɧɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɭɫɤɨɪɟɧɢɹ ɩɨɥɸɫɚ ɢ ɭɫɤɨɪɟɧɢɹ ɷɬɨɣ ɬɨɱɤɢ ɜɨ ɜɪɚɳɚɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɜɨɤɪɭɝ ɩɨɥɸɫɚ.

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aM aA aMA aA aMAɜɪ aMAɰɫ

ɝɞɟ aMAɜɪ MA H, aMAɜɪ A MA , aMAɰɫ MAZ2 , aMAɜɪ o A.

ɍɫɤɨɪɟɧɢɟ ɬɨɱɤɢ M ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɭɬɺɦ ɩɨɫɬɪɨɟɧɢɹ

ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɭɫɤɨɪɟɧɢɣ.

ɇɚɡɨɜɢɬɟ ɫɥɟɞɫɬɜɢɹ ɬɟɨɪɟɦɵ ɨɛ ɭɫɤɨɪɟɧɢɹɯ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ.

ɋɥɟɞɫɬɜɢɟ 1: ɉɪɨɟɤɰɢɹ ɭɫɤɨɪɟɧɢɹ ɥɸɛɨɣ ɬɨɱɤɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɧɚ ɨɫɶ,

ɩɪɨɜɟɞɺɧɧɭɸ ɢɡ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɩɨɥɸɫɚ ɱɟɪɟɡ ɷɬɭ ɬɨɱɤɭ, ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɟ ɩɪɨɟɤɰɢɢ ɭɫɤɨɪɟɧɢɹ ɩɨɥɸɫɚ ɧɚ ɬɭ ɠɟ ɨɫɶ.

ɋɥɟɞɫɬɜɢɟ 2: Ʉɨɧɰɵ ɭɫɤɨɪɟɧɢɣ ɬɨɱɟɤ ɧɟɢɡɦɟɧɹɟɦɨɝɨ ɨɬɪɟɡɤɚ ɥɟɠɚɬ ɧɚ ɨɞɧɨɣ ɩɪɹɦɨɣ ɢ ɞɟɥɹɬ ɷɬɭ ɩɪɹɦɭɸ ɧɚ ɱɚɫɬɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɪɚɫɫɬɨɹ-

ɧɢɹɦ ɦɟɠɞɭ ɷɬɢɦɢ ɬɨɱɤɚɦɢ.

Ʉɚɤɭɸ ɬɨɱɤɭ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɧɚɡɵɜɚɸɬ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧɬɪɨɦ ɭɫɤɨɪɟɧɢɣ,

ɢ ɦɨɠɟɬ ɥɢ ɦɝɧɨɜɟɧɧɵɣ ɰɟɧɬɪ ɭɫɤɨɪɟɧɢɣ ɫɨɜɩɚɞɚɬɶ ɫ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧ-

ɬɪɨɦ ɫɤɨɪɨɫɬɟɣ?

Ɍɨɱɤɚ Q, ɭɫɤɨɪɟɧɢɟ ɤɨɬɨɪɨɣ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɪɚɜɧɨ ɧɭɥɸ, ɧɚɡɵɜɚɟɬɫɹ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧɬɪɨɦ ɭɫɤɨɪɟɧɢɣ (Ɇɐɍ).

Ɇɝɧɨɜɟɧɧɵɣ ɰɟɧɬɪ ɫɤɨɪɨɫɬɟɣ P ɢ ɦɝɧɨɜɟɧɧɵɣ ɰɟɧɬɪ ɭɫɤɨɪɟɧɢɣ Q ɹɜ-

ɥɹɸɬɫɹ ɪɚɡɥɢɱɧɵɦɢ ɬɨɱɤɚɦɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ.

ɉɟɪɟɱɢɫɥɢɬɟ ɢɡɜɟɫɬɧɵɟ ɜɚɦ ɫɩɨɫɨɛɵ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɥɨɠɟɧɢɹ ɦɝɧɨɜɟɧɧɨɝɨ

ɰɟɧɬɪɚ ɭɫɤɨɪɟɧɢɣ.

ɚ) ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɢɡɜɟɫɬɧɚ ɬɨɱɤɚ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ, ɭɫɤɨɪɟɧɢɟ ɤɨɬɨ-

ɪɨɣ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɪɚɜɧɨ ɧɭɥɸ. ɗɬɚ ɬɨɱɤɚ ɹɜɥɹɟɬɫɹ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧ-

ɬɪɨɦ ɭɫɤɨɪɟɧɢɣ.

ɛ) ɂɡɜɟɫɬɧɵ ɦɨɞɭɥɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ,

ɚɥɝɟɛɪɚɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ Z ɢ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ H .

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Ɇɐɍ ɧɚɯɨɞɢɬɫɹ ɧɚ ɨɬɪɟɡɤɟ, ɫɨɫɬɚɜɥɹɸɳɟɦ ɫ ɜɟɤɬɨɪɨɦ ɭɫɤɨɪɟɧɢɹ aM

H

ɭɝɨɥ D arctg Z2 , ɤɨɬɨɪɵɣ ɨɬɥɨɠɟɧ ɨɬ ɜɟɤɬɨɪɚ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ ɜ ɫɬɨ-

ɪɨɧɭ H ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɬɨɱɤɢ Ɇ , ɪɚɜɧɨɦ:

MQ aM .

H2 Z4

ɜ) ɂɡɜɟɫɬɧɵ ɦɨɞɭɥɢ ɢ ɧɚɩɪɚɜɥɟɧɢɹ ɭɫɤɨɪɟɧɢɣ ɞɜɭɯ ɬɨɱɟɤ Ⱥ ɢ Ɇ ɩɥɨ-

ɫɤɨɣ ɮɢɝɭɪɵ.

ɉɪɢɦɟɦ ɬɨɱɤɭ Ⱥ ɡɚ ɩɨɥɸɫ, ɬɨɝɞɚ:

aM aA aMA .

ɉɨɫɬɪɨɢɦ ɩɪɢ ɬɨɱɤɟ Ɇ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦ ɭɫɤɨɪɟɧɢɣ ɩɨ ɡɚɞɚɧɧɨɣ ɞɢɚɝɨ-

ɧɚɥɢ aM ɢ ɨɞɧɨɣ ɢɡ ɫɬɨɪɨɧ aA . Ⱦɪɭɝɚɹ ɫɬɨɪɨɧɚ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦɚ ɨɩɪɟɞɟ-

ɥɢɬ ɭɫɤɨɪɟɧɢɟ aMA . ɍɫɤɨɪɟɧɢɟ aGMA ɫɨɫɬɚɜɥɹɟɬ ɭɝɨɥ D arctg H ɫ ɨɬ-

Z2

ɪɟɡɤɨɦ ɆȺ. Ɉɬɥɨɠɢɦ ɭɝɨɥ D ɨɬ ɭɫɤɨɪɟɧɢɣ ɬɨɱɟɤ ȺɢɆ ɩɨ ɧɚɩɪɚɜɥɟ-

ɧɢɸH . Ɍɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɩɨɥɭɩɪɹɦɵɯ Q ɢ ɛɭɞɟɬ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧɬɪɨɦ ɭɫɤɨɪɟɧɢɣ.

Ʉɚɤ ɨɩɪɟɞɟɥɹɸɬɫɹ ɭɫɤɨɪɟɧɢɹ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɱɟɪɟɡ ɦɝɧɨɜɟɧɧɵɣ

ɰɟɧɬɪ ɭɫɤɨɪɟɧɢɣ?

Ɇɨɞɭɥɢ ɭɫɤɨɪɟɧɢɣ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɪɚɫɫɬɨɹɧɢ-

ɹɦ ɨɬ ɷɬɢɯ ɬɨɱɟɤ ɞɨ ɦɝɧɨɜɟɧɧɨɝɨ ɰɟɧɬɪɚ ɭɫɤɨɪɟɧɢɣ, ɚ ɜɟɤɬɨɪɵ ɭɫɤɨɪɟɧɢɣ ɫɨɫɬɚɜɥɹɸɬ ɫ ɨɬɪɟɡɤɚɦɢ, ɫɨɟɞɢɧɹɸɳɢɦɢ ɷɬɢ ɬɨɱɤɢ ɫ ɦɝɧɨɜɟɧɧɵɦ ɰɟɧ-

	ɬɪɨɦ ɭɫɤɨɪɟɧɢɣ, ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɭɝɨɥ D arctg					H	.
					Z2
	aM	QM H2 Z4 ,	aM			QM
			aB			QB

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Ʉɚɤɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɥɨɠɟɧɢɟ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɫ ɨɞɧɨɣ ɧɟ-

ɩɨɞɜɢɠɧɨɣ ɬɨɱɤɨɣ?

Ⱦɜɢɠɟɧɢɟ ɬɜɺɪɞɨɝɨ ɬɟɥɚ, ɨɞɧɚ ɢɡ ɬɨɱɟɤ ɤɨɬɨɪɨɝɨ ɜɨ ɜɫɺ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɨɫɬɚɺɬɫɹ ɧɟɩɨɞɜɢɠɧɨɣ, ɧɚɡɵɜɚɸɬ ɫɮɟɪɢɱɟɫɤɢɦ ɞɜɢɠɟɧɢɟɦ ɬɜɺɪɞɨɝɨ ɬɟ-

ɥɚ. ɉɪɢ ɬɚɤɨɦ ɞɜɢɠɟɧɢɢ ɜɫɟ ɨɫɬɚɥɶɧɵɟ ɬɨɱɤɢ ɬɟɥɚ ɞɜɢɠɭɬɫɹ ɩɨ ɫɮɟɪɢɱɟ-

ɫɤɢɦ ɩɨɜɟɪɯɧɨɫɬɹɦ. ɉɨɥɨɠɟɧɢɹ ɬɟɥɚ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɪɟɦɹ ɭɝɥɚɦɢ ɗɣɥɟɪɚ:

\ f1(t) , T f2 (t) , M f3(t),

ɝɞɟ \ — ɭɝɨɥ ɩɪɟɰɟɫɫɢɢ, T — ɭɝɨɥ ɧɭɬɚɰɢɢ, M — ɭɝɨɥ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɪɚɳɟɧɢɹ.

Ʉɚɤ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɬɟɨɪɟɦɚ ɗɣɥɟɪɚ-Ⱦɚɥɚɦɛɟɪɚ ɨ ɩɟɪɟɦɟɳɟɧɢɢ ɬɜɺɪɞɨɝɨ

ɬɟɥɚ ɫ ɨɞɧɨɣ ɧɟɩɨɞɜɢɠɧɨɣ ɬɨɱɤɨɣ?

Ɍɜɺɪɞɨɟ ɬɟɥɨ, ɢɦɟɸɳɟɟ ɨɞɧɭ ɧɟɩɨɞɜɢɠɧɭɸ ɬɨɱɤɭ, ɦɨɠɧɨ ɩɟɪɟɦɟɫɬɢɬɶ ɢɡ ɨɞɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɜ ɥɸɛɨɟ ɞɪɭɝɨɟ ɩɨɜɨɪɨɬɨɦ ɜɨɤɪɭɝ ɧɟɤɨɬɨɪɨɣ ɨɫɢ,

ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɧɟɩɨɞɜɢɠɧɭɸ ɬɨɱɤɭ.

ɑɬɨ ɧɚɡɵɜɚɸɬ ɦɝɧɨɜɟɧɧɨɣ ɨɫɶɸ ɜɪɚɳɟɧɢɹ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɫ ɨɞɧɨɣ ɧɟɩɨɞ-

ɜɢɠɧɨɣ ɬɨɱɤɨɣ ɢ ɤɚɤɨɜɵ ɭɪɚɜɧɟɧɢɹ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ ɜ ɧɟɩɨɞɜɢɠ-

ɧɨɣ ɢ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɚɯ ɨɫɟɣ ɞɟɤɚɪɬɨɜɵɯ ɤɨɨɪɞɢɧɚɬ?

Ɇɝɧɨɜɟɧɧɚɹ ɨɫɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɝɟɨɦɟɬɪɢɱɟɫɤɨɟ ɦɟɫɬɨ ɬɨɱɟɤ ɬɟɥɚ,

ɫɤɨɪɨɫɬɢ ɤɨɬɨɪɵɯ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɪɚɜɧɵ ɧɭɥɸ.

ɍɪɚɜɧɟɧɢɹ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɫɟɣ:

Zy z Zz y	0½			x		y		z
Zz x Zx z		°
	0	¾							.
			ɢɥɢ	Zx	Zy
Zx y Zy x		°					Zz
	0¿

Ɂɞɟɫɶ x, y, z - ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ.

ɍɪɚɜɧɟɧɢɹ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɫɟɣ:

34

	Z9] Z] 9	0½
	Z][ Z[]		°	[		9		]
		0¾ ɢɥɢ							.
				Z[	Z9
	Z[9 Z9[	0	°				Z]
			¿

Ɂɞɟɫɶ [,9,] — ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ.

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɨɞɭɥɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɬɟɥɚ ɩɪɢ ɫɮɟ-

ɪɢɱɟɫɤɨɦ ɞɜɢɠɟɧɢɢ?

ȼɟɤɬɨɪ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɪɚɜɟɧ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ ɜɟɤɬɨɪɚ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ ɜɟɤɬɨɪɚ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ:

HZ ,

ɬ. ɟ. ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɬɟɥɚ ɝɟɨɦɟɬɪɢɱɟɫɤɢ ɪɚɜɧɨ ɥɢɧɟɣɧɨɣ ɫɤɨɪɨɫɬɢ ɤɨɧɰɚ ɜɟɤɬɨɪɚ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ. ɉɪɹɦɚɹ ɩɨ ɤɨɬɨɪɨɣ ɧɚɩɪɚɜɥɟɧ ɜɟɤɬɨɪ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ H , ɧɚɡɵɜɚɟɬɫɹ ɨɫɶɸ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ.

Ʉɚɤ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɤɨɪɨɫɬɢ ɬɨɱɟɤ ɬɟɥɚ ɩɪɢ ɫɮɟɪɢɱɟɫɤɨɦ ɞɜɢɠɟɧɢɢ?

ɋɤɨɪɨɫɬɶ ɥɸɛɨɣ ɬɨɱɤɢ ɬɟɥɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ ɫɤɨɪɨɫɬɶ ɜɨ ɜɪɚɳɚ-

ɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɜɨɤɪɭɝ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ:

vZ ur ,

ɝɞɟ r - ɪɚɞɢɭɫ-ɜɟɤɬɨɪ ɬɨɱɤɢ, ɩɪɨɜɟɞɺɧɧɵɣ ɢɡ ɧɟɩɨɞɜɢɠɧɨɣ ɬɨɱɤɢ.

Ɇɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ:

v Z r sin J Z hZ ,

ɝɞɟ J — ɭɝɨɥ ɦɟɠɞɭ rG ɢ ɦɝɧɨɜɟɧɧɨɣ ɨɫɶɸ ɜɪɚɳɟɧɢɹ,

hZ — ɤɪɚɬɱɚɣɲɟɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɱɤɢ ɨɬ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ.

ɉɪɨɟɤɰɢɢ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ ɧɚ ɧɟɩɨɞɜɢɠɧɵɟ ɨɫɢ ɞɟɤɚɪɬɨɜɵɯ ɤɨɨɪɞɢɧɚɬ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ ɗɣɥɟɪɚ:

Vx Zy z Zz y, Vy Zz x Zx z, Vz Zx y Zy x .

35

Ʉɚɤɢɟ ɦɨɞɭɥɢ ɢ ɧɚɩɪɚɜɥɟɧɢɹ ɢɦɟɸɬ ɫɨɫɬɚɜɥɹɸɳɢɟ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ ɬɟɥɚ

ɩɪɢ ɫɮɟɪɢɱɟɫɤɨɦ ɞɜɢɠɟɧɢɢ?

ɍɫɤɨɪɟɧɢɟ ɥɸɛɨɣ ɬɨɱɤɢ ɬɟɥɚ ɩɪɢ ɫɮɟɪɢɱɟɫɤɨɦ ɞɜɢɠɟɧɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɫɭɦɦɚ ɟɺ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɢ ɨɫɟɫɬɪɟɦɢɬɟɥɶɧɨɝɨ ɭɫɤɨ-

ɪɟɧɢɣ:

ɚɚɜɪ ɚɨɫ .

ȼɟɤɬɨɪ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɚɜɪ H ur ɧɚɩɪɚɜɥɟɧ ɩɟɪɩɟɧɞɢɤɭɥɹɪ-

ɧɨ ɩɥɨɫɤɨɫɬɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ H ɢ r ɜ ɬɭ ɫɬɨɪɨɧɭ, ɨɬɤɭɞɚ ɩɨɜɨɪɨɬ H ɤ r ɧɚ ɧɚɢɦɟɧɶɲɢɣ ɭɝɨɥ ɜɢɞɟɧ ɩɪɨɯɨɞɹɳɢɦ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ.

Ɇɨɞɭɥɶ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ:

ɚɜɪ hHH ,

ɝɞɟ hH — ɤɪɚɬɱɚɣɲɟɟ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɬɨɱɤɢ ɞɨ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ.

ȼɟɤɬɨɪ ɨɫɟɫɬɪɟɦɢɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɚɨɫ Z uV ɧɚɩɪɚɜɥɟɧ ɩɟɪɩɟɧɞɢ-

ɤɭɥɹɪɧɨ ɤ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ.

Ɇɨɞɭɥɶ ɨɫɟɫɬɪɟɦɢɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ:

ɚɨɫ h Z2	,
Z

ɝɞɟ hZ - ɤɪɚɬɱɚɣɲɟɟ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɬɨɱɤɢ ɞɨ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ.

Ɇɨɞɭɥɶ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ ɤɚɤ ɞɢɚɝɨɧɚɥɢ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦɚ ɭɫɤɨɪɟɧɢɣ ɨɩ-

ɪɟɞɟɥɹɟɬɫɹ:

ɚɚɜɪ2 ɚɨɫ2 2ɚɜɪɚɨɫ cos(ɚɜɪ,ɚɨɫ) .

ɇɚ ɤɚɤɢɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɪɚɡɥɨɠɢɬɶ ɞɜɢɠɟɧɢɟ ɫɜɨɛɨɞ-

ɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɢ ɤɚɤ ɨɧɢ ɡɚɜɢɫɹɬ ɨɬ ɜɵɛɨɪɚ ɩɨɥɸɫɚ?

36

Ⱦɜɢɠɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɥɨɠɧɨɟ,

ɫɨɫɬɨɹɳɟɟ ɢɡ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɜɦɟɫɬɟ ɫ ɩɨɥɸɫɨɦ, ɢ ɫɮɟɪɢɱɟɫɤɨɟ ɞɜɢɠɟ-

ɧɢɟ ɜɨɤɪɭɝ ɷɬɨɝɨ ɩɨɥɸɫɚ.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɜɢɠɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɲɟ-

ɫɬɶɸ ɭɪɚɜɧɟɧɢɹɦɢ:

x0	f1(t), y0 f2 (t), z0 f3 (t),
\	f4 (t), T f5 (t), M f6 (t).

ɉɨɫɬɭɩɚɬɟɥɶɧɚɹ ɱɚɫɬɶ ɞɜɢɠɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɜɵɛɨɪɚ ɩɨɥɸɫɚ, ɫɮɟɪɢɱɟɫɤɚɹ ɱɚɫɬɶ ɨɬ ɜɵɛɨɪɚ ɩɨɥɸɫɚ ɧɟ ɡɚɜɢɫɢɬ.

Ʉɚɤ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɤɨɪɨɫɬɢ ɬɨɱɟɤ ɫɜɨɛɨɞɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ?

ɋɤɨɪɨɫɬɶ ɥɸɛɨɣ ɬɨɱɤɢ ɫɜɨɛɨɞɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɪɚɜɧɚ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɫɤɨɪɨɫɬɢ ɩɨɥɸɫɚ ɢ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ ɜ ɟɺ ɫɮɟɪɢɱɟɫɤɨɦ ɞɜɢɠɟɧɢɢ ɜɨɤɪɭɝ ɩɨɥɸɫɚ

vv0 Zur .

Ʉɚɤ ɨɩɪɟɞɟɥɹɸɬɫɹ ɭɫɤɨɪɟɧɢɹ ɬɨɱɟɤ ɫɜɨɛɨɞɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ?

ɍɫɤɨɪɟɧɢɟ ɬɨɱɤɢ ɫɜɨɛɨɞɧɨɝɨ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɪɚɜɧɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɭɫɤɨɪɟɧɢɹ ɩɨɥɸɫɚ, ɨɫɟɫɬɪɟɦɢɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɢ ɟɺ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ, ɨɩɪɟɞɟɥɺɧɧɵɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɢ ɨɫɢ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ, ɩɪɨɯɨɞɹɳɟɝɨ ɱɟɪɟɡ ɩɨɥɸɫ

ɚɚ0 ɚɜɪ ɚɨɫ .

Ⱦɚɣɬɟ ɨɩɪɟɞɟɥɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ, ɩɟɪɟɧɨɫɧɨɝɨ ɢ ɚɛɫɨɥɸɬɧɨɝɨ ɞɜɢɠɟ-

ɧɢɹ ɬɨɱɤɢ.

Ⱦɜɢɠɟɧɢɟ ɬɨɱɤɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ ɧɚɡɵɜɚɸɬ

ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɞɜɢɠɟɧɢɟɦ ɬɨɱɤɢ.

37

Ⱦɜɢɠɟɧɢɟ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɺɬɚ ɢ ɧɟɢɡɦɟɧɧɨ ɫɜɹɡɚɧɧɨɝɨ ɫ ɧɟɣ ɬɟ-

ɥɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ ɹɜɥɹɟɬɫɹ ɞɥɹ ɬɨɱɤɢ ɩɟɪɟɧɨɫɧɵɦ ɞɜɢɠɟɧɢɟɦ.

Ⱦɜɢɠɟɧɢɟ ɬɨɱɤɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ ɧɚɡɵ-

ɜɚɸɬ ɚɛɫɨɥɸɬɧɵɦ.

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚɛɫɨɥɸɬɧɚɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ ɜ ɫɨɫɬɚɜɧɨɦ ɞɜɢɠɟɧɢɢ?

Ⱥɛɫɨɥɸɬɧɚɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ ɪɚɜɧɚ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɟɺ ɩɟɪɟɧɨɫɧɨɣ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɟɣ:

vve vr .

Ɍɚɤ ɤɚɤ ɚɛɫɨɥɸɬɧɚɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɢɚɝɨɧɚɥɶɸ ɩɚɪɚɥɥɟ-

ɥɨɝɪɚɦɦɚ, ɩɨɫɬɪɨɟɧɧɨɣ ɧɚ ɩɟɪɟɧɨɫɧɨɣ ɫɤɨɪɨɫɬɢ ve ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨ-

ɪɨɫɬɢ vr , ɬɨ ɟɺ ɦɨɞɭɥɶ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ:

vve2 vr2 2ve vr cos ve ,vr .

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚɛɫɨɥɸɬɧɨɟ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ ɩɪɢ ɧɟɩɨɫɬɭɩɚɬɟɥɶɧɨɦ ɩɟɪɟɧɨɫɧɨɦ ɞɜɢɠɟɧɢɢ?

ȼ ɫɥɭɱɚɟ ɧɟɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɩɟɪɟɧɨɫɧɨɝɨ ɞɜɢɠɟɧɢɹ ɚɛɫɨɥɸɬɧɨɟ ɭɫɤɨɪɟ-

ɧɢɟ ɪɚɜɧɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɩɟɪɟɧɨɫɧɨɝɨ, ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɢ ɤɨɪɢɨ-

ɥɢɫɨɜɚ (ɩɨɜɨɪɨɬɧɨɝɨ) ɭɫɤɨɪɟɧɢɣ.

aae ar ac .

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚɛɫɨɥɸɬɧɨɟ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ ɩɪɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɦ ɩɟ-

ɪɟɧɨɫɧɨɦ ɞɜɢɠɟɧɢɢ?

ȼ ɫɥɭɱɚɟ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɩɟɪɟɧɨɫɧɨɝɨ ɞɜɢɠɟɧɢɹ ɚɛɫɨɥɸɬɧɨɟ ɭɫɤɨɪɟɧɢɟ ɪɚɜɧɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɟɺ ɩɟɪɟɧɨɫɧɨɝɨ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟ-

ɧɢɣ.

a ae ar .

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Ʉɚɤɨɜɵ ɩɪɢɱɢɧɵ ɩɨɹɜɥɟɧɢɹ ɤɨɪɢɨɥɢɫɨɜɚ (ɩɨɜɨɪɨɬɧɨɝɨ) ɭɫɤɨɪɟɧɢɹ?

ɉɨɹɜɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ Ʉɨɪɢɨɥɢɫɚ (ɩɨɜɨɪɨɬɧɨɝɨ ɭɫɤɨɪɟɧɢɹ) ɨɛɭɫɥɚɜɥɢɜɚ-

ɟɬɫɹ ɞɜɭɦɹ ɩɪɢɱɢɧɚɦɢ:

ɚ) ɜɫɥɟɞɫɬɜɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɨɱɤɢ, ɩɟɪɟɦɟɳɚɸɳɟɣɫɹ ɩɨ ɨɬ-

ɧɨɲɟɧɢɸ ɤ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ, ɢɡɦɟɧɹɟɬɫɹ ɩɟɪɟɧɨɫɧɚɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ;

ɛ) ɜɫɥɟɞɫɬɜɢɟ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɟɪɟɧɨɫɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɢɡ-

ɦɟɧɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɟɩɨɞ-

ɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ.

Ʉɚɤɨɜɵ ɦɨɞɭɥɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ Ʉɨɪɢɨɥɢɫɚ ɢ ɩɪɢ ɤɚɤɢɯ ɭɫɥɨɜɢɹɯ ɭɫɤɨɪɟɧɢɟ ɨɧɨ ɪɚɜɧɨ ɧɭɥɸ?

ɚɫ 2Zɟ uvr

Ɇɨɞɭɥɶ ɭɫɤɨɪɟɧɢɹ Ʉɨɪɢɨɥɢɫɚ:

ɚɫ 2 Ze vr sin Ze ,vr .

ɇɚɩɪɚɜɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ Ʉɨɪɢɨɥɢɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɩɪɚɜɢɥɭ ɜɟɤɬɨɪɧɨɝɨ ɩɪɨɢɡɜɟɞɟɧɢɹ.

ɍɫɤɨɪɟɧɢɟ Ʉɨɪɢɨɥɢɫɚ ɪɚɜɧɨ ɧɭɥɸ ɜ ɬɪɺɯ ɫɥɭɱɚɹɯ:

1)ɟɫɥɢ Zɟ 0;

2)ɟɫɥɢ vr 0;

3) ɟɫɥɢ sin Ze ,vr 0, ɬ. ɟ. ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ vr ɩɚɪɚɥɥɟɥɶɧɚ ɨɫɢ ɩɟɪɟɧɨɫɧɨɝɨ ɜɪɚɳɟɧɢɹ.

ɑɬɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɚɛɫɨɥɸɬɧɨɟ ɞɜɢɠɟɧɢɟ ɬɟɥɚ, ɤɨɬɨɪɨɟ ɭɱɚɫɬɜɭɟɬ ɜ ɧɟɫɤɨɥɶɤɢɯ ɜɪɚɳɟɧɢɹɯ ɜɨɤɪɭɝ ɫɯɨɞɹɳɢɯɫɹ ɦɝɧɨɜɟɧɧɵɯ ɨɫɟɣ?

ȿɫɥɢ ɬɜɺɪɞɨɟ ɬɟɥɨ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫɨɜɟɪɲɚɟɬ ɜɪɚɳɟɧɢɟ ɜɨɤɪɭɝ ɧɟɫɤɨɥɶ-

ɤɢɯ ɦɝɧɨɜɟɧɧɵɯ ɨɫɟɣ, ɩɟɪɟɫɟɤɚɸɳɢɯɫɹ ɜ ɨɞɧɨɣ ɬɨɱɤɟ ɪɟɡɭɥɶɬɢɪɭɸɳɢɦ ɞɜɢɠɟɧɢɟɦ, ɛɭɞɟɬ ɜɪɚɳɟɧɢɟ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z ɚɛɫɨɥɸɬɧɨɝɨ ɜɪɚ-

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ɳɟɧɢɹ ɬɟɥɚ, ɪɚɜɧɨɣ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɟ ɫɤɨɪɨɫɬɟɣ ɫɨɫɬɚɜɥɹɸɳɢɯ ɞɜɢɠɟɧɢɣ.

n

Z¦Zk .

i 1

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɬɜɺɪɞɨɝɨ ɬɟɥɚ, ɜɪɚɳɚɸɳɟɝɨɫɹ ɜɨɤɪɭɝ ɞɜɭɯ ɩɚɪɚɥɥɟɥɶɧɵɯ ɨɫɟɣ ɜ ɨɞɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ?

Ɇɨɞɭɥɶ ɚɛɫɨɥɸɬɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɪɚɜɟɧ ɫɭɦɦɟ ɦɨɞɭɥɟɣ ɭɝɥɨɜɵɯ ɫɤɨɪɨɫɬɟɣ ɫɨɫɬɚɜɥɹɸɳɢɯ ɜɪɚɳɟɧɢɣ:

ZZr Ze .

Ɇɝɧɨɜɟɧɧɚɹ ɨɫɶ ɚɛɫɨɥɸɬɧɨɝɨ ɜɪɚɳɟɧɢɹ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɥɟɠɢɬ ɜ ɩɥɨɫ-

ɤɨɫɬɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɨɫɢ ɩɟɪɟɧɨɫɧɨɝɨ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɜɪɚɳɟɧɢɣ, ɢ

ɛɭɞɭɱɢ ɢɦ ɩɚɪɚɥɥɟɥɶɧɨɣ, ɞɟɥɢɬ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɨɫɹɦɢ ɜɧɭɬɪɟɧɧɢɦ ɨɛɪɚɡɨɦ ɧɚ ɱɚɫɬɢ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɭɝɥɨɜɵɦ ɫɤɨɪɨɫɬɹɦ.

Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɬɜɺɪɞɨɝɨ ɬɟɥɚ, ɜɪɚɳɚɸɳɟɝɨɫɹ ɜɨɤɪɭɝ ɞɜɭɯ ɩɚɪɚɥɥɟɥɶɧɵɯ ɨɫɟɣ ɜ ɪɚɡɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ?

Ɇɨɞɭɥɶ ɚɛɫɨɥɸɬɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɪɚɜɟɧ ɪɚɡɧɨɫɬɢ ɭɝɥɨɜɵɯ ɫɤɨɪɨ-

ɫɬɟɣ ɫɨɫɬɚɜɥɹɸɳɢɯ ɜɪɚɳɟɧɢɣ:

ZZr Ze .

Ɇɝɧɨɜɟɧɧɚɹ ɨɫɶ ɚɛɫɨɥɸɬɧɨɝɨ ɜɪɚɳɟɧɢɹ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɩɚɪɚɥɥɟɥɶɧɚ ɨɫɹɦ ɩɟɪɟɧɨɫɧɨɝɨ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɜɪɚɳɟɧɢɣ ɢ ɥɟɠɢɬ ɜ ɩɥɨɫɤɨɫɬɢ, ɩɪɨ-

ɯɨɞɹɳɟɣ ɱɟɪɟɡ ɷɬɢ ɨɫɢ, ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɜɨɤɪɭɝ ɤɨɬɨɪɨɣ ɛɨɥɶɲɟ.

Ɋɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɨɫɶɸ ɚɛɫɨɥɸɬɧɨɝɨ ɜɪɚɳɟɧɢɹ ɢ ɨɫɹɦɢ ɩɟɪɟɧɨɫɧɨɝɨ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɜɪɚɳɟɧɢɹ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɭɝɥɨɜɵɦ ɫɤɨɪɨɫɬɹɦ.

ɑɬɨ ɧɚɡɵɜɚɸɬ ɩɚɪɨɣ ɜɪɚɳɟɧɢɣ ɢ ɱɟɦɭ ɪɚɜɧɚ ɫɤɨɪɨɫɬɶ ɷɬɨɝɨ ɪɟɡɭɥɶɬɢ-

ɪɭɸɳɟɝɨ ɞɜɢɠɟɧɢɹ?

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