The application of topological models in the problem of the dynamic interaction of a rigid bodies system

<jats:p>The differential equations of beam motion considering of moving, elastic and dissipative forces are presented on types of oscillations and integrate longitudinal, torsional, bending as well as shearing vibrations. The basic topological structure is figured in the form of the weighed and dual graphs for determination of force and kinematic parameters. The representing algebraic system is noted as tensor relations. </jats:p>

section_content: The differential equations of beam motion considering of moving, elastic and dissipative forces are presented on types of oscillations and integrate longitudinal, torsional, bending as well as shearing vibrations. The basic topological structure is figured in the form of the weighed and dual graphs for determination of force and kinematic parameters. The representing algebraic system is noted as tensor relations. 

Ɉɬɦɟɱɟɧɧɵɟ ɜ [1] ɬɪɭɞɧɨɫɬɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɩɨɥɭɱɟɧɢɟɦ ɬɨɱɧɨɝɨ ɪɟɲɟɧɢɹ ɧɟɤɨɬɨɪɵɯ ɫɥɨɠɧɵɯ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɧɟɥɢɧɟɣɧɵɯ ɡɚɞɚɱ ɞɢɧɚɦɢɤɢ ɞɢɫɤɪɟɬɧɨ-ɤɨɧɬɢɧɭɚɥɶɧɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ, ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɨɞɨɥɟɧɵ ɫ ɩɨɦɨɳɶɸ ɩɪɢɛɥɢɠɟɧɧɵɯ ɦɟɬɨɞɨɜ, ɨɫɧɨɜɚɧɧɵɯ ɧɚ ɡɚɦɟɧɟ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɫɢɫɬɟɦɵ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɨɣ ɫ ɤɨɧɟɱɧɵɦ ɱɢɫɥɨɦ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ. ȼ ɱɚɫɬɧɨɫɬɢ, ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɦɨɫɬɨɜɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɩɪɢ ɞɟɣɫɬɜɢɢ ɩɨɞɜɢɠɧɨɣ ɧɚɝɪɭɡɤɢ, ɬɚɤɠɟ ɦɨɞɟɥɢɪɭɟɦɨɣ ɫɢɫɬɟɦɨɣ ɞɢɫɤɪɟɬɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɬɚɤɨɣ ɩɨɞɯɨɞ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɦ. 

ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɧɟɤɨɬɨɪɵɟ ɩɪɟɞɩɨɫɵɥɤɢ, ɩɨɡɜɨɥɹɸɳɢɟ ɪɚɫɫɱɢɬɵɜɚɬɶ ɫɬɟɪɠɧɟɜɵɟ ɢ ɛɚɥɨɱɧɵɟ ɤɨɧɫɬɪɭɤɰɢɢ ɫ ɨɛɴɟɦɧɵɦɢ (ɞɢɫɤɨɜɵɦɢ) ɦɚɫɫɚɦɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɷɥɟɦɟɧɬɚɪɧɚɹ ɛɚɥɤɚ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɬɜɟɪɞɵɯ ɬɟɥ, ɰɟɧɬɪɵ ɬɹɠɟɫɬɢ ɤɨɬɨɪɵɯ ɫɨɟɞɢɧɟɧɵ ɛɟɡɵɧɟɪɰɢɨɧɧɵɦɢ ɭɩɪɭɝɢɦɢ ɫɜɹɡɹɦɢɫɬɟɪɠɧɹɦɢ, ɨɛɥɚɞɚɸɳɢɦɢ ɠɟɫɬɤɨɫɬɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɢɫɯɨɞɧɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɛɚɥɤɢ.

section_content: Ʉɚɠɞɨɟ ɬɜɟɪɞɨɟ ɬɟɥɨ ɢɦɟɟɬ ɲɟɫɬɶ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɢ ɦɨɠɟɬ ɫɨɜɟɪɲɚɬɶ, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɩɨɫɬɭɩɚɬɟɥɶɧɵɟ ɢ ɜɪɚɳɚɬɟɥɶɧɵɟ ɞɜɢɠɟɧɢɹ. ȼ ɰɟɥɨɦ, ɧɟɪɚɡɪɟɡɧɚɹ ɤɨɧɫɬɪɭɤɰɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ ɫɢɫɬɟɦɵ ɬɜɟɪɞɵɯ ɬɟɥ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɜɹɡɚɧɧɵɯ ɦɟɠɞɭ ɫɨɛɨɣ ɭɩɪɭɝɢɦɢ ɫɬɟɪɠɧɹɦɢ (ɪɢɫ. 1). 

Ʉɨɥɟɛɚɧɢɹ ɷɥɟɦɟɧɬɚɪɧɨɣ ɛɚɥɤɢ ɫ ɲɟɫɬɶɸ ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ ɧɚ ɤɚɠɞɨɦ ɤɨɧɰɟ ɨɩɢɫɵɜɚɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɨɛɵɤɧɨɜɟɧɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɪɚɡɥɨɠɢɬɶ ɩɨ ɨɬɞɟɥɶɧɵɦ ɜɢɞɚɦ ɤɨɥɟɛɚɧɢɣ ɞɥɹ ɤɚɠɞɨɝɨ k -ɝɨ ɬɟɥɚ [2]. ɇɚɩɪɢɦɟɪ, ɩɪɢ 1 k ɭɪɚɜɧɟɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ ɩɪɨɞɨɥɶɧɵɯ ɢ ɤɪɭɬɢɥɶɧɵɯ ɤɨɥɟɛɚɧɢɣ ɢɦɟɸɬ ɜɢɞ

ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɥɹ ɤɨɥɟɛɚɧɢɣ ɫɞɜɢɝɚ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɹɯ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ

ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɭɪɚɜɧɟɧɢɹ ɢɡɝɢɛɧɵɯ ɤɨɥɟɛɚɧɢɣ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɟɣ y, z ɩɪɢɜɨɞɹɬɫɹ ɤ ɜɢɞɭ || ||

F m m m q q qɜɟɤɬɨɪ ɫɢɥɨɜɵɯ ɩɚɪɚɦɟɬɪɨɜ;

ɋɜɹɡɶ ɦɟɠɞɭ ɜɟɤɬɨɪɨɦ ɭɫɢɥɢɣ ɢ ɜɟɤɬɨɪɨɦ ɩɟɪɟɦɟɳɟɧɢɣ ɬɚɤɠɟ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɦɚɬɪɢɰɭ ɩɨɞɚɬɥɢɜɨɫɬɟɣ (ɢɦɩɟɞɚɧɫɨɜ) Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɨɫɧɨɜɧɵɦɢ ɤɨɦɩɨɧɟɧɬɚɦɢ ɝɪɚɮɚ GR ɛɭɞɭɬ ɩɨɞɝɪɚɮɵ x G, G M, y G, z G, ɤɨɥɶɰɟɜɚɹ ɫɭɦɦɚ ɤɨɬɨɪɵɯ ɜ ɪɚɡɥɢɱɧɵɯ ɫɨɱɟɬɚɧɢɹɯ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɝɪɚɮɵ GL ɢ GT ɞɥɹ ɫɨɜɦɟɫɬɧɵɯ ɢɡɝɢɛɧɨ-ɩɪɨɞɨɥɶɧɵɯ ɢ ɢɡɝɢɛɧɨɤɪɭɬɢɥɶɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɚ ɬɚɤɠɟ ɝɪɚɮ GR ɞɥɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɛɚɥɤɢ [6]. 

Ⱦɥɹ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɬɟɥ, ɧɚɯɨɞɹɳɢɯɫɹ ɜɧɭɬɪɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɦɚɬɪɢɰɵ Y, Z ɞɥɹ ɫɨɫɟɞɧɢɯ ɫɬɟɪɠɧɟɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:

ȼ ɤɨɨɪɞɢɧɚɬɧɨɣ ɮɨɪɦɟ ɫ ɭɱɟɬɨɦ (8) ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɤɨɬɨɪɚɹ ɨɛɴɟɞɢɧɹɟɬ ɩɪɨɞɨɥɶɧɵɟ, ɤɪɭɬɢɥɶɧɵɟ, ɢɡɝɢɛɧɵɟ ɤɨɥɟɛɚɧɢɹ ɢ ɤɨɥɟɛɚɧɢɹ ɫɞɜɢɝɚ k -ɝɨ ɬɟɥɚ

) (

2) ɩɪɢɧɢɦɚɸɬ ɡɧɚɱɟɧɢɹ 0 ɢɥɢ 1 [6], ɬɨ ɧɟɫɥɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɟɪɟɦɟɧɧɵɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɧɚɩɪɚɜɥɟɧɢɹɦ, ɜɞɨɥɶ ɤɨɬɨɪɵɯ ɫɢɥɵ ɧɟ ɞɟɣɫɬɜɭɸɬ ɢ ɢɫɤɥɸɱɢɬɶ ɢɯ ɢɡ ɫɢɫɬɟɦɵ (9). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɨɠɧɨ ɭɱɟɫɬɶ ɭɫɥɨɜɢɹ ɡɚɤɪɟɩɥɟɧɢɹ ɤɨɧɰɟɜɵɯ ɢɥɢ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɫɟɱɟɧɢɣ ɛɚɥɤɢ. 

ɉɪɢɦɟɪ ɝɪɚɮɚ ɞɥɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɛɚɥɤɢ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɬɪɟɯ ɞɢɫɤɪɟɬɧɵɯ ɦɚɫɫ ɢ ɞɜɭɯ ɫɜɹɡɵɜɚɸɳɢɯ ɫɬɟɪɠɧɟɣ, ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 3. k k m m m q q q m m g m q q l q l ; 1 \ 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
section_name: Ɋɢɫ. 1. Ⱦɢɫɤɪɟɬɧɚɹ ɦɨɞɟɥɶ ɛɚɥɤɢ

section_content: . ɍɪɚɜɧɟɧɢɹ ɫɜɹɡɢ ɦɟɠɞɭ ɩɟɪɟɦɟɧɧɵɦɢ F ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɨɞɧɨɝɨ ɤɨɧɰɚ ɛɚɥɤɢ ɤ ɞɪɭɝɨɦɭ ɢ ɩɟɪɟɦɟɧɧɵɦɢ S ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɣ ɮɨɪɦɟ

Ɇɚɬɪɢɰɭ ɚɞɦɢɬɚɧɫɨɜ ɜɫɟɣ ɤɨɧɫɬɪɭɤɰɢɢ ɦɨɠɟɦ ɩɨɥɭɱɢɬɶ ɮɨɪɦɚɥɶɧɵɦ ɩɭɬɟɦ, ɨɛɴɟɞɢɧɢɜ ɜɫɟ ɚɞɦɢɬɚɧɫɵ ɷɥɟɦɟɧɬɚɪɧɵɯ ɛɚɥɨɤ ɜ ɨɞɧɭ ɤɜɚɞɪɚɬɧɭɸ ɤɜɚɡɢɞɢɚɝɨɧɚɥɶɧɭɸ ɦɚɬɪɢɰɭ

ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɨɬɞɟɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɞɢɫɤɪɟɬɧɨɣ ɫɢɫɬɟɦɵ, ɩɪɢɦɵɤɚɸɳɢɟ ɤ ɨɞɧɢɦ ɢ ɬɟɦ ɠɟ ɭɡɥɚɦ ɧɟɨɛɯɨɞɢɦɨ ɫɨɟɞɢɧɢɬɶ ɜ ɨɞɧɭ ɫɢɫɬɟɦɭ ɥɢɛɨ ɫ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɣ (8), ɥɢɛɨ ɫ ɩɨɦɨɳɶɸ ɦɚɬɪɢɰɵ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ '

Ʉɚɠɞɵɣ ɷɥɟɦɟɧɬ ɦɚɬɪɢɰɵ g C ɹɜɥɹɟɬɫɹ ɟɞɢɧɢɱɧɨɣ ɢɥɢ ɧɭɥɟɜɨɣ ɦɚɬɪɢɰɟɣ ɲɟɫɬɨɝɨ ɩɨɪɹɞɤɚ, ɤɨɬɨɪɵɟ ɨɛɪɚɡɭɸɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɨɝɨ, ɫɬɵɤɭɟɬɫɹ ɥɢ ɫ ɞɚɧɧɵɦ ɭɡɥɨɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɫɬɟɪɠɟɧɶ: ɟɫɥɢ ɞɚ -E, ɟɫɥɢ ɧɟɬ -[0]. ɋɬɪɨɤɢ ɦɚɬɪɢɰɵ g C ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɩɟɪɟɦɟɳɟɧɢɹɦ ɤɨɧɰɨɜ (ɬɟɥ) ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɯ ɷɥɟɦɟɧɬɚɪɧɵɯ ɛɚɥɨɤ, ɚ ɫɬɨɥɛɰɵɨɛɨɛɳɟɧɧɵɦ ɤɨɨɪɞɢɧɚɬɚɦ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɵ. 

Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɩɨɥɭɱɚɟɦ ɦɚɬɪɢɰɭ ɢɦɩɟɞɚɧɫɨɜ ɫɨɟɞɢɧɟɧɧɨɣ ɫɢɫɬɟɦɵ ɜ ɤɜɚɡɢɞɢɚɝɨɧɚɥɶɧɨɣ ɮɨɪɦɟ

Ɋɟɡɭɥɶɬɢɪɭɸɳɚɹ ɦɚɬɪɢɰɚ ɞɥɹ ɩɚɪɚɦɟɬɪɨɜ ɫɢɫɬɟɦɵ ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɢɞɭ

ȼ ɫɥɭɱɚɟ, ɟɫɥɢ ɦɚɬɪɢɰɵ (15), (17), ɩɨɥɭɱɟɧɧɵɟ ɫɭɦɦɢɪɨɜɚɧɢɟɦ ɠɟɫɬɤɨɫɬɟɣ ɢɥɢ ɩɨɞɚɬɥɢɜɨɫɬɟɣ ɨɬɞɟɥɶɧɵɯ ɫɬɟɪɠɧɟɣ ɫɜɨɛɨɞɧɨɣ ɤɨɧɫɬɪɭɤɰɢɢ, ɹɜɥɹɸɬɫɹ ɨɫɨɛɟɧɧɵɦɢ (ɜɵɪɨɠɞɟɧɧɵɦɢ), ɬɨ ɧɟɨɛɯɨɞɢɦɨ ɫ ɭɱɟɬɨɦ ɭɫɥɨɜɢɣ ɡɚɤɪɟɩɥɟɧɢɹ ɷɥɟɦɟɧɬɨɜ ɞɥɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɡɚɞɚɱɢ ɢɫɤɥɸɱɢɬɶ

ɝɞɟ v Pɩɨɞɜɢɠɧɚɹ ɫɢɥɚ, ɤɨɬɨɪɚɹ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɚɥɝɨɪɢɬɦɭ, ɩɪɢɜɟɞɟɧɧɨɦɭ ɜ ɪɚɛɨɬɟ [8]. 

Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɭɬɢ ɧɚ ɩɪɨɥɟɬɧɨɦ ɫɬɪɨɟɧɢɢ ɪɟɥɶɫɨɜɵɟ ɧɢɬɢ ɡɚɞɚɸɬ ɫ ɩɨɦɨɳɶɸ ɫɩɥɚɣɧɚ, ɨɩɨɪɧɵɟ ɬɨɱɤɢ ɤɨɬɨɪɨɝɨ ɠɟɫɬɤɨ ɡɚɤɪɟɩɥɟɧɵ ɫ ɭɱɚɫɬɤɚɦɢ ɩɭɬɢ. ɉɨɞɜɢɠɧɚɹ ɧɚɝɪɭɡɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫ ɭɱɟɬɨɦ ɩɨɥɨɠɟɧɢɹ ɤɨɥɟɫɧɨɣ ɩɚɪɵ ɢ ɫɩɥɚɣɧɨɜɨɝɨ ɩɭɬɢ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɞɜɢɠɟɧɢɹ ɩɨɟɡɞɚ ɩɨ ɦɨɫɬɭ. ȼɵɜɨɞɵ ɉɨɥɭɱɟɧɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɜɢɞɨɜ ɤɨɥɟɛɚɧɢɣ ɛɚɥɤɢ ɜ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɫɨɞɟɪɠɚɬ ɤɢɧɟɦɚɬɢɱɟɫɤɢɟ, ɦɚɫɫɨɜɨ-ɢɧɟɪɰɢɨɧɧɵɟ ɢ ɠɟɫɬɤɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɥɟɦɟɧɬɨɜ ɛɚɥɤɢ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. ɂɧɬɟɝɪɢɪɭɹ ɫɢɫɬɟɦɭ ɦɚɬɪɢɱɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (4) ɩɨɥɭɱɚɟɦ ɤɢɧɟɦɚɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɚɠɞɨɝɨ ɬɟɥɚ ɜɨ ɜɪɟɦɟɧɢ. ȼ ɫɥɭɱɚɟ ɭɩɪɭɝɨɝɨ ɡɚɤɪɟɩɥɟɧɢɹ ɢ ɞɟɦɩɮɢɪɨɜɚɧɢɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɭɪɚɜɧɟɧɢɹ (20). ɋɢɫɬɟɦɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɞɥɹ ɛɚɥɨɱɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɝɨ ɜ ɞɢɫɤɪɟɬɧɨɣ ɫɢɫɬɟɦɟ ɜ ɜɢɞɟ k ɬɟɥ ɫ r ɡɚɤɪɟɩɥɟɧɢɹɦɢ, ɫɨɞɟɪɠɢɬ (6 ) k r ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜɵɧɭɠɞɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɩɪɨɥɟɬɧɵɯ ɫɬɪɨɟɧɢɣ ɦɨɫɬɨɜ ɩɪɢ ɞɟɣɫɬɜɢɢ ɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɚɜɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɭɪɚɜɧɟɧɢɹ (20) ɫ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦɢ ɫɥɚɝɚɟɦɵɦɢ ɜ ɜɢɞɟ ɛɥɨɱɧɵɯ ɦɚɬɪɢɰ (21), (22). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɟɞɥɨɠɟɧɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ ɩɨɡɜɨɥɹɸɬ ɨɩɪɟɞɟɥɢɬɶ ɞɢɧɚɦɢɱɟɫɤɢɟ ɪɟɚɤɰɢɢ, ɜɨɡɧɢɤɚɸɳɢɟ ɜ ɩɪɨɰɟɫɫɟ ɞɜɢɠɟɧɢɹ ɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɚɜɚ ɩɨ ɞɟɮɨɪɦɢɪɭɟɦɨɦɭ ɩɪɨɥɟɬɧɨɦɭ ɫɬɪɨɟɧɢɸ ɦɨɫɬɚ.
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