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Файл:Функции Грина и проводимость. Учебное пособие
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ȿ. Ⱥ. Ⱦɨɪɨɮɟɟɜ
Ɏɭɧɤɰɢɢ Ƚɪɢɧɚ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
«ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ»
2025
1
ɍȾɄ 517.9
ȻȻɄ 22.31
Ⱦ69
ɞɨɤɬɨɪ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɡɚɜɟɞɭɸɳɢɣ ɤɚɮɟɞɪɨɣ ɬɟɨɪɟɬɢɱɟɫɤɨɣ
ɮɢɡɢɤɢ ɢɦ. Ʌ. Ⱦ. Ʌɚɧɞɚɭ (Ɇɨɫɤɨɜɫɤɢɣ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ (ɧɚɰɢɨɧɚɥɶɧɵɣ
ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ)) Ⱥɯɦɟɞɨɜ ɗɦɢɥɶ Ɍɨɮɢɤ ɨɝɥɵ;
ɞɨɤɬɨɪ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɝɥɚɜɧɵɣ ɧɚɭɱɧɵɣ ɫɨɬɪɭɞɧɢɤ
ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɨɬɞɟɥɚ (ɂɧɫɬɢɬɭɬ ɮɢɡɢɤɢ ɜɵɫɨɤɢɯ ɞɚɜɥɟɧɢɣ ɢɦ Ʌ. Ɏ. ȼɟɪɟɳɚɝɢɧɚ ɊȺɇ)
Ɋɟɰɟɧɡɟɧɬɵ:
Ɇɢɯɟɟɧɤɨɜ Ⱥɧɞɪɟɣ ȼɢɬɚɥɶɟɜɢɱ
Ⱦɨɪɨɮɟɟɜ, ȿ. Ⱥ.
Ⱦ69 Ɏɭɧɤɰɢɢ Ƚɪɢɧɚ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ : ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ / ȿ. Ⱥ. Ⱦɨɪɨɮɟɟɜ. –
Ɇɨɫɤɜɚ ; ȼɨɥɨɝɞɚ : ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ, 2025. – 152 ɫ. : ɢɥ., ɬɚɛɥ.
ISBN 978-5-9729-2675-6
ɇɚ ɨɫɧɨɜɟ ɬɟɨɪɢɢ ɥɢɧɟɣɧɨɝɨ ɨɬɤɥɢɤɚ ɩɪɢ ɩɨɦɨɳɢ ɦɟɬɨɞɚ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɩɨɫɬɪɨɟɧɚ ɬɟɨɪɢɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɮɟɪɦɢ-ɝɚɡɚ ɜ ɫɥɭɱɚɣɧɨɦ ɩɨɬɟɧɰɢɚɥɟ ɩɪɢɦɟɫɟɣ ɞɥɹ ɫɢɫɬɟɦ ɪɚɡɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ. Ɋɚɫɫɦɨɬɪɟɧɵ ɤɜɚɧɬɨɜɵɟ ɩɨɩɪɚɜɤɢ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɬɪɟɯ- ɢ ɞɜɭɦɟɪɧɵɯ ɫɢɫɬɟɦɚɯ. Ȼɨɥɶɲɨɣ ɨɛɴɟɦ ɦɚɬɟɪɢɚɥɚ ɩɨɫɜɹɳɟɧ ɨɞɧɨɦɟɪɧɨɦɭ ɮɟɪɦɢ-ɝɚɡɭ, ɞɥɹ ɤɨɬɨɪɨɝɨ ɪɚɫɫɦɨɬɪɟɧɨ ɹɜɥɟɧɢɟ ɥɨɤɚɥɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɢ ɜɥɢɹɧɢɟ ɩɪɢɦɟɫɧɨɝɨ ɛɟɫɩɨɪɹɞɤɚ ɧɚ ɩɚɣɟɪɥɫɨɜɫɤɢɣ ɩɟɪɟɯɨɞ ɦɟɬɚɥɥ-ɞɢɷɥɟɤɬɪɢɤ.
Ⱦɥɹ ɫɬɭɞɟɧɬɨɜ ɦɚɝɢɫɬɪɚɬɭɪɵ, ɨɛɭɱɚɸɳɢɯɫɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ 03.04.01 «ɉɪɢɤɥɚɞɧɵɟ
ɦɚɬɟɦɚɬɢɤɚ ɢ ɮɢɡɢɤɚ», ɚ ɬɚɤɠɟ ɞɥɹ ɚɫɩɢɪɚɧɬɨɜ, ɫɩɟɰɢɚɥɢɡɢɪɭɸɳɢɯɫɹ ɜ ɨɛɥɚɫɬɢ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ ɤɨɧɞɟɧɫɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ.
ɍȾɄ 517.9
ȻȻɄ 22.31
ISBN 978-5-9729-2675-6 Ⱦɨɪɨɮɟɟɜ ȿ. Ⱥ., 2025
ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2025
Ɉɮɨɪɦɥɟɧɢɟ. ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2025
2
ɈȽɅȺȼɅȿɇɂȿ
ɉɪɟɞɢɫɥɨɜɢɟ ............................................................................................................. 5
ɋɩɢɫɨɤ ɨɛɨɡɧɚɱɟɧɢɣ ................................................................................................ 7
1. Ɍɟɨɪɢɹ ɥɢɧɟɣɧɨɝɨ ɨɬɤɥɢɤɚ. Ɏɨɪɦɭɥɚ Ʉɭɛɨ ................................................... 8
1.1. Ⱦɢɧɚɦɢɱɟɫɤɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ .................................................................... 8
1.2. Ɏɨɪɦɭɥɚ Ʉɭɛɨ ................................................................................................... 9
2. Ɇɚɰɭɛɚɪɨɜɫɤɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ................................................................ 14
2.1. Ɇɚɰɭɛɚɪɨɜɫɤɨɟ ɜɪɟɦɹ .................................................................................... 14
2.2. Ɇɚɰɭɛɚɪɨɜɫɤɢɣ ɚɧɚɥɨɝ ɮɨɪɦɭɥɵ Ʉɭɛɨ ........................................................ 16
2.3. ɋɜɹɡɶ ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɫ ɞɢɧɚɦɢɱɟɫɤɨɣ ......................... 18
3. Ƚɪɢɧɨɜɫɤɢɟ ɮɭɧɤɰɢɢ ɷɥɟɤɬɪɨɧɨɜ ................................................................. 21
3.1. Ɉɩɟɪɚɬɨɪɵ ɪɨɠɞɟɧɢɹ ɢ ɭɧɢɱɬɨɠɟɧɢɹ .......................................................... 21
3.2. Ɂɚɩɚɡɞɵɜɚɸɳɚɹ ɢ ɨɩɟɪɟɠɚɸɳɚɹ ɮɭɧɤɰɢɢ Ƚɪɢɧɚ ....................................... 23
3.3. Ɇɚɰɭɛɚɪɨɜɫɤɚɹ ɮɭɧɤɰɢɹ
3.4. ɉɪɢɱɢɧɧɚɹ ɮɭɧɤɰɢɹ Ƚɪɢɧɚ ............................................................................ 29
4. Ɉɛɳɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ «ɬɨɤ-ɬɨɤ» ............................ 32
4.1. Ɏɨɪɦɭɥɚ Ʉɭɛɨ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ............................................................... 32
4.2. Ɇɚɰɭɛɚɪɨɜɫɤɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɞɥɹ ɬɨɤɚ ................................................. 34
4.3. ɉɨɫɬɪɨɟɧɢɟ ɮɭɧɤɰɢɢ ࣥሺȳሻ ........................................................................... 35
4.4. «Ɍɨɠɞɟɫɬɜɨ ɍɨɪɞɚ» ........................................................................................ 39
4.5. Ɉɛɳɚɹ ɮɨɪɦɭɥɚ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪɨɧɨɜ .......................... 40
5. ȼɵɪɨɠɞɟɧɧɵɣ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɩɨɬɟɧɰɢɚɥɟ ɩɪɢɦɟɫɟɣ ......................... 43
5.1. ɍɫɪɟɞɧɟɧɢɟ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɩɨ ɛɟɫɩɨɪɹɞɤɭ
5.2. ɍɫɪɟɞɧɟɧɢɟ ɩɪɨɜɨɞɢɦɨɫɬɢ. Ɏɨɪɦɭɥɚ Ⱦɪɭɞɟ ............................................... 50
5.3. Ɏɨɪɦɭɥɚ Ⱦɪɭɞɟ ɫ ɬɪɚɧɫɩɨɪɬɧɵɦ ɜɪɟɦɟɧɟɦ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ .............. 53
6. Ʉɜɚɧɬɨɜɵɟ ɩɨɩɪɚɜɤɢ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ .......................................................... 57
6.1. Ʉɭɩɟɪɨɧ ɢ ɤɜɚɧɬɨɜɚɹ ɩɨɩɪɚɜɤɚ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɬɪɟɯɦɟɪɧɨɦ ɫɥɭɱɚɟ .... 57
6.2. ɉɪɨɜɨɞɢɦɨɫɬɶ ɞɜɭɦɟɪɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ ............................................ 62
7. ɉɪɨɜɨɞɢɦɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨ-ɞɵɪɨɱɧɨɝɨ ɧɟɜɵɪɨɠɞɟɧɧɨɝɨ ɝɚɡɚ ................. 66
7.1. ɏɢɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɞɜɭɯɡɨɧɧɨɝɨ ɩɨɥɭɩɪɨɜɨɞɧɢɤɚ .............................. 66
7.2. Ɏɭɧɤɰɢɢ Ƚɪɢɧɚ ɫɜɨɛɨɞɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ ........................................ 68
7.3. ɍɫɪɟɞɧɟɧɢɟ
ɩɪɢɦɟɫɟɣ ................................................................................................................. 70
7.4. Ɏɨɪɦɭɥɚ Ⱦɪɭɞɟ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɨɥɭɩɪɨɜɨɞɧɢɤɚ ................................. 72
7.5. Ʉɢɧɟɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ .............................................................................. 74
8. Ɉɞɧɨɦɟɪɧɵɣ ɦɟɬɚɥɥ ɜ ɩɨɬɟɧɰɢɚɥɟ ɩɪɢɦɟɫɟɣ. S-ɦɚɬɪɢɰɚ
ɢ ɨɛɳɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ........................................................................................... 77
8.1. Ɏɭɧɤɰɢɢ Ƚɪɢɧɚ ɢ ɫɥɭɱɚɣɧɵɟ ɩɨɥɹ ............................................................... 77
8.2. ܵ-ɦɚɬɪɢɰɚ ........................................................................................................ 81
8.3. ȼɵɪɚɠɟɧɢɟ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɱɟɪɟɡ ɷɥɟɦɟɧɬɵ ܵ-ɦɚɬɪɢɰɵ ........................... 85
8.4. ȼɵɪɚɠɟɧɢɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɱɟɪɟɡ ɷɥɟɦɟɧɬɵ ܵ-ɦɚɬɪɢɰɵ ............................. 86
9. ɋɬɚɬɢɱɟɫɤɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɨɞɧɨɦɟɪɧɨɝɨ ɦɟɬɚɥɥɚ .................................... 89
9.1. S-ɦɚɬɪɢɰɚ ɢ ɫɥɭɱɚɣɧɵɟ ɛɥɭɠɞɚɧɢɹ ɧɚ ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ .............. 89
ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ ɩɨ ɩɨɥɨɠɟɧɢɸ
Ƚɪɢɧɚ .................................................................... 25
................................................ 43
3
9.2. Ɏɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɭɪɚɜɧɟɧɢɟ ɞɢɮɮɭɡɢɢ ɧɚ ɩɥɨɫɤɨɫɬɢ
Ʌɨɛɚɱɟɜɫɤɨɝɨ ......................................................................................................... 92
9.3. ȼɵɱɢɫɥɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ..................................................... 98
10. ɉɪɨɜɨɞɢɦɨɫɬɶ ɨɞɧɨɦɟɪɧɨɝɨ ɦɟɬɚɥɥɚ ɜ ɩɟɪɟɦɟɧɧɨɦ ɩɨɥɟ ..................... 101
10.1. Ʉɚɱɟɫɬɜɟɧɧɚɹ ɨɰɟɧɤɚ Ɇɨɬɬɚ ɞɥɹ ߪሺȳሻ...................................................... 101
10.2. ɍɫɪɟɞɧɟɧɢɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɨ ɛɟɫɩɨɪɹɞɤɭ ɩɪɢ ȳ്Ͳ ............................ 102
10.3. Ɋɟɤɤɭɪɟɧɬɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɫɪɟɞɧɢɯ ɜɟɥɢɱɢɧ ...................................... 106
10.4. ɉɪɨɢɡɜɨɞɹɳɢɟ ɮɭɧɤɰɢɢ ɢ ɜɵɱɢɫɥɟɧɢɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ߪሺȳሻ ................. 109
11. ɉɟɪɟɯɨɞ ɉɚɣɟɪɥɫɚ ɦɟɬɚɥɥ-ɞɢɷɥɟɤɬɪɢɤ ɜ ɨɞɧɨɦɟɪɧɨɦ
ɮɟɪɦɢ-ɫɢɫɬɟɦɟ ...................................................................................................... 117
11.1. Ɉɞɧɨɦɟɪɧɵɣ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɩɨɥɟ ɞɟɮɨɪɦɚɰɢɢ ɪɟɲɟɬɤɢ.
ɍɫɥɨɜɢɟ ɪɚɜɧɨɜɟɫɢɹ ............................................................................................ 117
11.2. Ɋɚɜɧɨɜɟɫɧɚɹ ɞɟɮɨɪɦɚɰɢɹ ɪɟɲɟɬɤɢ. Ɍɟɦɩɟɪɚɬɭɪɚ ɩɟɪɟɯɨɞɚ ................... 119
11.3. ɉɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɳɟɥɶ ......................................... 123
12. ɉɚɣɟɪɥɫɨɜɫɤɢɣ ɩɟɪɟɯɨɞ ɜ ɫɥɭɱɚɣɧɨɦ ɩɨɬɟɧɰɢɚɥɟ ɩɪɢɦɟɫɟɣ ............... 127
12.1. ȼɥɢɹɧɢɟ ɩɪɢɦɟɫɟɣ ɧɚ ɬɟɦɩɟɪɚɬɭɪɭ ɢ ɩɚɪɚɦɟɬɪ ɩɨɪɹɞɤɚ ........................ 127
12.2. ȼɥɢɹɧɢɟ ɩɪɢɦɟɫɟɣ ɧɚ ɩɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ............................................ 138
13. ɉɪɨɜɨɞɢɦɨɫɬɶ ɩɚɣɟɪɥɫɨɜɫɤɨɝɨ ɞɢɷɥɟɤɬɪɢɤɚ .......................................... 142
13.1. ɍɪɚɜɧɟɧɢɟ
ɞɢɮɮɭɡɢɢ ɫɨ ɫɧɨɫɨɦ ɧɚ ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ ............... 142
13.2. ɉɨɫɬɪɨɟɧɢɟ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɞɢɮɮɭɡɢɢ ............................................. 144
13.3. ɋɬɚɬɢɱɟɫɤɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ. ɋɥɭɱɚɣ ܶൌͲ .............................................. 145
13.4. ɋɬɚɬɢɱɟɫɤɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ. ɋɥɭɱɚɣ ɤɨɧɟɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ................ 147
13.5. ɉɪɨɜɨɞɢɦɨɫɬɶ ɜ ɩɟɪɟɦɟɧɧɨɦ ɩɨɥɟ ........................................................... 149
14. Ʌɢɬɟɪɚɬɭɪɚ ..................................................................................................... 151
4
ɉɊȿȾɂɋɅɈȼɂȿ
Ɇɟɬɨɞ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɹɜɥɹɟɬɫɹ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɹɡɵɤɨɦ ɜ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɟ. ȼɩɟɪɜɵɟ ɩɪɟɞɥɨɠɟɧɧɵɣ Ɋ. Ɏɟɣɧɦɚɧɨɦ ɜ ɤɜɚɧɬɨɜɨɣ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɟ, ɨɧ ɫɪɚɡɭ ɫɬɚɥ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɜ ɬɟɨɪɢɢ ɤɨɧɞɟɧɫɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɩɨɦɨɝɚɹ ɢɡɭɱɚɬɶ ɪɚɡɥɢɱɧɵɟ ɫɜɨɣɫɬɜɚ ɦɧɨɝɨɱɚɫɬɢɱɧɵɯ ɤɜɚɧɬɨɜɵɯ ɫɢɫɬɟɦ. ɋɸɞɚ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɜɵɪɨɠɞɟɧɧɵɟ ɮɟɪɦɢ-ɫɢɫɬɟɦɵ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɷɥɟɤɬɪɨɧɚɦɢ ɜ ɦɟɬɚɥɥɚɯ, ɮɨɧɨɧɵ ɜ
ɬɟɤɭɱɢɣ ɠɢɞɤɢɣ ɝɟɥɢɣ, ɫɜɟɪɯɩɪɨɜɨɞɹɳɢɟ ɫɢɫɬɟɦɵ ɢ ɬ. ɞ.
ɉɪɢɦɟɧɟɧɢɟ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɜ ɬɟɨɪɢɢ ɤɨɧɞɟɧɫɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɯɨɪɨɲɨ
ɨɫɜɟɳɟɧɨ ɜ ɨɛɲɢɪɧɨɣ ɥɢɬɟɪɚɬɭɪɟ. ɉɪɟɠɞɟ ɜɫɟɝɨ, ɧɟɥɶɡɹ ɧɟ ɨɬɦɟɬɢɬɶ ɦɨɧɨɝɪɚɮɢɸ Ⱥ. Ⱥ. Ⱥɛɪɢɤɨɫɨɜɚ, Ʌ. ɉ. Ƚɨɪɶɤɨɜɚ, ɂ. ȿ. Ⱦɡɹɥɨɲɢɧɫɤɨɝɨ, «Ɇɟɬɨɞɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɩɨɥɹ
ɤɧɢɝɚ» ɞɨ ɫɢɯ ɩɨɪ ɢɝɪɚɟɬ ɜɚɠɧɭɸ ɪɨɥɶ ɜ ɨɛɪɚɡɨɜɚɧɢɢ ɮɢɡɢɤɨɜ-ɬɟɨɪɟɬɢɤɨɜ. Ɍɚɤɠɟ
ɯɨɪɨɲɢɦ ɜɜɟɞɟɧɢɟɦ ɜ ɦɟɬɨɞ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɢ ɞɢɚɝɪɚɦɦɧɭɸ ɬɟɯɧɢɤɭ ɹɜɥɹɟɬɫɹ
9-ɣ ɬɨɦ ɤɭɪɫɚ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ Ʌ. Ⱦ. Ʌɚɧɞɚɭ ɢ ȿ. Ɇ. Ʌɢɮɲɢɰɚ [2], ɧɚɩɢɫɚɧ-
ɧɵɣ ȿ. Ɇ. Ʌɢɮɲɢɰɨɦ ɢ Ʌ
Ɉɞɧɚɤɨ, ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɚɜɬɨɪɚ, ɜ ɷɬɢɯ ɡɚɦɟɱɚɬɟɥɶɧɵɯ ɤɧɢɝɚɯ ɦɚɥɨ ɢɥɢ ɫɨɜɫɟɦ
ɧɟ ɭɞɟɥɹɟɬɫɹ ɜɧɢɦɚɧɢɟ ɞɜɭɦ ɜɚɠɧɵɦ ɚɫɩɟɤɬɚɦ ɬɟɨɪɢɢ ɤɨɧɞɟɧɫɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. ȼɨ-ɩɟɪɜɵɯ, ɜɚɠɧɵɣ ɤɪɭɝ ɡɚɞɚɱ, ɜ ɤɨɬɨɪɨɦ ɦɟɬɨɞɵ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɧɚɯɨɞɹɬ
ɩɪɢɦɟɧɟɧɢɟ, ɫɜɹɡɚɧ ɫ ɤɜɚɧɬɨɜɵɦɢ ɷɮɮɟɤɬɚɦɢ ɜ ɧɟɭɩɨɪɹɞɨɱɟɧɧɵɯ ɫɢɫɬɟɦɚɯ. Ɉɞɧɨɣ ɢɡ ɧɚɢɛɨɥɟɟ ɢɧɬɟɪɟɫɧɵɯ ɡɚɞɚɱ
ɷɥɟɤɬɪɨɧɨɜ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɦɟɬɚɥɥɚɯ, ɨɩɢɫɵɜɚɟɦɵɣ ɫ ɩɨɦɨɳɶɸ ɦɨɞɟɥɢ ɢɞɟɚɥɶɧɨɝɨ ɮɟɪɦɢ-ɝɚɡɚ ɜ ɩɪɢɫɭɬɫɬɜɢɢ ɛɟɫɩɨɪɹɞɤɚ.
ȼɨ-ɜɬɨɪɵɯ, ɜ ɩɨɫɥɟɞɧɢɟ ɞɟɫɹɬɢɥɟɬɢɹ ɬɟɨɪɟɬɢɱɟɫɤɚɹ ɮɢɡɢɤɚ ɫɬɨɥɤɧɭɥɚɫɶ ɫ
ɦɧɨɝɨɨɛɪɚɡɧɵɦ ɤɪɭɝɨɦ ɹɜɥɟɧɢɣ ɫɜɹɡɚɧɧɵɯ ɫ ɦɚɥɨɣ ɪɚɡɦɟɪɧɨɫɬɶɸ ɫɢɫɬɟɦ. Ɉɤɚɡɚɥɨɫɶ, ɱɬɨ ɤɜɚɧɬɨɜɚɹ ɮɢɡɢɤɚ ɨɞɧɨ- ɢ ɞɜɭɦɟɪɧɵɯ ɫɢɫɬɟɦ ɜɟɫɶɦɚ ɛɨɝɚɬɚ ɧɚ ɧɟɬɪɢ
ɜɢɚɥɶɧɵɟ ɷɮɮɟɤɬɵ. ɗɬɨ ɩɪɟɠɞɟ ɜɫɟɝɨ ɹɜɥɟɧɢɟ ɥɨɤɚɥɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɜ ɫɥɭɱɚɣɧɨɦ ɩɨɬɟɧɰɢɚɥɟ ɩɪɢɦɟɫɟɣ, ɩɟɪɟɯɨɞ ɉɚɣɟɪɥɫɚ ɫ ɭɞɜɨɟɧɢɟɦ ɩɟɪɢɨɞɚ
ɜ ɨɞɧɨɦɟɪɧɵɯ ɦɟɬɚɥɥɚɯ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɜɨɥɧɵ ɡɚɪɹɞɨɜɨɣ ɩɥɨɬɧɨɫɬɢ, ɫɨɥɢɬɨɧɵ ɫ
ɧɟɰɟɥɵɦ ɡɚɪɹɞɨɦ, ɜɨɥɧɵ ɫɩɢɧɨɜɨɣ ɩɥɨɬɧɨɫɬɢ, ɢ ɷɬɨ ɞɚɥɟɤɨ ɧɟɩɨɥɧɵɣ ɫɩɢɫɨɤ ɧɟɬɪɢɜɢɚɥɶɧɵɯ ɹɜɥɟɧɢɣ ɨɞɧɨ- ɢ ɞɜɭɦɟɪɧɨɣ ɮɢɡɢɤɢ.
ɂɦɟɧɧɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɩɪɨɜɨɞɢɦɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ
ɫɥɭɱɚɣɧɨɦ ɩɨɬɟɧɰɢɚɥɟ ɩɪɢɦɟɫɟɣ ɩɨɫɜɹɳɟɧɨ ɷɬɚ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ. ɗɬɚ ɡɚɞɚɱɚ ɪɟɲɚɟɬɫɹ ɞɥɹ ɫɢɫɬɟɦ ɪɚɡɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ, ɧɨ ɞɨɜɨɥɶɧɨ ɛɨɥɶɲɨɣ ɨɛɴɟɦ ɦɚɬɟɪɢɚɥɚ
ɩɨɫɜɹɳɟɧ ɨɞɧɨɦɟɪɧɨɦɭ ɷɥɟɤɬɪɨɧɧɨɦɭ ɮɟɪɦɢ-ɝɚɡɭ. Ⱦɥɹ ɷɬɨɣ ɫɢɫɬɟɦɵ ɩɨɫɬɪɨɟɧɚ
ɬɟɨɪɢɹ S-ɦɚɬɪɢɰɵ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɣ ɜɵɱɢɫɥɟɧɚ ɫɬɚɬɢɱɟɫɤɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɢ
ɩɪɨɜɨɞɢɦɨɫɬɶ ɜ ɩɨɥɟ ɫ ɤɨɧɟɱɧɨɣ ɱɚɫɬɨɬɨɣ, ɢ
ɡɚɰɢɢ ɜɫɟɯ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɨɫɬɪɨɟɧɚ ɬɟɨɪɢɹ ɩɚɣɟɪɥɫɨɜɫɤɨɝɨ ɩɟɪɟɯɨɞɚ ɦɟɬɚɥɥ-ɞɢɷɥɟɤɬɪɢɤ ɜ ɨɞɧɨɦɟɪɧɨɣ ɮɟɪɦɢ-ɫɢɫɬɟɦɟ ɢ ɢɡɭɱɟɧɨ ɜɥɢɹɧɢɟ ɫɥɭɱɚɣɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɩɪɢɦɟɫɟɣ ɧɚ ɩɚɪɚɦɟɬɪɵ ɷɬɨɝɨ ɩɟɪɟɯɨɞɚ. ȼɵɱɢɫɥɟɧɚ
ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɚɣɟɪɥɫɨɜɫɤɨɝɨ ɞɢɷɥɟɤɬɪɢɤɚ ɢ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɜɨɥɧɚ ɡɚɪɹɞɨɜɨɣ
ɩɥɨɬɧɨɫɬɢ ɭɫɢɥɢɜɚɟɬ ɥɨɤɚɥɢɡɚɰɢɸ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ.
Ⱦɚɧɧɨɟ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɪɟɞɧɚɡɧɚɱɟɧɨ ɩɪɟɠɞɟ
ɬɚɦ ɫɬɚɪɲɢɯ ɤɭɪɫɨɜ, ɜɵɛɪɚɜɲɢɦ ɜ ɤɚɱɟɫɬɜɟ ɫɩɟɰɢɚɥɶɧɨɫɬɢ ɬɟɨɪɟɬɢɱɟɫɤɭɸ ɮɢ-
ɜ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɮɢɡɢɤɟ» [5]. ɗɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ «ɡɟɥɟɧɚɹ
ɬɜɟɪɞɵɯ ɬɟɥɚɯ, ɮɨɬɨɧɵ ɱɟɪɧɨɝɨ ɢɡɥɭɱɟɧɢɹ, ɫɜɟɪɯ-
. ɉ. ɉɢɬɚɟɜɫɤɢɦ.
ɬɚɤɨɝɨ ɬɢɩɚ ɹɜɥɹɟɬɫɹ ɤɜɚɧɬɨɜɵɣ ɬɪɚɧɫɩɨɪɬ
-
ɷɥɟɤɬɪɨɧɧɨɝɨ ɮɟɪɦɢ-ɝɚɡɚ ɜ
ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧ ɷɮɮɟɤɬ ɥɨɤɚɥɢ-
ɜɫɟɝɨ ɚɫɩɢɪɚɧɬɚɦ ɢ ɫɬɭɞɟɧ-
5
ɡɢɤɭ ɤɨɧɞɟɧɫɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. ɉɨɫɨɛɢɟ ɬɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɢɧɬɟɪɟɫɧɨ ɧɚɭɱɧɵɦ ɫɨɬɪɭɞɧɢɤɚɦ, ɠɟɥɚɸɳɢɦ ɩɨɡɧɚɤɨɦɢɬɶɫɹ ɫ ɬɟɨɪɢɣ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɪɚɧɫɩɨɪɬɚ
ɜ ɧɢɡɤɨɪɚɡɦɟɪɧɵɯ ɫɢɫɬɟɦɚɯ.
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɫɨɫɬɨɢɬ ɢɡ ɬɪɢɧɚɞɰɚɬɢ ɝɥɚɜ. ȼ ɩɟɪɜɵɯ ɞɜɭɯ ɝɥɚɜɚɯ ɢɡɥɨɠɟɧɚ
ɬɟɨɪɢɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɢ ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɟɣ ɢ ɜɵɜɟɞɟɧɨ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɧɢɦɢ. Ƚɥɚɜɚ 3 ɩɨɫɜɹɳɟɧɚ ɢɡɥɨɠɟɧɢɸ ɬɟɨɪɢɢ ɝɪɢɧɨɜɫɤɢɯ ɮɭɧɤɰɢɣ
ɷɥɟɬɪɨɧɨɜ, ɜ
ɧɟɣ ɢɡɭɱɟɧɵ ɨɩɟɪɟɠɚɸɳɚɹ, ɡɚɩɚɡɞɵɜɚɸɳɚɹ, ɩɪɢɱɢɧɧɚɹ ɢ ɦɚɰɭɛɚɪɨɜɫɤɚɹ ɮɭɧɤɰɢɢ Ƚɪɢɧɚ. ȼ ɝɥɚɜɟ 4 ɩɨɫɬɪɨɟɧɚ ɬɟɨɪɢɹ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ «ɬɨɤ-ɬɨɤ»
ɢ ɢɡɥɨɠɟɧɚ ɩɪɨɰɟɞɭɪɚ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɩɪɨɞɨɥɠɟɧɢɹ ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɮɭɧɤɰɢɢ ɨɬ-
ɤɥɢɤɚ ɫ ɞɢɫɤɪɟɬɧɨɝɨ ɧɚɛɨɪɚ ɦɧɢɦɵɯ ɬɨɱɟɤ ɧɚ ɜɫɸ ɤɨɦɩɥɟɤɫɧɭɸ ɩɥɨɫɤɨɫɬɶ ɱɚɫɬɨɬ. ȼ ɝɥɚɜɚɯ 5 ɢ 6 ɩɨɫɬɪɨɟɧɚ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ «ɤɪɟɫɬɨɜɚɹ» ɞɢɚɝɪɚɦɦɧɚɹ ɬɟɯɧɢɤɚ,
ɩɪɟɞɧɚɡɧɚɱɟɧɚɹ ɞɥɹ
ɜɵɱɢɫɥɟɧɢɹ ɭɫɪɟɞɧɟɧɧɵɯ ɩɨ ɛɟɫɩɨɪɹɞɤɭ ɝɪɢɧɨɜɫɤɢɯ ɮɭɧɤɰɢɣ ɢ ɩɪɨɜɨɞɢɦɨɫɬɢ ɮɟɪɦɢ-ɝɚɡɚ ɜ ɩɨɥɟ ɫɥɭɱɚɣɧɵɯ ɩɪɢɦɟɫɟɣ ɜ ɬɪɟɯɦɟɪɧɨɦ ɢ ɞɜɭ-
ɦɟɪɧɨɦ ɫɥɭɱɚɹɯ. ɉɨɥɭɱɟɧɚ ɮɨɪɦɭɥɚ Ⱦɪɭɞɟ ɢ ɩɨɤɚɡɚɧɵ ɩɪɟɞɟɥɵ ɟɟ ɩɪɢɦɟɧɢɦɨɫɬɢ. ɉɪɨɫɭɦɦɢɪɨɜɚɧɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ ɜɟɟɪɧɵɯ ɞɢɚɝɪɚɦɦ ɢ
ɜɜɟɞɟɧɨ ɩɨɧɹɬɢɟ ɤɭɩɟɪɨɧɚ. ɉɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɨ ɩɨɹɜɥɟɧɢɟ ɥɨɝɚɪɢɮɦɢɱɟɫɤɨɣ
ɨɫɨɛɟɧɧɨɫɬɢ ɜ ɤɜɚɧɬɨɜɨɣ ɩɨɩɪɚɜɤɟ ɤ ɞɜɭɦɟɪɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ
. Ƚɥɚɜɚ 7 ɩɨɫɜɹɳɟɧɚ ɜɵɜɨɞɭ ɫ ɩɨɦɨɳɶɸ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɩɨɞɯɨɞɚ, ɮɨɪɦɭɥɵ Ⱦɪɭɞɟ ɞɥɹ ɞɜɭɯɡɨɧɧɨɝɨ ɩɨɥɭɩɪɨɜɨɞɧɢɤɚ. Ƚɥɚɜɵ 813 ɩɨɫɜɹɳɟɧɵ ɨɞɧɨɦɟɪɧɨɣ ɮɟɪɦɢ-ɫɢɫɬɟɦɟ
ɷɥɟɤɬɪɨɧɨɜ. ȼ ɝɥɚɜɟ 8 ɢɡɥɨɠɟɧɚ ɬɟɨɪɢɹ S-ɦɚɬɪɢɰɵ, ɱɟɪɟɡ ɷɥɟɦɟɧɬɵ ɤɨɬɨɪɨɣ ɜɵɪɚɠɚɸɬɫɹ ɝɪɢɧɨɜɫɤɢɟ ɮɭɧɤɰɢɢ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ. Ƚɥɚɜɚ 9 ɩɨɫɜɹɳɟɧɚ ɜɵɱɢɫɥɟɧɢɸ
ɫɬɚɬɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɞɧɨɦɟɪɧɨɝɨ ɦɟɬɚɥɥɚ ɢ ɬɚɤɠɟ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɷɬɚ ɡɚɞɚɱɚ ɫɜɨɞɢɬɫɹ
ɤ ɢɡɭɱɟɧɢɸ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɧɚ ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ.
ȼ ɝɥɚɜɟ 10 ɩɨɫɬɪɨɟɧɚ ɬɟɨɪɢɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɪɢ ɤɨɧɟɱɧɨɣ ɱɚɫɬɨɬɟ. Ƚɥɚɜɵ 1113
ɩɨɫɜɹɳɟɧɵ ɪɚɫɫɦɨɬɪɟɧɢɸ ɩɟɪɟɯɨɞɚ ɉɟɣɪɥɫɚ ɜ ɨɞɧɨɦɟɪɧɨɦ ɦɟɬɚɥɥɟ ɢ ɢɡɭɱɟɧɢɸ
ɜɥɢɹɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɫɥɭɱɚɣɧɵɯ ɩɪɢɦɟɫɟɣ ɧɚ ɫɜɨɣɫɬɜɚ ɷɬɨɝɨ ɩɟɪɟɯɨɞɚ. ȼ ɝɥɚɜɟ 13
ɢɡɭɱɚɟɬɫɹ ɜɥɢɹɧɢɟ ɩɚɣɟɪɥɫɨɜɫɤɨɝɨ ɩɟɪɟɯɨɞɚ ɧɚ ɷɮɮɟɤɬ ɥɨɤɚɥɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ.
Ⱥɜɬɨɪ ɜɵɪɚɠɚɟɬ ɛɥɚɝɨɞɚɪɧɨɫɬɶ
ɗ. Ɍ. Ⱥɯɦɟɞɨɜɭ, ɩɪɨɱɢɬɚɜɲɟɦɭ ɛɨɥɶɲɭɸ
ɱɚɫɬɶ ɪɭɤɨɩɢɫɢ ɢ ɫɞɟɥɚɜɲɟɦɭ ɪɹɞ ɰɟɧɧɵɯ ɡɚɦɟɱɚɧɢɣ, ɚ ɬɚɤɠɟ ȼ. ɂ. Ⱥɜɪɭɬɫɤɨɦɭ,
ɨɤɚɡɚɜɲɟɦɭ ɛɨɥɶɲɭɸ ɩɨɦɨɳɶ ɩɪɢ ɨɮɨɪɦɥɟɧɢɢ ɪɭɤɨɩɢɫɢ.
6
ɋɉɂɋɈɄ ɈȻɈɁɇȺɑȿɇɂɃ
ߝ
ɷɧɟɪɝɢɹ Ɏɟɪɦɢ;
ி
ɮɟɪɦɢɟɜɫɤɢɣ ɢɦɩɭɥɶɫ;
m ɦɚɫɫɚ ɷɥɟɤɬɪɨɧɚ;
ݒ
ߦ
ߚൌͳȀܶ ɨɛɪɚɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ;
݊
ۃǥۄ
ۃǥۄ
߬
ɜ ɨɞɧɨɦɟɪɧɨɦ ɦɟɬɚɥɥɟ;
߬
ɜ ɨɞɧɨɦɟɪɧɨɦ ɦɟɬɚɥɥɟ;
߬ൌቀ
ߣ
ɜ ɩɨɥɟ ɫɥɭɱɚɣɧɵɯ ɩɪɢɦɟɫɟɣ;
݃ ɤɨɧɫɬɚɧɬɚ ɷɥɟɤɬɪɨɧ-ɮɨɧɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ.
ɇɚɱɢɧɚɹ ɫ ɝɥɚɜɵ 8, ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ ɩɨɥɚɝɚɟɬɫɹ ɪɚɜɧɨɣ ɟɞɢɧɢɰɟ.
Ɍɟɦɩɟɪɚɬɭɪɚ ɜɟɡɞɟ ɜɵɪɚɠɚɟɬɫɹ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ (݇
Ȁ݉ ɮɟɪɦɢɟɜɫɤɚɹ ɫɤɨɪɨɫɬɶ;
ൌ
ሺ
ȁpȁ
ൌݒ
p
ሺ߱ሻ
ൌ
ி
ɭɫɪɟɞɧɟɧɢɟ ɩɨ ɚɧɫɚɦɛɥɸ Ƚɢɛɛɫɚ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ܶ;
்
ɭɫɪɟɞɧɟɧɢɟ ɩɨ ɫɥɭɱɚɣɧɨɦɭ ɩɨɥɨɠɟɧɢɸ ɩɪɢɦɟɫɟɣ;
ɜɪɟɦɹ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɷɥɟɤɬɪɨɧɚ ɞɨ ɪɚɫɫɟɹɧɢɹ ɧɚ ɩɪɢɦɟɫɢ «ɜɩɟɪɟɞ»
ଵ
ɜɪɟɦɹ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɷɥɟɤɬɪɨɧɚ ɞɨ ɪɚɫɫɟɹɧɢɹ ɧɚ ɩɪɢɦɟɫɢ «ɧɚɡɚɞ»
ଶ
ଶ
ఛ
భ
ɞɥɢɧɚ ɥɨɤɚɥɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɜ ɨɞɧɨɦɟɪɧɨɣ ɫɢɫɬɟɦɟ
ሻ
െ
ɫɩɟɤɬɪ ɷɥɟɤɬɪɨɧɨɜ ɥɢɧɟɚɪɢɡɨɜɚɧɧɵɣ ɜɛɥɢɡɢ ɭɪɨɜɧɹ Ɏɟɪɦɢ;
ଵ
ɮɟɪɦɢɟɜɫɤɚɹ ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ;
ഁഘ
ାଵ
ିଵ
ଵ
ቁ
;
ఛ
మ
ൌͳሻ.
7
Ƚɥɚɜɚ 1
ɌȿɈɊɂə ɅɂɇȿɃɇɈȽɈ ɈɌɄɅɂɄȺ.
ɎɈɊɆɍɅȺ ɄɍȻɈ
1.1. Ⱦɢɧɚɦɢɱɟɫɤɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ
Ɋɚɫɫɦɨɬɪɢɦ ɫɢɫɬɟɦɭ ɫ ɝɚɦɢɥɶɬɨɧɢɚɧɨɦ ܪ
ɫɤɢɯ ɜɟɥɢɱɢɧ, ɬɚɤɢɯ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɜɧɟɲɧɟɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɫɢɫɬɟɦɭ, ɩɪɢɜɨɞɹɳɟɟ ɤ ɩɨɹɜɥɟɧɢɸ ɜ ɝɚɦɢɥɶɬɨɧɢɚɧɟ ɫɢɫɬɟɦɵ ɜɨɡɦɭɳɚɸɳɟɝɨ ɨɩɟɪɚɬɨɪɚ ɜɢɞɚ
, ɢ ɩɭɫɬɶ ሼݔොఈሽ ɨɩɟɪɚɬɨɪɵ ɮɢɡɢɱɟ-
ɝɞɟ ݂
ܸൌെݔො
ఈ
ሺݐሻ
ɧɟɤɨɬɨɪɵɟ ɡɚɞɚɧɧɵɟ ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ, ɤɨɬɨɪɵɟ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɨɛɨɛ-
ఈ
ሺݐሻ
ǡ
Ԝ݂
ఈ
ఈ
ሺ
ͳǤͳ
ɳɟɧɧɵɦɢ ɫɢɥɚɦɢ. ɂɧɞɟɤɫ ߙ ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɨɞɧɨ ɡɧɚɱɟɧɢɟ, ɬɨɝɞɚ ɟɝɨ ɬɚɤ ɠɟ,
ɤɚɤ ɢ ɫɭɦɦɭ ɦɨɠɧɨ ɨɩɭɫɬɢɬɶ, ɦɨɠɟɬ ɩɪɨɛɟɝɚɬɶ ɧɚɛɨɪ ɤɨɧɟɱɧɵɯ ɡɧɚɱɟɧɢɣ, ɧɚɩɪɢ-
ሺ
ɦɟɪ,
ɧɢɟ ɜ ɧɟɩɪɟɪɵɜɧɨɦ ɦɧɨɠɟɫɬɜɟ, ɧɚɩɪɢɦɟɪ
ሻ
ݔǡݕǡݖ
, ɬɨ ɟɫɬɶ ɛɵɬɶ ɜɟɤɬɨɪɧɵɦ ɢɧɞɟɤɫɨɦ, ɦɨɠɟɬ ɬɚɤɠɟ ɩɪɢɧɢɦɚɬɶ ɡɧɚɱɟ-
ɜ R3, ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɫɭɦɦɭ ɜ (1.1) ɧɚɞɨ
ɩɨɧɢɦɚɬɶ ɤɚɤ ɢɧɬɟɝɪɚɥ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɦɟɪɟ. ȼ ɞɚɥɶɧɟɣɲɟɦ ɦɵ ɩɪɟɞɩɨɥɚɝɚɟɦ, ɱɬɨ ɜ ɪɚɜɧɨɜɟɫɧɨɦ ɫɨɫɬɨɹɧɢɢ ɫɢɫɬɟɦɵ, ɜ ɨɬɫɭɬɫɬɜɢɢ ɜɨɡɦɭɳɟɧɢɹ, ɬɨ ɟɫɬɶ
ɤɨɝɞɚ ɞɥɹ ɜɫɟɯ ߙ ݂
ሺݐሻ
ൌͲ, ɜɫɟ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ ݔ᪄
ఈ
ɪɚɜɧɵ ɧɭɥɸ.
ɉɪɢ ɧɚɥɢɱɢɢ ɜɨɡɦɭɳɟɧɢɹ (1.1) ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ ݔ᪄
ɨɬɥɢɱɧɵ ɨɬ ɧɭɥɹ ɢ ɜ ɥɢɧɟɣɧɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɜɢɞɟ
ஶ
ሺݐሻ
ݔ᪄
ൌන߯
ఈ
ఉ
ɝɞɟ ɧɚɛɨɪ ɜɟɥɢɱɢɧ ߯
ɧɢɚɧɨɦ ܪ
ɢ ɫɬɚɰɢɨɧɚɪɧɵɦ ɫɨɫɬɨɹɧɢɟɦ, ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɥɚɫɶ ɫɢɫɬɟɦɚ ɞɨ ɧɚɥɨ-
ሺ߬ሻ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɜɨɣɫɬɜɚɦɢ ɫɢɫɬɟɦɵ, ɬɨ ɟɫɬɶ ɝɚɦɢɥɶɬɨ-
ఈఉ
ɠɟɧɢɹ ɜɨɡɦɭɳɟɧɢɹ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɡɧɚɱɟɧɢɟ ݔ᪄
ሺ
ሻ
ݐ
ɜɢɫɟɬɶ ɨɬ ɡɧɚɱɟɧɢɹ ɫɢɥ ݂
ɩɪɢ ݐݐ
, ɩɪɟɞɟɥɵ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜ (1.2) ɜɵɛɪɚɧɵ ɬɚɤ, ɱɬɨ ɷɬɨ ɬɪɟɛɨɜɚɧɢɟ ɜɵ-
ଵ
ɥɢɲɶ ɜ ɩɪɟɞɲɟɫɬɜɭɸɳɢɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ, ɬɨ ɟɫɬɶ
ఉ
ଵ
ሺ߬ሻ
ሺ
݂
ఈఉ
ݐെ߬ሻԜ݀߬ǡ
ఉ
ሺݐሻ
ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ݐ ɦɨɠɟɬ ɡɚ-
ఈ
ሺ
ͳǤʹ
ɩɨɥɧɹɟɬɫɹ.
ȼɫɹɤɨɟ ɡɚɜɢɫɹɳɟɟ ɨɬ ɜɪɟɦɟɧɢ ɜɨɡɦɭɳɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɫɜɟɞɟɧɨ ɩɭɬɟɦ ɮɭɪɶɟ-
ɪɚɡɥɨɠɟɧɢɹ ɤ ɫɨɜɨɤɭɩɧɨɫɬɢ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɯ ɤɨɦɩɨɧɟɧɬ, ɡɚɜɢɫɹɳɢɯ ɨɬ ɜɪɟ-
ɦɟɧɢ ɤɚɤ ݁
ିఠ௧
, ɩɨɞɫɬɚɜɢɜ ɜ (1.2) ݂
ሺఠሻ
ሺݐሻ
ఉ
ɢ ݔ᪄
ሺݐሻ
ఈ
ɜ ɜɢɞɟ ݂
ିఠ௧
݁
ఉ
ɢ ݔ᪄
ሺఠሻ
ఈ
݁
ିఠ௧
, ɩɨ-
ɥɭɱɢɦ ɫɜɹɡɶ ɦɟɠɞɭ ɮɭɪɶɟ-ɤɨɦɩɨɧɟɧɬɚɦɢ ɫɢɥ ɢ ɨɬɤɥɢɤɚ ɜ ɜɢɞɟ
ݔ᪄
ሺఠሻ
ఈ
ൌ߯
ఉ
ఈఉ
ሺ߱ሻ
ሺఠሻ
Ԝ݂
ǡ
ఉ
ሺ
ͳǤ͵
ሻ
ఈ
ఈ
ሻ
ሻ
8
ሺ߱ሻ
ɝɞɟ ɮɭɧɤɰɢɢ ߯
ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ
ఈఉ
ஶ
ሺ߱ሻ
ఈఉ
ൌන߯
߯
ఈఉ
ሺݐሻ
ఠ௧
݁
݀ݐǤ
ሺ
ͳǤͶ
Ɂɚɞɚɧɢɟ ɷɬɢɯ ɮɭɧɤɰɢɣ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɟɬ ɩɨɜɟɞɟɧɢɟ ɫɢɫɬɟɦɵ ɩɨɞ ɜɥɢɹ-
ሺ߱ሻ
ɧɢɟɦ ɞɚɧɧɨɝɨ ɜɨɡɦɭɳɟɧɢɹ. ɋɨɜɨɤɭɩɧɨɫɬɶ ɜɟɥɢɱɢɧ ߯
ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɞɢɧɚ-
ఈఉ
ɦɢɱɟɫɤɨɣ (ɨɛɨɛɳɟɧɧɨɣ) ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶɸ ([2], § 123).
Ɏɭɧɤɰɢɹ ߯
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ߱ ɤɚɤ ɤɨɦɩɥɟɤɫɧɭɸ ɩɟɪɟɦɟɧɧɭɸ (߱ൌ߱
ɞɭɟɦ ɫɜɨɣɫɬɜɚ ɮɭɧɤɰɢɢ ߯
ɨɩɪɟɞɟɥɟɧɢɹ (1.4) ɢ ɢɡ ɮɚɤɬɚ ɤɨɧɟɱɧɨɫɬɢ ߯
ɞɭɟɬ, ɱɬɨ ߯
ɧɢɝɞɟ ɧɟ ɨɛɪɚɳɚɸɬɫɹ ɜ ɛɟɫɤɨɧɟɱɧɨɫɬɶ, ɬ. ɟ. ɧɟ ɢɦɟɸɬ ɨɫɨɛɵɯ ɬɨɱɟɤ. Ⱦɟɣɫɬɜɢ-
ɬɟɥɶɧɨ, ɩɪɢ ߱
ɚɥɶɧɨ ɭɛɵɜɚɸɳɢɣ ɦɧɨɠɢɬɟɥɶ ሺെݐ߱
ሺ߱ሻ
ɤɨɦɩɥɟɤɫɧɚ, ɢ ɢɡ ɨɩɪɟɞɟɥɟɧɢɹ (1.4) ɜɢɞɧɨ, ɱɬɨ
ఈఉ
ሺെ߱ሻ
߯
ఈఉ
ሺ߱ሻ
ɜ ɜɟɪɯɧɟɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɷɬɨɣ ɩɟɪɟɦɟɧɧɨɣ. ɂɡ
ఈఉ
ሺ߱ሻ
ɟɫɬɶ ɨɞɧɨɡɧɚɱɧɚɹ ɮɭɧɤɰɢɹ ɜɨ ɜɫɟɣ ɜɟɪɯɧɟɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɢ
ఈఉ
ᇳ
Ͳ ɜ ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɦ ɜɵɪɚɠɟɧɢɢ ɜ (1.4) ɢɦɟɟɬɫɹ ɷɤɫɩɨɧɟɧɰɢ-
כ
ሺ߱ሻ
ൌ߯
ᇳ
ሻ
, ɚ ɩɨɫɤɨɥɶɤɭ ɮɭɧɤɰɢɹ ߯
Ǥ
ఈఉ
ሺݐሻ
ɩɪɢ ɜɫɟɯ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ݐ ɫɥɟ-
ఈఉ
ᇱ
݅߱
ఈఉ
ሺݐሻ
ሺ
ᇳ
) ɢ ɢɫɫɥɟ-
ɤɨɧɟɱɧɚ
ͳǤͷ
ɜɨ ɜɫɟɣ ɨɛɥɚɫɬɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ, ɬɨ ɢɧɬɟɝɪɚɥ ɫɯɨɞɢɬɫɹ.
ȼ ɧɢɠɧɟɣ ɠɟ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɟ (1.4) ɧɟɩɪɢɦɟɧɢɦɨ, ɬɚɤ ɤɚɤ ɢɧɬɟ-
ɝɪɚɥ ɪɚɫɯɨɞɢɬɫɹ. ɉɨɷɬɨɦɭ ɮɭɧɤɰɢɹ ߯
ሺ߱ሻ
ɜ ɧɢɠɧɟɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɦɨɠɟɬ ɛɵɬɶ
ఈఉ
ɨɩɪɟɞɟɥɟɧɚ ɥɢɲɶ ɤɚɤ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɩɪɨɞɨɥɠɟɧɢɟ ɜɵɪɚɠɟɧɢɹ (1.4) ɢɡ ɜɟɪɯɧɟɣ
ሺ߱ሻ
ɩɨɥɭɩɥɨɫɤɨɫɬɢ. ȼ ɷɬɨɣ ɨɛɥɚɫɬɢ ɮɭɧɤɰɢɹ ߯
ɉɨɥɟɡɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜɵɜɨɞ ɨɛ ɨɬɫɭɬɫɬɜɢɢ ɨɫɨɛɵɯ ɬɨɱɟɤ ɭ ɮɭɧɤɰɢɣ ߯
ɢɦɟɟɬ ɨɫɨɛɵɟ ɬɨɱɤɢ.
ఈఉ
ఈఉ
ሺ߱ሻ
ɜ ɜɟɪɯɧɟɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɹɜɥɹɟɬɫɹ ɫ ɮɢɡɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɫɥɟɞɫɬɜɢɟɦ ɩɪɢɧɰɢɩɚ ɩɪɢɱɢɧɧɨɫɬɢ. ɉɨɫɥɟɞɧɢɣ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɜ (1.2)
ɩɪɨɢɡɜɨɞɢɬɫɹ ɥɢɲɶ ɩɨ ɜɪɟɦɟɧɢ, ɩɪɟɞɲɟɫɬɜɭɸɳɟɦɭ ɞɚɧɧɨɦɭ ɦɨɦɟɧɬɭ ݐ.
1.2. Ɏɨɪɦɭɥɚ Ʉɭɛɨ
ሺ߱ሻ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɢɧɚɦɢɱɟɫɤɚɹ (ɨɛɨɛɳɟɧɧɚɹ) ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ߯
ɫɵɜɚɟɬ ɥɢɧɟɣɧɵɣ ɨɬɤɥɢɤ ɫɢɫɬɟɦɵ ɧɚ ɜɧɟɲɧɢɟ ɩɟɪɟɦɟɧɧɵɟ ɩɨɥɹ. ɋ ɩɪɚɤɬɢɱɟɫɤɨɣ
ɬɨɱɤɢ ɡɪɟɧɢɹ ɜɨɩɪɨɫ ɨ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɵɣ ɢɧɬɟɪɟɫ, ɩɨɫɤɨɥɶɤɭ ɛɨɥɶɲɢɧɫɬɜɨ ɜɟɥɢɱɢɧ, ɢɡɦɟɪɹɟɦɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ, ɢɦɟɸɬ ɯɚɪɚɤɬɟɪ
ɥɢɧɟɣɧɵɯ ɨɬɤɥɢɤɨɜ. Ʉɚɤ ɠɟ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɞɢɧɚɦɢɱɟɫɤɭɸ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ
ɫɢɫɬɟɦɵ ɩɨ ɟɟ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɦ ɫɜɨɣɫɬɜɚɦ? Ɉɤɚɡɵɜɚɟɬɫɹ, ɢɦɟɟɬ ɦɟɫɬɨ ɬɚɤ
ɧɚɡɵɜɚɟɦɚɹ ɮɨɪɦɭɥɚ Ʉɭɛɨ. Ⱦɥɹ ɜɵɜɨɞɚ
ɬɨɜɨɦɟɯɚɧɢɱɟɫɤɨɟ ɜɵɱɢɫɥɟɧɢɟ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ ݔ᪄
ɷɬɨɣ ɮɨɪɦɭɥɵ ɩɪɨɢɡɜɟɞɟɦ ɩɪɹɦɨɟ ɤɜɚɧ-
ሺݐሻ
ɜ ɜɨɡɦɭɳɟɧɧɨɣ ɫɢɫɬɟɦɟ
ఈ
ɫ ɨɩɟɪɚɬɨɪɨɦ ɜɨɡɦɭɳɟɧɢɹ (1.1).
ሺݐሻ
Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɩɨɥɨɠɢɦ, ɱɬɨ ɮɭɧɤɰɢɢ ݂
ɱɢɫɬɨ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɟ ɢ ɡɚɞɚ-
ఈ
ɸɬɫɹ ɜɟɳɟɫɬɜɟɧɧɵɦ ɜɵɪɚɠɟɧɢɟɦ
ఈఉ
ɨɩɢ-
ሻ
ሻ
9
ሺݐሻ
ൌܴ݂݁
݂
ఈ
ఈ
Ԝ݁
ିఠ௧
ൌ
ʹ
ൣ݂ఈԜ݁
ିఠ௧
ͳ
݂
ఈ
כ
ఠ௧
Ԝ݁
൧ǡ
ɩɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ (1.1) ɤ ɷɬɢɦ ɮɭɧɤɰɢɹɦ, ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ
ͳ
ሺݐሻ
ൌ
ݔ᪄
ఈ
ൣ߯
ʹ
ఈఉ
ሺ߱ሻ
Ɍɟɩɟɪɶ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ݔ᪄
ሺሻ
ߖ
ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ ɧɟɜɨɡɦɭɳɟɧɧɨɣ ɫɢɫɬɟɦɵ:
ߖ
ܪ
ିఠ௧
Ԝ݂
Ԝ݁
ఉ
ఈ
ሺሻ
߯
ሺݐሻ
, ɢɫɩɨɥɶɡɭɹ ɬɟɨɪɢɸ ɜɨɡɦɭɳɟɧɢɣ. ɉɭɫɬɶ
ሺሻ
ൌܧ
ሺሻ
ߖ
Ɇɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɨɬ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɨɩɟɪɚɬɨɪɚ ܱ
ఈఉ
Ǥ
ሺെ߱ሻ
כ
ఠ௧
Ԝ݂
Ԝ݁
൧ఉǤ
ఉ
ɩɨ ɷɬɢɦ ɮɭɧɤɰɢɹɦ ɛɭ-
ɞɟɦ ɨɛɨɡɧɚɱɚɬɶ ɫ ɩɨɦɨɳɶɸ ɫɤɨɛɨɤ Ⱦɢɪɚɤɚ
ܱ
ൌߖ
ሺሻ
כ
ሺݍሻ
ܱߖ
ሺሻ
ሺݍሻ
݀ݍൌൻ݉หܱห݊ൿǤ
ɋɥɟɞɭɹ ɨɛɳɟɦɭ ɦɟɬɨɞɭ, ɢɳɟɦ ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ ɜɨɡɦɭɳɟɧɧɨɣ ɫɢɫɬɟɦɵ ɜ
ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɜ ɜɢɞɟ
ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ܽ
ሺሻ
ɝɞɟ ߱
ൌቀܧ
െܧ
݅
ൌߖ
݀ܽ
݀ݐ
ሺሻ
ܽ
ሺݐሻ
ൌܸ
ሺݐሻ
, ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɨɩɟɪɚɬɨɪɚ ɜɨɡɦɭ-
ߖ
ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɪɚɜɧɟɧɢɹɦ
ሺሻ
ቁȀ, ɚ ܸ
݁
Ԝߖ
ఠ௧
ሺሻ
ǡ
ǡ
ɳɟɧɢɹ
ሺݐሻ
ൌൻ݉หܸ
ܸ
ሺݐሻ
ห݊ൿǡ
ɩɨɞɫɬɚɜɥɹɹ (1.6) ɢ (1.1) ɩɨɥɭɱɢɦ
ሺݐሻ
ܸ
ͳ
ൌെ
ൻ݉หݔොఉห݊ൿఉ൫݂ఉԜ݁
ʹ
ିఠ௧
݂
ఉ
כ
ఠ௧
Ԝ݁
൯Ǥ
ሺ
ሺ
ሺ
ሺ
ሺ
ͳǤͳͲ
ሺ
ͳǤͳͳ
ሺ
ͳǤͳʹ
ሺ
ͳǤͳ͵
ͳǤ
ͳǤ
ͳǤͺ
ͳǤͻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
Ɋɟɲɚɹ ɭɪɚɜɧɟɧɢɟ (1.11), ɫɥɟɞɭɟɬ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɨɡɦɭɳɟɧɢɟ ɚɞɢɚɛɚɬɢɱɟɫɤɢ
ɜɤɥɸɱɚɟɬɫɹ ɤ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ ݐ ɨɬ ɜɪɟɦɟɧɢ ݐൌെλ, ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɦɧɨɠɢ-
േఠ௧
ɬɟɥɹɯ ݁
ɧɚɞɨ ɡɚɦɟɧɢɬɶ ߱՜߱ט݅ߜ ɩɪɢ ߜ՜Ͳ. Ɍɨɝɞɚ
ିఠ௧
݂
ͳ
ൌ
ܽ
ൻ݉หݔොఉห݊ൿఉ݁
ʹ
ఠ௧
Ԝ݁
ఉ
ቈ
߱െ߱െ݅ߜ
כ
ఠ௧
݂
Ԝ݁
ఉ
߱߱െ݅ߜ
Ǥ
ሺ
ͳǤͳͶ
10
ሻ
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