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Файл:Моделирование и конструирование элементов летательных аппаратов. Учебное пособие
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ɆɈȾȿɅɂɊɈȼȺɇɂȿ ɂ ɄɈɇɋɌɊɍɂɊɈȼȺɇɂȿ
ɗɅȿɆȿɇɌɈȼ ɅȿɌȺɌȿɅɖɇɕɏ ȺɉɉȺɊȺɌɈȼ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
«ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ»
2025
1
ɍȾɄ 629.735
ȻȻɄ 39.52
Ɇ74
Ⱥɜɬɨɪɵ:
ɉɪɢɩɚɞɱɟɜ Ⱥ. Ⱦ., Ƚɨɪɛɭɧɨɜ Ⱥ. Ⱥ., Ɇɚɝɞɢɧ Ⱥ. Ƚ., Ʉɚɥɢɧɢɧɚ ɂ. ɋ.
Ɋɟɰɟɧɡɟɧɬ:
ɡɚɦɟɫɬɢɬɟɥɶ ɧɚɱɚɥɶɧɢɤɚ ɮɢɥɢɚɥɚ
ȺɈ «ȼɉɄ «ɇɉɈ ɦɚɲɢɧɨɫɬɪɨɟɧɢɹ» – ɄȻ «Ɉɪɢɨɧ»
ɋ. ȼ. Ȼɟɥɨɜ
Ɇ74 Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɢ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɟ ɷɥɟɦɟɧɬɨɜ
ɥɟɬɚɬɟɥɶɧɵɯ ɚɩ-
ɩɚɪɚɬɨɜ : ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ / [ɉɪɢɩɚɞɱɟɜ Ⱥ. Ⱦ. ɢ ɞɪ.]. – Ɇɨɫɤɜɚ ; ȼɨɥɨɝɞɚ :
ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ, 2025. – 136 ɫ. : ɢɥ., ɬɚɛɥ.
ISBN 978-5-9729-2569-8
ɉɪɢɜɟɞɟɧɵ ɢɧɠɟɧɟɪɧɵɟ ɦɟɬɨɞɵ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ
ɷɥɟɦɟɧɬɨɜ ɤɨɧɫɬɪɭɤɰɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɢɩɨɜɵɟ
ɤɨɧɫɬɪɭɤɬɨɪɫɤɢɟ ɡɚɞɚɱɢ.
Ⱦɥɹ ɨɛɭɱɚɸɳɢɯɫɹ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɞɝɨɬɨɜɤɢ 24.03.01 «Ɋɚɤɟɬɧɵɟ ɤɨɦ-
ɩɥɟɤɫɵ ɢ ɤɨɫɦɨɧɚɜɬɢɤɚ».
ɍȾɄ 629.735
ȻȻɄ 39.52
ISBN 978-5-9729-2569-8 ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2025
Ɉɮɨɪɦɥɟɧɢɟ. ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2025
2
ɋɈȾȿɊɀȺɇɂȿ
ȼɜɟɞɟɧɢɟ .................................................................................................................... 4
Ɉɛɨɡɧɚɱɟɧɢɹ ɢ ɫɨɤɪɚɳɟɧɢɹ ................................................................................... 5
1. Ɇɟɬɨɞɨɥɨɝɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ ɥɟɬɚɬɟɥɶɧɵɯ
ɚɩɩɚɪɚɬɨɜ .................................................................................................................. 7
1.1. Ɉɛɳɢɟ ɩɨɧɹɬɢɹ ɨ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ ................... 7
1.2. Ɍɪɟɛɨɜɚɧɢɹ, ɩɪɟɞɴɹɜɥɹɟɦɵɟ ɤ ɤɨɧɫɬɪɭɤɰɢɢ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ .... 10
1.3. ȼɵɛɨɪ ɦɚɬɟɪɢɚɥɚ ɤɨɧɫɬɪɭɤɰɢɢ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ .......................... 12
2. Ʉɨɧɫɬɪɭɢɪɨɜɚɧɢɟ ɷɥɟɦɟɧɬɨɜ ɤɨɪɩɭɫɚ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ ................ 22
2.1. Ɉɛɨɥɨɱɤɢ ɤɨɪɩɭɫɚ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ ............................................... 22
2.2. ɍɫɢɥɟɧɧɵɟ ɲɩɚɧɝɨɭɬɵ ɤɨɪɩɭɫɚ ................................................................ 25
2.3. Ʌɨɧɠɟɪɨɧɵ ɤɪɵɥɚ ....................................................................................... 39
2.4. ɇɟɪɚɡɴɟɦɧɵɟ ɫɨɟɞɢɧɟɧɢɹ ........................................................................... 48
2.4.1. Ɂɚɤɥɟɩɨɱɧɵɟ ɫɨɟɞɢɧɟɧɢɹ
2.4.2. ɋɨɟɞɢɧɟɧɢɟ ɫ ɩɨɦɨɳɶɸ ɤɨɧɬɚɤɬɧɨɣ ɫɜɚɪɤɢ ...................................... 61
2.5. Ɋɚɡɴɟɦɧɵɟ ɫɨɟɞɢɧɟɧɢɹ ............................................................................... 63
2.5.1. ɋɨɟɞɢɧɟɧɢɹ ɫɢɥɨɜɵɯ ɷɥɟɦɟɧɬɨɜ ɨɛɨɥɨɱɤɢ ɤɨɪɩɭɫɚ ......................... 63
2.5.2. ɋɨɟɞɢɧɟɧɢɟ ɤɨɧɫɨɥɟɣ ɤɪɵɥɚ ɫ ɤɨɪɩɭɫɨɦ ........................................... 70
2.5.2.1. ɍɲɤɨɜɵɣ ɦɨɦɟɧɬɧɵɣ ɭɡɟɥ ɫ ɧɚɪɭɠɧɵɦɢ ɤɪɵɥɶɟɜɵɦɢ
ɩɪɨɭɲɢɧɚɦɢ ................................................................................................. 70
2.5.2.2. Ɏɥɚɧɰɟɜɵɣ ɦɨɦɟɧɬɧɵɣ ɭɡɟɥ ......................................................... 78
2.6. ɍɡɥɵ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɦɟɯɚɧɢɡɦɨɜ ɭɩɪɚɜɥɟɧɢɹ ............................. 83
3. ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɷɥɟɦɟɧɬɨɜ ɤɨɪɩɭɫɚ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ ................ 101
3.1. ɉɪɨɟɤɬɢɪɨɜɨɱɧɵɣ ɪɚɫɱɟɬ ɬɨɩɥɢɜɧɵɯ ɛɚɤɨɜ ɥɟɬɚɬɟɥɶɧɨɝɨ
ɚɩɩɚɪɚɬɚ
3.2. ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɷɥɟɦɟɧɬɨɜ ɤɨɦɩɟɧɫɚɰɢɢ ɨɬɜɟɪɫɬɢɣ ɜ ɬɨɩɥɢɜɧɵɯ
ɛɚɤɚɯ.................................................................................................................. 106
3.3. ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɤɨɧɫɬɪɭɤɰɢɣ ɜ ɡɨɧɟ ɜɵɪɟɡɨɜ ɩɨɞ ɥɸɤɢ
ɜ ɤɨɪɩɭɫɟ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ ................................................................... 110
3.4. ɉɪɨɟɤɬɢɪɨɜɨɱɧɵɣ ɪɚɫɱɟɬ ɬɨɥɳɢɧɵ ɨɛɟɱɚɣɤɢ ɢ ɞɧɢɳ ɪɚɤɟɬɧɨɝɨ
ɞɜɢɝɚɬɟɥɹ ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ ........................................................................... 113
3.5. ɉɪɨɟɤɬɢɪɨɜɨɱɧɵɣ ɪɚɫɱɟɬ ɫɨɟɞɢɧɟɧɢɹ ɨɛɟɱɚɣɤɢ ɪɚɤɟɬɧɨɝɨ
ɞɜɢɝɚɬɟɥɹ ɬɜɟɪɞɨɝɨ ɬɨɩɥɢɜɚ ɢɡ ɤɨɦɩɨɡɢɰɢɨɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ
ɫ ɦɟɬɚɥɥɢɱɟɫɤɢɦ ɞɧɢɳɟɦ ............................................................................... 116
Ɂɚɤɥɸɱɟɧɢɟ ........................................................................................................... 120
Ƚɥɨɫɫɚɪɢɣ .............................................................................................................. 121
ɋɩɢɫɨɤ ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ ɢɫɬɨɱɧɢɤɨɜ .............................................................. 124
ɉɪɢɥɨɠɟɧɢɟ Ⱥ. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɫɩɨɥɶɡɭɟɦɵɯ ɦɚɬɟɪɢɚɥɨɜ
ɩɪɢ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɢ ............................................................................................ 126
............................................................................................................ 101
ɫɢɥɨɜɵɯ ɷɥɟɦɟɧɬɨɜ ɨɛɨɥɨɱɟɤ .................. 48
3
ȼȼȿȾȿɇɂȿ
Ɋɚɡɪɚɛɨɬɤɚ ɥɸɛɨɝɨ ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ (ɅȺ) ɫɨɫɬɨɢɬ ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɷɬɚ-
ɩɨɜ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬ ɧɚɩɪɚɜɥɟɧɢɟ ɢ ɫɨɞɟɪɠɚɧɢɟ ɧɚɭɱɧɨ-ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɣ
ɢ ɤɨɧɫɬɪɭɤɬɨɪɫɤɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɪɚɛɨɬɵ, ɚ ɬɚɤɠɟ ɪɚɛɨɬ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɨɜɟɞɟɧɢɟɦ ɢɫɩɵɬɚɧɢɣ ɅȺ ɢ ɜɧɟɞɪɟɧɢɟɦ ɢɯ ɜ ɷɤɫɩɥɭɚɬɚɰɢɸ. ɉɪɟɞɜɚɪɢɬɟɥɶɧɚɹ ɪɚɡɪɚɛɨɬɤɚ ɅȺ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɟɟ ɧɚɡɧɚɱɟɧɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɜɨɤɭɩɧɨɫɬɶ ɜɡɚɢɦɨɫɜɹɡɚɧɧɵɯ ɦɟɬɨɞɢɱɟɫɤɢɯ
ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ.
ɇɚ ɷɬɚɩɟ ɨɛɳɟɝɨ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɪɢɧɰɢɩɢɚɥɶɧɵɟ ɤɨɧ-
ɫɬɪɭɤɬɢɜɧɵɟ ɪɟɲɟɧɢɹ, ɞɚɸɳɢɟ ɨɛɳɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨɛ ɭɫɬɪɨɣɫɬɜɟ ɅȺ ɢ ɟɟ ɫɨɫɬɚɜɧɵɯ ɱɚɫɬɟɣ, ɨ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɚɝɪɟɝɚɬɨɜ ɢ ɨɬɫɟɤɨɜ, ɨ ɫɩɨɫɨɛɚɯ ɢɯ ɫɨɱɥɟɧɟɧɢɹ, ɨ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɦɟɪɚɯ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ
ɪɚɤɬɟɪɢɫɬɢɤɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɢ ɭɩɪɚɜɥɹɟɦɨɫɬɢ ɅȺ, ɚ ɬɚɤɠɟ ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ
ɨɫɧɨɜɧɵɦ ɬɪɟɛɨɜɚɧɢɹɦ ɩɪɨɢɡɜɨɞɫɬɜɚ, ɢɫɩɵɬɚɧɢɣ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɅȺ.
Ʉɨɧɫɬɪɭɤɬɨɪɫɤɚɹ ɩɨɞɝɨɬɨɜɤɚ ɫɬɭɞɟɧɬɨɜ, ɨɫɨɛɟɧɧɨ ɛɚɤɚɥɚɜɪɨɜ, ɨɞɧɨ ɢɡ
ɧɚɢɛɨɥɟɟ ɬɪɭɞɧɵɯ ɧɚɩɪɚɜɥɟɧɢɣ ɜ ɢɧɠɟɧɟɪɧɨɦ ɨɛɪɚɡɨɜɚɧɢɢ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ,
ɱɬɨ ɜ ɨɛɥɚɫɬɢ ɫɨɡɞɚɧɢɹ ɅȺ ɛɵɫɬɪɨ ɪɚɡɜɢɜɚɸɬɫɹ ɧɨɜɵɟ ɬɟɧɞɟɧɰɢɢ ɢ ɧɚɩɪɚɜɥɟɧɢɹ, ɩɪɢɲɟɞɲɢɟ
ɩɪɨɢɡɜɨɞɫɬɜɚ, ɤɨɬɨɪɵɟ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɤɚɡɚɥɢɫɶ ɜɨ ɦɧɨɝɨɦ ɢɫɱɟɪɩɚɧɧɵɦɢ ɢ
ɧɚɱɚɥɢ ɬɨɪɦɨɡɢɬɶ ɞɚɥɶɧɟɣɲɟɟ ɩɨɜɵɲɟɧɢɟ ɬɟɯɧɢɱɟɫɤɨɝɨ ɭɪɨɜɧɹ ɚɜɢɚɰɢɨɧɧɨɤɨɫɦɢɱɟɫɤɨɣ ɬɟɯɧɢɤɢ.
ɇɨɜɵɟ ɜɨɡɦɨɠɧɨɫɬɢ ɨɬɤɪɵɜɚɸɬɫɹ ɧɚ ɨɫɧɨɜɟ ɛɨɥɟɟ ɝɥɭɛɨɤɨɝɨ ɢɫɩɨɥɶɡɨɜɚ-
ɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɧɚɭɱɧɨ-ɬɟɯɧɢɱɟɫɤɨɝɨ ɩɪɨɝɪɟɫɫɚ ɢ ɜɧɟɞɪɟɧɢɹ ɜ ɢɧɠɟɧɟɪɧɭɸ
ɩɪɚɤɬɢɤɭ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ
Ʉɨɧɫɬɪɭɢɪɨɜɚɧɢɟ – ɷɬɨ ɡɚɤɥɸɱɢɬɟɥɶɧɵɣ ɷɬɚɩ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ, ɜɤɥɸɱɚɸɳɢɣ ɜ
ɫɟɛɹ ɄɌɉ ɤɨɧɫɬɪɭɤɬɢɜɧɨɣ ɫɯɟɦɵ, ɜɵɛɪɚɧɧɨɣ ɧɚ ɩɪɟɞɵɞɭɳɟɦ ɷɬɚɩɟ ɢ ɜɵɩɭɫɤ
ɪɚɛɨɱɢɯ ɱɟɪɬɟɠɟɣ. Ɂɚɞɚɱɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɪɟɲɟɧɢɹ ɭɡɥɚ ɜ
ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɢɡɥɨɠɟɧɵ ɫ ɩɨɡɢɰɢɣ ɬɪɟɛɨɜɚɧɢɣ ɢ ɜɨɡɦɨɠɧɨɫɬɟɣ ɩɪɢɦɟɧɟɧɢɹ
ɝɪɚɮɢɱɟɫɤɢɯ ɪɟɞɚɤɬɨɪɨɜ. Ɉɫɨɛɨɟ ɜɧɢɦɚɧɢɟ ɭɞɟɥɹɟɬɫɹ ɨɪɝɚɧɢɡɚɰɢɢ ɞɢɚɥɨɝɚ ɤɨɧɫɬɪɭɤɬɨɪ – ɗȼɆ.
ȼ
ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜɚɪɢɚɧɬɵ ɧɟɫɤɨɥɶɤɢɯ ɬɢɩɨɜɵɯ ɷɥɟɦɟɧɬɨɜ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɪɟɲɟɧɢɹ ɭɡɥɚ. ɉɨɫɥɟ ɬɨɝɨ ɤɚɤ ɜɵɛɪɚɧɚ
ɫɢɥɨɜɚɹ ɫɯɟɦɚ ɭɡɥɚ, ɩɪɨɜɟɞɟɧɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɩɪɨɱɧɨɫɬɢ ɜ ɡɨɧɚɯ ɜɫɟɯ ɦɟɫɬɧɵɯ
ɜɵɪɟɡɨɜ ɢ ɨɩɪɟɞɟɥɟɧ ɜɚɪɢɚɧɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɪɟɲɟɧɢɹ ɭɡɥɚ,
ɭɡɟɥ ɪɚɡɞɟɥɹɟɬɫɹ ɧɚ ɤɨɧɤɪɟɬɧɵɟ ɞɟɬɚɥɢ. Ȼɥɢɡɤɢɟ ɩɨ ɫɬɨɢɦɨɫɬɢ ɦɧɨɠɟɫɬɜɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɪɟɲɟɧɢɣ ɨɞɧɨɝɨ
ɥɹɸɬɫɹ ɩɨɧɹɬɢɟɦ ɨɛɥɢɤɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɪɟɲɟɧɢɹ. Ʉɨɦɩɥɟɤɫɧɵɦ ɩɪɢɡɧɚɤɨɦ ɤɨɬɨɪɨɝɨ ɹɜɥɹɟɬɫɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɬɢɩɨɜ Ɍɉ ɢ ɄɆ. Ɉɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɨɦɩɨɡɢɰɢɨɧɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɩɪɢɥɨɠɟɧɢɢ ɢ ɜ ɫɩɪɚɜɨɱɧɨɣ ɥɢɬɟɪɚɬɭɪɟ.
ɷɬɚɩɨɜ, ɬɚɤɢɯ ɤɚɤ: ɚɧɚɥɢɡɚ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɅȺ, ɟɝɨ ɨɛɳɟɝɨ
ɬɪɟɛɭɟɦɵɟ ɯɚ-
ɧɚ ɫɦɟɧɭ ɬɪɚɞɢɰɢɨɧɧɵɦ ɩɨɞɯɨɞɚɦ ɤ ɦɟɬɨɞɚɦ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ
ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ.
ɢ ɬɨɝɨ ɠɟ ɭɡɥɚ ɢɥɢ ɞɟɬɚɥɢ ɨɛɴɹɜ-
4
ɈȻɈɁɇȺɑȿɇɂə ɂ ɋɈɄɊȺɓȿɇɂə
ȺɋɄ – ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɚɹ ɫɢɫɬɟɦɚ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ;
ɄɆ – ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɟ ɦɚɬɟɪɢɚɥɵ;
ɄɌɉ – ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɚɹ ɩɪɨɪɚɛɨɬɤɚ;
ɄɌɊ – ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ;
Ʉɋɋ – ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɫɢɥɨɜɚɹ ɫɯɟɦɚ;
ɅȺ – ɥɟɬɚɬɟɥɶɧɵɣ ɚɩɩɚɪɚɬ;
ɋɗ – ɫɢɥɨɜɨɣ ɷɥɟɦɟɧɬ;
Ɍɉ – ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ;
ɌɌɁ – ɬɚɤɬɢɤɨ-ɬɟɯɧɢɱɟɫɤɨɟ ɡɚɞɚɧɢɟ;
ɌɁ – ɬɟɯɧɢɱɟɫɤɨɟ ɡɚɞɚɧɢɟ;
ɌɌɌ – ɬɚɤɬɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ;
ɗȻɄ – ɷɥɟɦɟɧɬɧɚɹ ɛɚɡɚ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ;
Ⱥ – ɤɨɧɫɬɚɧɬɚ; ɨɛɨɡɧɚɱɟɧɢɟ ɡɜɟɧɶɟɜ ɪɚɡɦɟɪɧɨɣ ɰɟɩɢ;
ɚ – ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɦ;
ȼ – ɨɛɨɡɧɚɱɟɧɢɟ ɡɜɟɧɶɟɜ ɪɚɡɦɟɪɧɨɣ ɰɟɩɢ;
b – ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ;
ɫ – ɬɨɥɳɢɧɚ ɤɪɵɥɚ, ɦ;
ɫ
– ɬɟɩɥɨɟɦɤɨɫɬɶ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ, ɤɝɄ;
ɪ
ɫ
– ɤɨɷɮɮɢɰɢɟɧɬ ɥɨɛɨɜɨɝɨ ɫɨɟɞɢɧɟɧɢɹ;
ɯ
D, d – ɞɢɚɦɟɬɪ, ɦ;
ȿ – ɦɨɞɭɥɶ ɘɧɝɚ, Ɇɉɚ;
F – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɦ
G – ɦɨɞɭɥɶ ɫɞɜɢɝɚ, Ɇɉɚ;
g – ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ, ɦ/ɫ
ɇ – ɜɵɫɨɬɚ ɩɨɥɟɬɚ; ɦɟɫɬɧɚɹ ɜɵɫɨɬɚ ɥɨɧɠɟɪɨɧɚ, ɦ;
ɇ
– ɫɬɪɨɢɬɟɥɶɧɚɹ ɜɵɫɨɬɚ ɥɨɧɠɟɪɨɧɚ, ɦ;
ɫɬɪ
h – ɫɬɪɨɢɬɟɥɶɧɚɹ ɜɵɫɨɬɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɦ;
J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɫɟɱɟɧɢɹ, ɦ
J
– ɩɨɥɹɪɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ, ɦ4;
ɪ
4
k – ɤɨɷɮɮɢɰɢɟɧɬ;
L – ɪɚɫɱɟɬɧɚɹ ɞɥɢɧɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɦ;
l – ɞɥɢɧɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɦ;
Ɇ – ɱɢɫɥɨ Ɇɚɯɚ; ɦɨɦɟɧɬ ɫɢɥɵ, ɇ
m – ɦɚɫɫɚ, ɤɝ;
N – ɨɫɟɜɚɹ ɫɢɥɚ, ɇ
ɦ;
ɩ – ɩɟɪɟɝɪɭɡɤɚ;
Ɋ – ɫɢɥɚ; ɬɹɝɚ ɞɜɢɝɚɬɟɥɹ, ɇ;
ɪ – ɞɚɜɥɟɧɢɟ, ɉɚ;
Q – ɫɢɥɚ, ɇ;
q – ɫɤɨɪɨɫɬɧɨɣ ɧɚɩɨɪ (ɫɤɨɪɨɫɬɧɨɟ ɞɚɜɥɟɧɢɟ), ɤɝ/(ɦ
ɥɟɧɧɵɯ ɫɢɥ, ɇ/ɦ;
R – ɪɟɚɤɰɢɹ ɫɢɥɵ, ɇ;
S – ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ, ɦ
3
;
2
;
;
ɦ;
5
2
;
ɫ2); ɩɨɬɨɤ ɪɚɫɩɪɟɞɟ-
– ɩɥɨɳɚɞɶ ɤɨɧɫɨɥɢ ɤɪɵɥɚ, ɦ2;
S
ɤ
F – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɨɛɨɥɨɱɤɢ, ɦɦ
2
;
T – ɫɢɥɚ, ɇ; ɞɨɩɭɫɤ ɡɜɟɧɚ ɜ ɪɚɡɦɟɪɧɨɣ ɰɟɩɢ, ɦɤɦ; ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭ-
ɪɚ, Ʉ;
t – ɜɪɟɦɹ ɩɨɥɟɬɚ, ɫ; ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɫɟɱɟɧɢɹ, ɦ; ɬɟɦɩɟɪɚɬɭɪɚ, °ɋ; ɲɚɝ
ɬɨɱɟɱɧɨɝɨ ɲɜɚ, ɦɦ;
W – ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɟɱɟɧɢɸ ɢɡɝɢɛɚ, ɦ
3
;
w – ɩɪɨɝɢɛ ɨɛɨɥɨɱɤɢ ɢɥɢ ɛɚɥɤɢ, ɦɦ;
X – ɫɢɥɚ ɥɨɛɨɜɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɇ;
x – ɤɨɨɪɞɢɧɚɬɚ ɜɞɨɥɶ ɨɫɢ Ɉɏ, ɦ;
Y
– ɩɨɞɴɟɦɧɚɹ ɫɢɥɚ, ɇ;
a
y – ɤɨɨɪɞɢɧɚɬɚ ɜɞɨɥɶ ɨɫɢ ɈY, ɦ;
– ɬɨɥɳɢɧɚ ɷɥɟɦɟɧɬɚ, ɦ;
G
– ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɚɫɫɨɧɚ;
P
– ɩɥɨɬɧɨɫɬɶ, ɤɝ/ ɦ3;
U
V
– ɧɨɪɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ, Ɇɉɚ;
V
– ɩɪɟɞɟɥ ɩɪɨɱɧɨɫɬɢ ɤɨɧɫɬɪɭɤɰɢɨɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɧɚ ɪɚɡɪɵɜ, Ɇɉɚ;
ȼ
W
– ɤɚɫɚɬɟɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ, Ɇɉɚ;
W
– ɩɪɟɞɟɥ ɩɪɨɱɧɨɫɬɢ ɤɨɧɫɬɪɭɤɰɢɨɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɧɚ ɫɞɜɢɝ, Ɇɉɚ;
ȼ
– ɭɝɨɥ ɡɚɤɪɭɬɤɢ.
M
6
1. ɆȿɌɈȾɈɅɈȽɂɑȿɋɄɂȿ
ɈɋɇɈȼɕ ɄɈɇɋɌɊɍɂɊɈȼȺɇɂə
ɅȿɌȺɌȿɅɖɇɕɏ ȺɉɉȺɊȺɌɈȼ
1.1. Ɉɛɳɢɟ ɩɨɧɹɬɢɹ ɨ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɢ
ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ
Ʉɨɧɫɬɪɭɤɰɢɹ – ɷɬɨ ɫɨɜɨɤɭɩɧɨɫɬɶ ɜɡɚɢɦɨɫɜɹɡɚɧɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯɫɹ ɨɩɪɟɞɟɥɟɧɧɵɦ ɤɨɦɩɥɟɤɫɨɦ ɫɜɨɣɫɬɜ, ɬɚɤɢɯ, ɤɚɤ ɫɬɪɭɤɬɭɪɚ (ɫɨɫɬɚɜ),
ɯɚɪɚɤɬɟɪ ɫɜɹɡɟɣ ɦɟɠɞɭ ɷɥɟɦɟɧɬɚɦɢ, ɫɩɨɫɨɛɵ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɫɜɨɣɫɬɜɚ (ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɪɚɡɦɟɪɵ, ɦɚɬɟɪɢɚɥ) ɷɥɟɦɟɧɬɨɜ [14].
ɉɨɢɫɤ ɧɚɢɥɭɱɲɟɝɨ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɪɟɲɟɧɢɹ – ɷɬɨ ɜɵɛɨɪ ɬɚɤɨɣ ɤɨɧɫɬɪɭɤɰɢɢ, ɤɨɬɨɪɚɹ ɨɛɟɫɩɟɱɢɜɚɟɬ ɪɟɲɟɧɢɟ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ (ɜɵɩɨɥɧɟɧɢɟ ɮɭɧɤɰɢɨ
ɧɚɥɶɧɨɝɨ ɧɚɡɧɚɱɟɧɢɹ) ɜ ɧɟɤɨɬɨɪɵɯ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɹɯ ɩɪɢ ɦɢɧɢɦɚɥɶɧɵɯ ɪɚɫɯɨɞɨɜ ɪɟɫɭɪɫɨɜ (ɦɚɬɟɪɢɚɥɶɧɵɯ, ɫɬɨɢɦɨɫɬɧɵɯ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ) ɫ ɭɱɟɬɨɦ ɨɝɪɚɧɢɱɟɧɢɣ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɝɨ, ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɢ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɨɝɨ ɯɚɪɚɤɬɟɪɚ.
ɋɢɥɨɜɨɣ ɨɫɧɨɜɨɣ ɅȺ ɹɜɥɹɟɬɫɹ ɤɨɪɩɭɫ, ɤɨɬɨɪɵɣ ɨɛɴɟɞɢɧɹɟɬ ɜ ɟɞɢɧɨɟ ɰɟɥɨɟ
ɨɬɫɟɤɢ ɢ ɚɝɪɟɝɚɬɵ, ɜɯɨɞɹɳɢɟ ɜ ɟɝɨ ɫɨɫɬɚɜ ɢ ɪɚɡɥɢɱɚɸɳɢɟɫɹ ɩɨ ɮɭɧɤɰɢɨɧɚɥɶɧɨɦɭ
(ɤɨɪɦɨɜɨɣ,
ɤɚɦ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɚ ɤɨɪɩɭɫ ɞɟɣɫɬɜɭɸɬ ɫɬɚɬɢɱɟɫɤɢɟ ɢ ɞɢɧɚɦɢɱɟɫɤɢɟ, ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɟ ɢ ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɧɚɝɪɭɡɤɢ, ɨɩɪɟɞɟɥɹɟɦɵɟ ɩɚɪɚɦɟɬɪɚɦɢ ɞɜɢɝɚɬɟɥɶɧɨɣ
ɭɫɬɚɧɨɜɤɢ, ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɨɣ ɅȺ ɢ ɭɫɥɨɜɢɹɦɢ ɩɨɥɟɬɚ. ɇɚɝɪɭɡɤɢ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɣ ɨɬɫɟɤ ɢɥɢ ɚɝɪɟɝɚɬ ɢ ɜɥɢɹɸɳɢɟ ɧɚ
ɬɢɜɧɨɝɨ ɪɟɲɟɧɢɹ, ɡɚɜɢɫɹɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɫɯɟɦɵ ɧɚɝɪɭɠɟɧɢɹ ɤɨɪɩɭɫɚ ɜ ɰɟɥɨɦ, ɧɨ ɢ
ɨɬ ɯɚɪɚɤɬɟɪɚ ɫɜɹɡɟɣ ɨɬɫɟɤɨɜ ɦɟɠɞɭ ɫɨɛɨɣ.
ɤɚ) ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ ɡɚɞɚɧɢɢ ɤɨɦɩɨɧɨɜɨɱɧɨ-ɫɢɥɨɜɨɣ ɫɯɟɦɵ ɅȺ, ɧɨɫɢɬ ɢɬɟɪɚɰɢɨɧɧɵɣ ɯɚɪɚɤɬɟɪ ɢ ɢɦɟɟɬ ɤɨɧɟɱɧɨɣ ɰɟɥɶɸ ɨɛɟɫɩɟɱɟɧɢɟ
ɤɨɧɫɬɪɭɤɰɢɢ ɤɨɪɩɭɫɚ ɜ ɰɟɥɨɦ, ɪɢɫɭɧɨɤ 1.1.
ɬɨɩɥɢɜɧɵɣ ɨɬɫɟɤ ɢ ɬ. ɞ.) ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦɭ ɩɪɢɡɧɚ-
ɜɵɛɨɪ ɤɨɧɫɬɪɭɤ-
ɉɨɢɫɤ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɪɟɲɟɧɢɹ ɞɥɹ ɤɚɠɞɨɝɨ ɭɡɥɚ (ɩɚɧɟɥɢ, ɫɟɤɰɢɢ, ɨɬɫɟ-
ɦɢɧɢɦɚɥɶɧɨɣ ɦɚɫɫɵ
-
Ɋɢɫɭɧɨɤ 1.1 – ɋɯɟɦɚ ɩɨɢɫɤɚ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɪɟɲɟɧɢɹ
7
ɂɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ, ɤɨɬɨɪɵɦɢ ɪɚɫɩɨɥɚɝɚɟɬ ɤɨɧɫɬɪɭɤɬɨɪ, ɩɪɢɫɬɭɩɚɹ ɤ
ɪɚɡɪɚɛɨɬɤɟ ɤɨɧɫɬɪɭɤɰɢɣ ɨɬɫɟɤɚ (ɭɡɥɚ, ɩɚɧɟɥɢ, ɫɟɤɰɢɢ), ɹɜɥɹɸɬɫɹ:
– ɤɨɦɩɨɧɨɜɨɱɧɚɹ ɫɯɟɦɚ ɅȺ;
– ɨɫɧɨɜɧɵɟ ɪɚɫɱɟɬɧɵɟ ɫɥɭɱɚɢ (ɡɧɚɱɟɧɢɹ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɧɚɝɪɭɡɨɤ, ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɛɟɡɨɩɚɫɧɨɫɬɢ);
– ɪɚɫɩɨɥɚɝɚɟɦɵɟ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɟ ɦɚɬɟɪɢɚɥɵ (ɢɯ ɫɜɨɣɫɬɜɚ);
– ɨɫɨɛɟɧɧɨɫɬɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɷɤɫɩɥɭɚɬɚ-
ɰɢɟɣ ɨɬɫɟɤɚ (ɪɚɡɦɟɪɵ
ɢ ɦɟɫɬɚ ɪɚɫɩɨɥɨɠɟɧɢɹ ɥɸɱɤɨɜ, ɦɟɫɬɚ ɭɫɬɚɧɨɜɤɢ ɚɷɪɨɞɢ-
ɧɚɦɢɱɟɫɤɢɯ ɭɫɬɪɨɣɫɬɜ ɢ ɩɪɢɛɨɪɨɜ, ɨɝɪɚɧɢɱɟɧɢɹ ɩɨ ɫɬɪɨɢɬɟɥɶɧɨɣ ɜɵɫɨɬɟ ɫɢɥɨɜɨɝɨ ɧɚɛɨɪɚ ɢɥɢ ɫɭɦɦɚɪɧɨɣ ɬɨɥɳɢɧɟ ɬɟɩɥɨɢɡɨɥɹɰɢɢ ɢ ɬ. ɞ.);
– ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ (ɢɥɢ ɪɟɤɨɦɟɧɞɚɰɢɢ) ɩɨ ɢɫɩɨɥɶɡɭɟɦɵɦ
ɩɨɥɭɮɚɛɪɢɤɚɬɚɦ ɢ ɡɚɝɨɬɨɜɤɚɦ (ɬɨɥɳɢɧɵ ɥɢɫɬɨɜ, ɫɨɪɬɚɦɟɧɬ ɩɪɨɮɢɥɟɣ ɢ ɬ. ɞ.);
– ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɭɫɥɨɜɢɹ,
ɨɩɪɟɞɟɥɹɸɳɢɟ ɤɚɱɟɫɬɜɨ ɢɡɝɨɬɨɜɥɟɧɢɹ.
ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɤɨɧɫɬɪɭɤɰɢɢ ɨɬɫɟɤɚ ɢɥɢ ɨɬɞɟɥɶɧɨɝɨ ɭɡɥɚ ɅȺ ɧɟɨɛɯɨɞɢɦɨ
ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɨɛɟɫɩɟɱɢɜɚɬɶ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɶ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ. ɍɫɥɨɜɢɹ
ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɡɚɜɢɫɹɬ ɨɬ ɢɫɩɨɥɶɡɭɟɦɵɯ ɤɪɢɬɟɪɢɟɜ ɩɪɢ ɨɰɟɧɤɟ ɩɪɨɱɧɨɫɬɢ ɢ
ɠɟɫɬɤɨɫɬɢ ɤɨɧɫɬɪɭɤɰɢɢ.
ȼ ɪɚɤɟɬɧɨ-ɤɨɫɦɢɱɟɫɤɨɣ ɬɟɯɧɢɤɟ ɩɪɢɧɹɬ ɦɟɬɨɞ ɪɚɫɱɟɬɚ ɩɨ ɪɚɡɪɭɲɚɸɳɢɦ
(ɩɪɟɞɟɥɶɧɵɦ) ɧɚɝɪɭɡɤɚɦ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɚɪɚɦɟɬɪɵ ɷɥɟɦɟɧɬɨɜ
ɜɵɛɢɪɚɸɬ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɨɧɚ ɪɚɡɪɭɲɚɥɚɫɶ ɩɪɢ ɧɟɤɨɬɨɪɨɣ ɧɨɪɦɢɪɨɜɚɧɧɨɣ ɧɚɝɪɭɡɤɟ – ɪɚɫɱɟɬɧɨɣ ɧɚɝɪɭɡɤɟ, N
P
, ɇ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɤɨɧɫɬɪɭɤɰɢɢ
Ɋɗ
N=fN
ɝɞɟ f – ɤɨɷɮɮɢɰɢɟɧɬ ɛɟɡɨɩɚɫɧɨɫɬɢ, ɪɚɜɟɧ ɨɬ 1,3 ɞɨ 1,6; N
, (1.1)
ɗ
– ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɚɹ
ɧɚɝɪɭɡɤɚ.
ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɤɨɧɫɬɪɭɤɰɢɢ ɛɚɡɢɪɭɟɬɫɹ ɧɚ ɪɚɫɱɟɬɚɯ ɧɚ ɩɪɨɱɧɨɫɬɶ, ɬ. ɟ.
ɨɫɧɨɜɧɵɟ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɪɚɡɦɟɪɵ ɢ ɫɨɨɬɧɨɲɟɧɢɹ ɜɵɛɢɪɚɸɬɫɹ ɢɡ ɭɫɥɨɜɢɣ
ɩɪɨɱɧɨɫɬɢ ɢɥɢ ɠɟɫɬɤɨɫɬɢ, ɪɢɫɭɧɨɤ 1.2 [8]. Ɉɞɧɚɤɨ ɩɪɟɠɞɟ, ɱɟɦ ɬɚɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɡɚɩɢɫɚɬɶ, ɤɨɧɫɬɪɭɤɰɢɹ (ɨɬɫɟɤ, ɨɬɞɟɥɶɧɵɣ ɟɝɨ ɷɥɟɦɟɧɬ) ɞɨɥɠɧɚ ɛɵɬɶ ɧɟɤɨɬɨɪɵɦ ɨɛɪɚɡɨɦ ɫɯɟɦɚɬɢɡɢɪɨɜɚɧɚ. Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ
ɨɫɧɨɜɧɵɟ ɫɢɥɨɜɵɟ ɷɥɟɦɟɧɬɵ ɢ ɢɯ ɮɭɧɤɰɢɨɧɚɥɶɧɨɟ ɧɚɡɧɚɱɟɧɢɟ. ɉɨɫɥɟ ɱɟɝɨ ɧɟɨɛɯɨɞɢɦɨ ɮɨɪɦɚɥɢɡɨɜɚɬɶ ɜɡɚɢɦɨɫɜɹɡɢ ɫɢɥɨɜɵɯ ɷɥɟɦɟɧɬɨɜ ɢ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ (ɡɚ-
ɞɟɥɤɭ) ɷɬɢɯ ɷɥɟɦɟɧɬɨɜ. ɏɚɪɚɤɬɟɪ ɡɚɞɟɥɤɢ (ɡɚɳɟɦɥɟɧɢɟ, ɲɚɪɧɢɪ) ɢɝɪɚɟɬ ɛɨɥɶɲɭɸ ɪɨɥɶ ɩɪɢ ɪɚɫɱɟɬɟ ɷɥɟɦɟɧɬɨɜ ɧɚ ɫɠɚɬɢɟ, ɜɥɢɹɹ ɤɚɤ ɧɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ
ɧɚɝɪɭɡɨɤ ɩɨ ɞɥɢɧɟ ɷɥɟɦɟɧɬɚ, ɬɚɤ ɢ
ɟɝɨ ɭɫɬɨɣɱɢɜɨɫɬɶ.
Ɉɬɦɟɱɟɧɧɵɟ ɩɨɥɨɠɟɧɢɹ ɨɩɪɟɞɟɥɹɸɬ ɬɚɤ ɧɚɡɵɜɚɟɦɭɸ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ
ɤɨɧɫɬɪɭɤɰɢɢ. ɗɬɚ ɫɯɟɦɚ ɦɨɠɟɬ ɛɵɬɶ ɫɥɨɠɧɟɟ ɢɥɢ ɩɪɨɳɟ, ɧɨ ɜ ɥɸɛɨɦ ɫɥɭɱɚɟ ɨɬ
ɨɛɨɫɧɨɜɚɧɧɨɫɬɢ ɞɨɩɭɳɟɧɢɣ ɢ ɩɪɟɞɩɨɥɨɠɟɧɢɣ ɡɚɜɢɫɹɬ ɬɨɱɧɨɫɬɶ ɪɚɫɱɟɬɨɜ ɢ ɞɨɫɬɨɜɟɪɧɨɫɬɶ ɧɚɲɢɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɨ ɩɨɜɟɞɟɧɢɢ ɤɨɧɫɬɪɭɤɰɢɢ ɜ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ. ȼɵɛɨɪ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɧɨɝɢɦɢ ɮɚɤɬɨɪɚɦɢ. ɗɬɨ
ɬɪɟɛɨɜɚɧɢɹ ɩɨ ɦɚɫɫɟ ɢ ɝɚɛɚɪɢɬɧɵɦ ɪɚɡɦɟɪɚɦ, ɡɧɚɱɢɦɨɫɬɶ ɩɪɨɟɤɬɢɪɭɟɦɨɣ ɤɨɧɫɬɪɭɤɰɢɢ
ɢ ɬ. ɞ.
8
Ɋɢɫɭɧɨɤ 1.2 – ɋɯɟɦɚ ɩɪɨɰɟɫɫɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɤɨɧɫɬɪɭɤɰɢɣ ɅȺ
Ɉɛɟɫɩɟɱɟɧɢɟ ɩɪɨɱɧɨɫɬɢ ɤɨɧɫɬɪɭɤɰɢɢ ɹɜɥɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɵɦ ɭɫɥɨɜɢɟɦ ɟɟ
ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ, ɧɨ ɧɟɞɨɫɬɚɬɨɱɧɵɦ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɢɯ ɧɚɝɪɭɡɨɤ ɤɨɧɫɬɪɭɤɰɢɹ ɞɟɮɨɪɦɢɪɭɟɬɫɹ (ɭɞɥɢɧɹɟɬɫɹ, ɢɡɝɢɛɚɟɬɫɹ, ɡɚɤɪɭɱɢɜɚɟɬɫɹ ɢ ɬ. ɞ.), ɢ ɷɬɢ
ɞɟɮɨɪɦɚɰɢɢ ɢɝɪɚɸɬ ɛɨɥɶɲɭɸ ɪɨɥɶ ɩɪɢ ɪɚɫɱɟɬɟ ɞɜɢɠɟɧɢɹ ɅȺ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɰɟɧɬɪɚ ɦɚɫɫ ɢ ɩɪɢ ɨɬɞɟɥɟɧɢɢ
ɨɬɪɚɛɨɬɚɜɲɢɯ ɛɥɨɤɨɜ, ɩɪɢ ɪɚɫɱɟɬɟ ɞɢɧɚɦɢɱɟɫɤɢɯ
ɧɚɝɪɭɡɨɤ, ɨɰɟɧɤɟ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɫɩɨɥɧɢɬɟɥɶɧɵɯ ɨɪɝɚɧɨɜ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ
ɢ ɬ. ɞ.
ɀɟɫɬɤɨɫɬɶ ɫɜɹɡɟɣ ɨɬɫɟɤɨɜ ɦɟɠɞɭ ɫɨɛɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɧɫɬɪɭɤɬɢɜɧɵɦ
ɢɫɩɨɥɧɟɧɢɟɦ ɫɨɟɞɢɧɟɧɢɣ ɨɬɞɟɥɶɧɵɯ ɨɬɫɟɤɨɜ ɜ ɟɞɢɧɭɸ ɤɨɧɫɬɪɭɤɰɢɸ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɜ ɫɨɟɞɢɧɟɧɢɢ ɩɥɨɫɤɢɯ ɫɬɵɤɨɜ ɠɟɫɬɤɨɫɬɶ ɫɨɟɞɢɧɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ
ɩɚɪɚɦɟɬɪɨɜ ɤɪɟɩɟɠɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɭɫɬɚɧɚɜɥɢɜɚɟɦɵɯ ɜ ɩɥɨɫɤɨɫɬɢ ɫɬɵɤɚ.
9
1.2. Ɍɪɟɛɨɜɚɧɢɹ, ɩɪɟɞɴɹɜɥɹɟɦɵɟ ɤ ɤɨɧɫɬɪɭɤɰɢɢ
ɥɟɬɚɬɟɥɶɧɨɝɨ ɚɩɩɚɪɚɬɚ
ɇɚɢɛɨɥɟɟ ɩɨɥɧɵɣ ɢ ɤɨɦɩɥɟɤɫɧɵɣ ɭɱɟɬ ɬɪɟɛɨɜɚɧɢɣ – ɨɫɧɨɜɧɚɹ ɬɪɭɞɧɨɫɬɶ
ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɪɟɞɩɨɫɵɥɤɚ ɩɨɥɭɱɟɧɢɹ ɧɚɞɟɠɧɨɝɨ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɪɟɲɟɧɢɹ. Ɍɪɟɛɨɜɚɧɢɹ, ɩɪɟɞɴɹɜɥɹɟɦɵɟ ɤ ɤɨɧɫɬɪɭɤɰɢɢ ɅȺ, ɞɢɤɬɭɸɬɫɹ
ɫɨɨɛɪɚɠɟɧɢɹɦɢ ɚɷɪɨɞɢɧɚɦɢɤɢ, ɩɪɨɱɧɨɫɬɢ, ɠɟɫɬɤɨɫɬɢ, ɦɢɧɢɦɚɥɶɧɨɣ ɦɚɫɫɵ,
ɷɤɫɩɥɭɚɬɚɰɢɢ, ɩɪɨɢɡɜɨɞɫɬɜɚ [9, 13].
Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ. ɋɢɧɬɟɡ ɅȺ ɬɟɫɧɨ ɫɜɹɡɚɧ ɫ ɚɧɚɥɢɡɨɦ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɩɪɨɟɤɬɢɪɭɟɦɨɣ ɤɨɧɫɬɪɭɤɰɢɢ. ȼɵɫɨɤɢɟ
ɬɟɯɧɢɱɟɫɤɢɟ ɞɚɧɧɵɟ ɅȺ ɜɨ ɦɧɨɝɨɦ ɨɛɭɫɥɨɜɥɟɧɵ ɭɞɚɱɧɵɦ ɜɵɛɨɪɨɦ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɵ. ɉɪɢɧɰɢɩɢɚɥɶɧɨ ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɧɚɢɥɭɱɲɟɣ, ɟɞɢɧɫɬɜɟɧɧɨɣ ɜ
ɫɜɨɟɦ ɪɨɞɟ, ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɵ, ɬ. ɤ. ɤɚɠɭɳɢɟɫɹ ɟɟ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ
ɩɪɟɢɦɭɳɟɫɬɜɚ ɦɨɝɭɬ ɛɵɬɶ ɱɚɫɬɢɱɧɨ ɢɥɢ ɩɨɥɧɨɫɬɶɸ ɨɬɜɟɪɝɧɭɬɵ ɤɨɧɫɬɪɭɤɬɢɜɧɵɦɢ ɢɥɢ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ. ɉɪɢ ɜɵɛɨɪɟ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ
ɫɯɟɦɵ ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɸɬ ɪɚɡɧɨɨɛɪɚɡɧɵɟ ɦɟɬɨɞɵ
ɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ, ɥɢɛɨ ɤɨɪɪɟɤɬɢɪɭɸɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɞɚɧɧɵɟ ɩɪɨɬɨɬɢɩɚ. ɋɨɜɟɪɲɟɧɫɬɜɨ ɅȺ, ɨɰɟɧɢɜɚɟɦɨɟ ɩɨ ɨɩɪɟɞɟɥɟɧɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɩɨɤɚɡɚɬɟɥɟɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ, ɜɨ ɦɧɨɝɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɛɨɪɨɦ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɵ. ɗɬɨ
ɨɬɧɨɫɢɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɤ ɤɪɵɥɚɬɵɦ ɅȺ. Ʉɪɵɥɚɬɵɟ ɅȺ, ɢɫɩɨɥɶɡɭɸɳɢɟ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɪɢɧɰɢɩ ɫɨɡɞɚɧɢɹ ɭɩɪɚɜɥɹɸɳɟɣ ɫɢɥɵ, ɩɪɢɧɹɬɨ ɤɥɚɫɫɢɮɢɰɢɪɨɜɚɬɶ ɩɨ ɪɚɫɩɨɥɨɠɟɧɢɸ ɨɪɝɚɧɨɜ
ɡɵɜɚɟɬ, ɱɬɨ ɧɚ ɜɵɛɨɪ ɰɟɥɟɫɨɨɛɪɚɡɧɨɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɵ ɜɥɢɹɸɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɅȺ, ɟɝɨ ɞɢɧɚɦɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɰɢɨɧɚɥɶɧɨɣ ɤɨɦɩɨɧɨɜɤɢ ɚɝɪɟɝɚɬɨɜ ɜ ɤɨɪɩɭɫɟ ɅȺ. ɜɵɛɨɪ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ
ɫɯɟɦɵ ɨɛɭɫɥɨɜɥɟɧ ɬɪɟɛɨɜɚɧɢɹɦɢ ɤɨɦɩɨɧɨɜɤɢ:
– ɬɢɩɨɦ ɞɜɢɝɚɬɟɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ ɢ ɭɫɥɨɜɢɹɦɢ ɟɟ ɪɚɛɨɬɵ;
– ɫɬɪɭɤɬɭɪɨɣ ɛɨɪɬɨɜɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ;
ɝɚɛɚɪɢɬɚɦɢ ɨɬɞɟɥɶɧɵɯ ɚɝɪɟɝɚɬɨɜ ɢ ɬ. ɞ.
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ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɜ ɨɫɨɛɟɧɧɨɫɬɢ ɪɚɡɥɢɱɧɵɯ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɯɟɦ, ɜ ɤɚɠɞɨɦ ɨɬɞɟɥɶɧɨɦ ɫɥɭɱɚɟ ɧɭɠɧɨ ɜɵɛɪɚɬɶ ɬɚɤɭɸ ɫɯɟɦɭ, ɤɨɬɨɪɚɹ ɜ ɞɨɫɬɚɬɨɱɧɨɣ ɦɟɪɟ
ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɬɪɟɛɭɟɦɵɦ ɭɫɥɨɜɢɹɦ ɢ ɦɨɠɟɬ ɛɵɬɶ ɫɤɨɦɩɨɧɨɜɚɧɚ ɜ ɟɞɢɧɨɟ ɰɟɥɨɟ ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɱɚɫɬɟɣ ɅȺ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɟɟ ɧɚɡɧɚɱɟɧɢɸ. Ɂɚɞɚɱɚ ɫɜɨɞɢɬɫɹ ɤ ɨɛɨɫɧɨɜɚɧɢɸ ɩɚɪɚɦɟɬɪɨɜ
ɦɭ ɩɨɤɚɡɚɬɟɥɸ ɫɨɜɟɪɲɟɧɫɬɜɚ ɩɪɢɧɹɬɨɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɵ. Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɚɹ ɤɨɦɩɨɧɨɜɤɚ ɞɨɥɠɧɚ ɨɛɟɫɩɟɱɢɬɶ ɡɚɞɚɧɧɵɟ ɬɚɤɬɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɅȺ, ɧɟɨɛɯɨɞɢɦɭɸ ɭɫɬɨɣɱɢɜɨɫɬɶ ɢ ɭɩɪɚɜɥɹɟɦɨɫɬɶ. Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɅȺ ɹɜɥɹɸɬɫɹ ɦɧɨɝɨɩɚɪɚɦɟɬɪɢɱɟɫɤɢɦɢ ɮɭɧɤɰɢɹɦɢ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ
ɟɟ ɱɚɫɬɟɣ, ɨɛɪɚɡɭɸɳɢɯ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɭɸ ɮɨɪɦɭ ɅȺ, ɢ ɭɫɥɨɜɢɣ ɩɨɥɟɬɚ. ɉɨɷɬɨɦɭ ɨɰɟɧɤɚ ɫɨɜɟɪɲɟɧɫɬɜɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ
ɞɢɬɶɫɹ ɩɨ ɤɪɢɬɟɪɢɸ, ɤɨɬɨɪɵɣ ɧɚɢɥɭɱɲɢɦ ɨɛɪɚɡɨɦ ɨɬɪɚɠɚɥ ɛɵ ɜɥɢɹɧɢɟ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɯɟɦɵ ɧɚ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɅȺ [4].
Ɍɪɟɛɨɜɚɧɢɹ ɩɪɨɱɧɨɫɬɢ. ɉɪɢ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɜ ɩɨɥɟɬɟ ɧɚɝɪɭɡɤɚɯ ɧɢ ɨɞɢɧ
ɢɡ ɷɥɟɦɟɧɬɨɜ ɤɨɧɫɬɪɭɤɰɢɢ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ. ȼɟɥɢɱɢɧɵ ɧɚɝɪɭɡɨɤ, ɯɚɪɚɤɬɟɪ ɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɥɹ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɟɣ ɅȺ ɧɚ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɩɨɥɟɬɚ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɤɨɦɩɨɧɨɜɤɢ ɅȺ ɩɨ ɜɵɛɪɚɧɧɨ-
ɭɩɪɚɜɥɟɧɢɹ. ɋɪɚɜɧɢɬɟɥɶɧɵɣ ɚɧɚɥɢɡ ɩɨɤɚ-
ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɚɷɪɨɞɢɧɚɦɢ-
ɤɨɦɩɨɧɨɜɤɢ ɞɨɥɠɧɚ ɩɪɨɢɡɜɨ-
ɬɚɤɬɢɤɨ–
10
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