Моделирование транспортных процессов. Учебное пособие
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ɋɢɫɬɟɦɧɵɣ ɩɨɞɯɨɞ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨɬɨɤɚ Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɦɨɞɟɥɟɣ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨɬɨɤɚ
ȼ ɬɟɪɦɢɧɚɯ ɫɢɫɬɟɦɧɨɝɨ ɩɨɞɯɨɞɚ Ɍɉ ɢ ɤɨɦɩɥɟɤɫ ɭɫɥɨɜɢɣ ɜ ɤɨɬɨɪɵɯ ɨɧ ɞɜɢɠɟɬɫɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɢɩɢɱɧɵɣ ɩɪɢɦɟɪ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ ɋɋ ɉɨɞ ɋɋ ɩɨɧɢɦɚɸɬ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɜɡɚɢɦɧɨ ɫɜɹɡɚɧɧɵɯ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɦɟɠɞɭ ɫɨɛɨɣ ɷɥɟɦɟɧɬɨɜ ɨɪɝɚɧɢɡɨɜɚɧɧɵɯ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɱɬɨɛɵ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɨ ɞɨɫɬɢɱɶ ɩɨɫɬɚɜɥɟɧɧɨɣ ɰɟɥɢ ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɩɪɨɛɥɟɦɵ ɫɜɹɡɚɧɧɨɣ ɫ ɞɜɢɠɟɧɢɟɦ Ɍɉ ɫɥɟɞɭɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɋɋ ©ɜɨɞɢɬɟɥɶ – ɫɪɟɞɫɬɜɚ ɭɩɪɚɜɥɟɧɢɹ ɚɜɬɨɦɨɛɢɥɟɦ – ɚɜɬɨɦɨɛɢɥɶ – ɞɨɪɨɝɚ – ɫɪɟɞɫɬɜɚ ɨɪɝɚɧɢɡɚɰɢɢ ɞɜɢɠɟɧɢɹ
– ɫɪɟɞɚª Ɉɫɨɛɟɧɧɨɫɬɶɸ ɷɬɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɜ ɭɫɥɨɜɢɹɯ ɞɟɣɫɬɜɢɹ ɛɨɥɶɲɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɫɥɭɱɚɣɧɵɯ ɮɚɤɬɨɪɨɜ
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɞɧɨɡɧɚɱɧɨɝɨ ɱɟɬɤɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ ɧɟɬ ɂɡɜɟɫɬɧɵ ɪɚɡɥɢɱɧɵɟ ɩɨɞɯɨɞɵ ɢ ɩɪɟɞɥɨɠɟɧɵ ɪɚɡɥɢɱɧɵɟ ɮɨɪɦɚɥɶɧɵɟ ɩɪɢɡɧɚɤɢ ɟɟ ɨɩɪɟɞɟɥɟɧɢɹ Ɍɚɤ ɫɨɜɟɬɫɤɢɣ ɭɱɟɧɵɣ Ƚ ɇ ɉɨɜɨɪɨɜ ɩɪɟɞɥɚɝɚɟɬ ɨɬɧɨɫɢɬɶ ɤ ɫɥɨɠɧɵɦ ɫɢɫɬɟɦɵ ɢɦɟɸɳɢɟ -107 ɷɥɟɦɟɧɬɨɜ ɤ ɭɥɶɬɪɨɫɥɨɠɧɵɦ - ɫɢɫɬɟɦɵ ɫɨɫɬɨɹɳɢɟ ɢɡ -1030 ɷɥɟɦɟɧɬɨɜ ɢ ɤ ɫɭɩɟɪɫɢɫɬɟɦɚɦ – ɫɢɫɬɟɦɵ ɢɡ - ɷɥɟɦɟɧɬɨɜ
Ɍɚɤɨɣ ɩɨɞɯɨɞ ɢɦɟɟɬ ɬɨɬ ɧɟɞɨɫɬɚɬɨɤ ɱɬɨ ɞɚɧɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɥɨɠɧɨɫɬɢ ɹɜɥɹɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɚ ɧɟ ɚɛɫɨɥɸɬɧɵɦ
Ⱥɧɝɥɢɣɫɤɢɣ ɤɢɛɟɪɧɟɬɢɤ ɋ Ȼɢɪ ɩɪɟɞɥɚɝɚɟɬ ɤ ɫɥɨɠɧɵɦ ɨɬɧɨɫɢɬɶ ɫɢɫɬɟɦɵ ɨɩɢɫɵɜɚɟɦɵɟ ɧɚ ɹɡɵɤɟ ɬɟɨɪɟɬɢɤɨ-ɜɟɪɨɹɬɧɨɫɬɧɵɯ ɦɟɬɨɞɨɜɦɨɡɝ ɷɤɨɧɨɦɢɤɚ ɮɨɪɦɚ ɢ ɬ ɩ
ɇɚɢɛɨɥɟɟ ɱɟɬɤɢɦ ɨɩɪɟɞɟɥɟɧɢɟɦ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ ɹɜɥɹɟɬɫɹ ɨɩɪɟɞɟɥɟɧɢɟ ɋɥɨɠɧɨɣ ɫɢɫɬɟɦɨɣ ɧɚɡɵɜɚɟɬɫɹ ɫɢɫɬɟɦɚ ɜ ɦɨɞɟɥɢ ɤɨɬɨɪɨɣ ɧɟɞɨɫɬɚɬɨɱɧɨ ɢɧɮɨɪɦɚɰɢɢ ɞɥɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɷɬɨɣ ɫɢɫɬɟɦɨɣ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɪɢɡɧɚɤɨɦ ɩɪɨɫɬɨɬɵ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɢɧɮɨɪɦɚɰɢɢ ɞɥɹ ɟɟ ɭɩɪɚɜɥɟɧɢɹ ȿɫɥɢ ɠɟ ɪɟɡɭɥɶɬɚɬ ɭɩɪɚɜɥɟɧɢɹ ɩɨɥɭɱɟɧɧɵɣ ɫ ɩɨɦɨɳɶɸ ɦɨɞɟɥɢ ɛɭɞɟɬ ɧɟɨɠɢɞɚɧɧɵɦ ɬɨ ɬɚɤɭɸ ɫɢɫɬɟɦɭ ɨɬɧɨɫɹɬ ɤ ɫɥɨɠɧɨɣ
Ɉɬ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ ɧɟɨɛɯɨɞɢɦɨ ɨɬɥɢɱɚɬɶ ɛɨɥɶɲɢɟ ɫɢɫɬɟɦɵ ɋɢɫɬɟɦɚ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɤɨɬɨɪɨɣ ɜ ɰɟɥɹɯ ɭɩɪɚɜɥɟɧɢɹ
ɧɟɞɨɫɬɚɟɬ ɦɚɬɟɪɢɚɥɶɧɵɯ ɪɟɫɭɪɫɨɜ ɦɚɲɢɧɧɨɝɨ ɜɪɟɦɟɧɢ ɟɦɤɨɫɬɢ ɩɚɦɹɬɢ ɞɪɭɝɢɯ ɦɚɬɟɪɢɚɥɶɧɵɯ ɫɪɟɞɫɬɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɛɨɥɶɲɨɣ
Ʉ ɬɚɤɢɦ ɫɢɫɬɟɦɚɦ ɨɬɧɨɫɹɬɫɹ ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɭɩɪɚɜɥɟɧɱɟɫɤɢɟ ɧɟɣɪɨɮɢɡɢɨɥɨɝɢɱɟɫɤɢɟ ɛɢɨɥɨɝɢɱɟɫɤɢɟ ɢ ɬ ɩ ɫɢɫɬɟɦɵ
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ɋɩɨɫɨɛɨɦ ɩɟɪɟɜɨɞɚ ɛɨɥɶɲɢɯ ɫɢɫɬɟɦ ɜ ɩɪɨɫɬɵɟ ɹɜɥɹɟɬɫɹ ɫɨɡɞɚɧɢɟ ɧɨɜɵɯ ɛɨɥɟɟ ɦɨɳɧɵɯ ɫɪɟɞɫɬɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɬɟɯɧɢɤɢ
Ⱦɜɢɠɟɧɢɟ Ɍɉ ɹɜɥɹɟɬɫɹ ɪɟɡɭɥɶɬɚɬɨɦ ɧɟɩɪɟɪɵɜɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɫɢɫɬɟɦɵ ɤɚɤ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɬɚɤ ɢ ɜɨ ɜɪɟɦɟɧɢ ɉɨɞɫɢɫɬɟɦɚɦɢ Ɍɉ ɤɚɤ ɋɋ ɦɨɝɭɬ ɛɵɬɶ ɩɨɞɫɢɫɬɟɦɚ ɩɨɬɨɤɚ ɚɜɬɨɦɨɛɢɥɟɣ ɩɨɞɫɢɫɬɟɦɵ ɞɨɪɨɠɧɵɯ ɭɫɥɨɜɢɣ ɢ ɫɪɟɞɫɬɜ ɨɪɝɚɧɢɡɚɰɢɢ ɞɜɢɠɟɧɢɹ ɩɨɞɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɚɜɬɨɦɨɛɢɥɟɦ ɢ ɬ ɞ ɪɢɫ 1.2 Ʉɚɠɞɚɹɢɡ ɷɬɢɯɩɨɞɫɢɫɬɟɦ ɬɚɤɠɟ ɹɜɥɹɟɬɫɹɋɋ ɬɪɟɛɭɸɳɟɣ ɩɪɢɦɟɧɟɧɢɹ ɬɟɯ ɠɟ ɦɟɬɨɞɨɜ ɚɧɚɥɢɡɚ ɢ ɨɰɟɧɤɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɤɚɤ ɜɫɹ ɫɥɨɠɧɚɹ ɫɢɫɬɟɦɚ ©ȼ-ɋɍȺ-Ⱥ-Ⱦ-ɋɈȾ-ɋª
ɑɬɨɛɵ ɨɛɟɫɩɟɱɢɬɶ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɨɟ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɬ ɟ ɧɚɢɛɨɥɟɟ ɛɟɡɨɩɚɫɧɵɟ ɭɞɨɛɧɵɟ ɢ ɷɤɨɧɨɦɢɱɧɵɟ ɭɫɥɨɜɢɹ ȾȾ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɵɟ ɫɜɹɡɢ ɜɧɭɬɪɢ ɫɢɫɬɟɦɵɩɨɫɬɪɨɢɬɶ ɦɨɞɟɥɶ ɫɬɪɭɤɬɭɪɵ ɢ ɭɫɬɚɧɨɜɢɬɶ ɢɯ ɜɥɢɹɧɢɟ ɧɚ ɩɨɜɟɞɟɧɢɟ ɜɫɟɣ ɫɢɫɬɟɦɵ ɤɚɤ ɟɞɢɧɨɝɨ ɰɟɥɨɝɨ – ɜɵɹɜɢɬɶ ɢɧɬɟɝɪɚɬɢɜɧɵɟɷɦɟɪɞɠɟɧɬɧɵɟ ɫɜɨɣɫɬɜɚ
Ɉɫɧɨɜɧɚɹ ɤɨɧɰɟɩɰɢɹ ɫɢɫɬɟɦɧɨɝɨ ɩɨɞɯɨɞɚ – ɷɬɨ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɢɫɫɥɟɞɭɟɦɨɝɨɨɛɴɟɤɬɚɢɥɢɩɪɨɰɟɫɫɚɜɜɢɞɟɫɢɫɬɟɦɵ6ɢɟɟɩɨɫɥɟɞɭɸɳɢɣ ɚɧɚɥɢɡ ɫ ɰɟɥɶɸ ɜɵɹɜɥɟɧɢɹ ɨɫɧɨɜɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɗɬɚɩɵ ɦɟɬɨɞɢɤɢ ɫɢɫɬɟɦɧɨɝɨ ɩɨɞɯɨɞɚ ɮɨɪɦɭɥɢɪɨɜɤɚ ɰɟɥɟɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɜɵɞɟɥɟɧɢɟ ɫɢɫɬɟɦɵ ɢɡ ɫɪɟɞɵ ɟɟ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɪɚɡɪɚɛɨɬɤɚ ɫɬɪɭɤɬɭɪɵ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɨɛɟɫɩɟɱɢɜɚɸɳɟɣ ɞɨɫɬɢɠɟɧɢɟ ɡɚɞɚɧɧɵɯ ɰɟɥɟɣ
ɋɢɫɬɟɦɚ ɩɨ ȼ ɇ ɋɨɝɚɬɨɜɫɤɨɦɭ – ɷɬɨ ©ɤɨɧɟɱɧɨɟ ɦɧɨɠɟɫɬɜɨ ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ $ ɢ ɨɬɧɨɲɟɧɢɣ ɦɟɠɞɭ ɧɢɦɢ 5 ɜɵɞɟɥɟɧɧɨɟ ɢɡ ɫɪɟɞɵ 65 ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɩɪɟɞɟɥɟɧɧɨɣ ɰɟɥɶɸ = ɜ ɪɚɦɤɚɯ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ 'T».
S{<A, R, Z, SR, 'T> |
(1.1) |
Ⱦɥɹ ɨɩɢɫɚɧɢɹ Ɍɉ ɤɚɤ ɋɋ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɬɟɨɪɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɫɬɚɬɢɫɬɢɤɚ ɜɵɱɢɫɥɢɬɟɥɶɧɚɹ ɬɟɯɧɢɤɚ ɬɟɨɪɢɹ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɟɨɪɢɹ ɢɝɪ ɥɢɧɟɣɧɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɬɟɨɪɢɹ ɢɧɮɨɪɦɚɰɢɢ ɢ ɩɫɢɯɨɮɢɡɢɨɥɨɝɢɹ ɱɟɥɨɜɟɤɚ > @
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Ɋɢɫ. 1.2 Ⱦɨɪɨɠɧɨɟ ɞɜɢɠɟɧɢɟ ɤɚɤ ɫɥɨɠɧɚɹ ɫɢɫɬɟɦɚ
ɂɡɜɟɫɬɧɵɟ ɢ ɧɚɲɟɞɲɢɟ ɩɪɚɤɬɢɱɟɫɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɆɆ ɜ ɈȾȾ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɞɜɟ ɝɪɭɩɩɵ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɟ ɢ ɫɬɨɯɚɫɬɢɱɟɫɤɢɟɪɢɫ .
Ɇɨɞɟɥɢ Ɍɉ ȾȾ
Ⱦɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɟ ɋɬɨɯɚɫɬɢɱɟɫɤɢɟ
Ɇɚɤɪɨɫɤɨɩɢɱɟɫɤɢɟ Ɇɢɤɪɨɫɤɨɩɢɱɟɫɤɢɟ
Ɋɢɫ 1.3 Ɇɨɞɟɥɢ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɩɨɬɨɤɚ
Ʉ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɦ ɞɢɧɚɦɢɱɟɫɤɢɦ ɨɬɧɨɫɹɬɫɹ ɦɨɞɟɥɢ ɜ ɨɫɧɨɜɭ ɤɨɬɨɪɵɯ ɡɚɥɨɠɟɧɚ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ Ɍɉ ɧɚɩɪɢɦɟɪ ɫɜɹɡɶ ɦɟɠɞɭ ɫɤɨɪɨɫɬɶɸ ɢ ɞɢɫɬɚɧɰɢɟɣ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɢ ɫɤɨɪɨɫɬɶɸ ɢ ɬ ɞ ȼ ɫɥɭɱɚɹɯ ɱɚɫɬɨ ɧɚɛɥɸɞɚɟɦɵɯ ɜ ɛɨɥɶɲɨɦ ɝɨɪɨɞɟ ɢɥɢ ɧɚ ɫɤɨɪɨɫɬɧɨɣ ɞɨɪɨɝɟ ɤɨɝɞɚ ɦɧɨɝɨ ɚɜɬɨɦɨɛɢɥɟɣ ɞɜɢɠɭɬɫɹ ɜ ɝɪɭɩɩɟ ɬɪɚɧɫɩɨɪɬɧɵɣ ɩɨɬɨɤ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɦɨɬɪɟɧ ɤɚɤ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɣ ɢ ɧɟɩɪɟɪɵɜɧɵɣ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɫ ɩɨɦɨɳɶɸ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɯ ɦɨɞɟɥɟɣ ɢɫɫɥɟɞɭɸɬ Ɍɉ ɜɵɫɨɤɨɣ
13
ɩɥɨɬɧɨɫɬɢ ɜ ɤɨɬɨɪɵɯ ɚɜɬɨɦɨɛɢɥɢ ɧɚɯɨɞɹɬɫɹ ɜ ɬɟɫɧɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɦɟɠɞɭ ɫɨɛɨɣ ɢ ɪɟɲɚɸɳɭɸ ɪɨɥɶ ɢɝɪɚɟɬ ɱɟɥɨɜɟɤ ɤɚɤ ɨɩɟɪɚɬɨɪ
ɋɬɨɯɚɫɬɢɱɟɫɤɢɟ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɦɨɞɟɥɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬ Ɍɉ ɤɚɤ ɜɟɪɨɹɬɧɨɫɬɧɵɣ ɫɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ ɧɚɩɪɢɦɟɪ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɢɧɬɟɪɜɚɥɨɜ ɦɟɠɞɭ ɚɜɬɨɦɨɛɢɥɹɦɢ ɜ Ɍɉ ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶɫɹ ɧɟ ɫɬɪɨɝɨ ɨɩɪɟɞɟɥɟɧɧɵɦ ɚ ɫɥɭɱɚɣɧɵɦ Ɍɉ ɞɜɢɠɭɳɢɣɫɹ ɩɨ ɍȾɋ ɫɨɫɬɨɢɬ ɢɡ ɦɧɨɠɟɫɬɜɚ ɚɜɬɨɦɨɛɢɥɟɣ ɤɨɬɨɪɵɟ ɭɩɪɚɜɥɹɸɬɫɹ ɩɨ ɛɨɥɟɟ ɢɥɢ ɦɟɧɟɟ ɫɜɨɛɨɞɧɨɦɭ ɠɟɥɚɧɢɸ ɜɨɞɢɬɟɥɟɣ ɢ ɦɚɧɟɜɪɵ ɤɚɠɞɨɝɨ ɚɜɬɨɦɨɛɢɥɹ ɦɨɝɭɬ ɛɵɬɶ ɪɚɫɰɟɧɟɧɵ ɤɚɤ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɫɨɛɵɬɢɹ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɫ ɩɨɦɨɳɶɸ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɢɫɫɥɟɞɭɸɬ Ɍɉ ɧɢɡɤɨɣ ɩɥɨɬɧɨɫɬɢ
ȿɫɥɢɨɛɫɭɠɞɚɸɬɫɹɭɫɥɨɜɢɹ ɜɥɢɹɸɳɢɟɧɚ ɛɟɡɨɩɚɫɧɨɫɬɶɞɜɢɠɟɧɢɹ ɧɚ ɞɨɪɨɝɟ ɢɥɢ ɫɬɚɪɬɨɜɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɚɜɬɨɦɨɛɢɥɟɣ ɧɚɱɢɧɚɸɳɢɯ ɞɜɢɠɟɧɢɟ ɨɬ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɩɟɪɟɤɪɟɫɬɤɚ ɬɨ ɫɥɟɞɭɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɟɪɨɹɬɧɨɫɬɧɵɣ ɩɨɞɯɨɞ ɢ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɤɨɬɨɪɵɟ ɩɪɟɞɫɬɚɜɥɹɸɬ ɞɜɢɠɟɧɢɟ ɨɬɞɟɥɶɧɵɯ ɚɜɬɨɦɨɛɢɥɟɣ & ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ ɢɦɟɹ ɞɟɥɨ ɫ Ɍɉ ɞɜɢɠɭɳɢɦɫɹ ɩɨ ɍȾɋ ɨɛɨɪɭɞɨɜɚɧɧɵɯ ɦɧɨɠɟɫɬɜɨɦ ɪɟɝɭɥɢɪɭɟɦɵɯ ɩɟɪɟɤɪɟɫɬɤɨɜ ɜɨɡɦɨɠɧɨ ɱɬɨ ɜɵɝɨɞɧɟɟ ɩɨɥɶɡɨɜɚɬɶɫɹ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɨɣ ɦɨɞɟɥɶɸ ɤɨɬɨɪɚɹ ɨɬɨɛɪɚɠɚɟɬ Ɍɉ ɤɚɤ ɫɬɚɰɢɨɧɚɪɧɨɟ ɹɜɥɟɧɢɟ ɩɪɟɞɫɬɚɜɥɹɟɦɨɟ ɨɛɳɟɣɫɪɟɞɧɟɣɫɤɨɪɨɫɬɶɸ ɩɥɨɬɧɨɫɬɶɸ ɩɨɬɨɤɚ ɢ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɩɨɫɤɨɥɶɤɭ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɥɢɲɤɨɦ ɞɟɬɚɥɶɧɚ ɞɥɹ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɩɨɬɨɤɨɜ ɫ ɜɵɫɨɤɨɣ ɩɥɨɬɧɨɫɬɶɸ
ȼɨɩɪɨɫɵ ɞɥɹ ɩɨɜɬɨɪɟɧɢɹ
1.ɑɬɨ ɬɚɤɨɟ ɫɥɨɠɧɚɹ ɫɢɫɬɟɦɚ"
2.ɉɨɱɟɦɭ Ɍɉ ɨɬɧɨɫɹɬ ɤ ɋɋ"
3.ȼ ɱɟɦ ɫɨɫɬɨɢɬ ɨɫɧɨɜɧɚɹ ɤɨɧɰɟɩɰɢɹ ɫɢɫɬɟɦɧɨɝɨ ɩɨɞɯɨɞɚ"
4.Ʉɚɤɢɟ ɷɥɟɦɟɧɬɵ ɜɤɥɸɱɚɟɬ ɫɢɫɬɟɦɚ ɩɨ ɋɨɝɚɬɨɜɫɤɨɦɭ"
5.ɉɟɪɟɱɢɫɥɢɬɟ ɨɫɧɨɜɧɵɟ ɜɢɞɵ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ Ɍɉ
6.ɑɟɦ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɟ ɦɨɞɟɥɢ Ɍɉ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ"
7.ȼ ɤɚɤɢɯ ɫɥɭɱɚɹɯ ɢɫɩɨɥɶɡɭɸɬ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɚ ɜ ɤɚɤɢɯ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɟ"
Ɇɚɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɦɨɞɟɥɢ Ɍɉ
Ɇɚɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬ Ɍɉ ɤɚɤ ɫɩɥɨɲɧɭɸ ɫɪɟɞɭ ɫɨɫɬɨɹɳɭɸ ɢɡ ɛɨɥɶɲɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɛɥɢɡɤɨ ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɞɪɭɝ ɤ ɞɪɭɝɭ ɚɜɬɨɦɨɛɢɥɟɣ Ⱦɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɫɨɫɬɨɹɧɢɹ ɞɜɢɠɭɳɟɝɨɫɹ Ɍɉ ɤɚɤ ɫɩɥɨɲɧɨɣ ɫɪɟɞɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ
14
ɫɥɟɞɭɸɳɢɟ ɨɫɧɨɜɧɵɟ ɡɚɤɨɧɵ ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɩɨɬɨɤɚ ɚɜɬɨɦɨɛɢɥɟɣ ɭɪɚɜɧɟɧɢɟ ɧɟɪɚɡɪɵɜɧɨɫɬɢ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɉɪɨɰɟɫɫɵ ɩɪɨɢɫɯɨɞɹɳɢɟ ɜɧɭɬɪɢ Ɍɉ ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɢɫɫɥɟɞɨɜɚɧɵ ɫ ɩɨɦɨɳɶɸ ɞɚɧɧɨɣ ɬɟɨɪɢɢ Ɉɫɧɨɜɧɨɟ ɩɪɚɤɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɚɧɚɥɢɡ ɜɨɥɧɨɜɨɝɨ ɞɜɢɠɟɧɢɹ Ɍɉ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɜɵɹɜɥɟɧɢɹ ɫɬɟɩɟɧɢ ɜɥɢɹɧɢɹ ɩɪɟɩɹɬɫɬɜɢɣ
Ɇɚɤɪɨɫɤɨɩɢɱɟɫɤɚɹ ɦɨɞɟɥɶ Ɍɉ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɦɨɞɟɥɶ ɩɪɟɞɫɬɚɜɥɹɸɳɚɹ ɫɪɟɞɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ɍɉ ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ Y ɩɥɨɬɧɨɫɬɶ T ɢ ɢɧɬɟɧɫɢɜɧɨɫɬɶ 1 ɫɨɫɬɨɹɳɟɝɨ ɢɡ ɚɜɬɨɦɨɛɢɥɟɣ ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɢɦɟɟɬ ɫɬɨɯɚɫɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɉɨɞ ɭɪɚɜɧɟɧɢɟɦ ɫɨɫɬɨɹɧɢɹ Ɍɉ ɤɚɤ ɫɩɥɨɲɧɨɣ ɫɪɟɞɵ ɩɨɧɢɦɚɸɬ ɫɥɟɞɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ
N q v . (1.2)
ɉɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɧɟɪɚɡɪɵɜɧɨɫɬɢ Ɍɉ ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɩɪɢɧɰɢɩɚɯ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɦɚɫɫ Ⱥɧɚɥɢɡɢɪɭɹ Ɍɉ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɩɨɫɬɨɹɧɫɬɜɨ ɨɛɳɟɝɨ ɱɢɫɥɚ ɚɜɬɨɦɨɛɢɥɟɣɜɨ ɜɪɟɦɟɧɢG. GW ɂɡɦɟɧɟɧɢɟ ɨɛɳɟɝɨ ɱɢɫɥɚ ɚɜɬɨɦɨɛɢɥɟɣ ɧɚ ɭɱɚɫɬɤɟ ɞɨɪɨɝɢ G[ ɡɚ ɜɪɟɦɹ GW ɪɢɫ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɤɚɤ ɜ ɪɟɡɭɥɶɬɚɬɟ ɢɡɦɟɧɟɧɢɹ ɩɥɨɬɧɨɫɬɢ T ɬɚɤ ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɢɡɦɟɧɟɧɢɹ ɢɧɬɟɧɫɢɜɧɨɫɬɢ 1
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Ɋɢɫ. 1.4 ɂɡɦɟɧɟɧɢɟ ɨɛɳɟɝɨ ɱɢɫɥɚ ɚɜɬɨɦɨɛɢɥɟɣ ɧɚ ɭɱɚɫɬɤɟ ɞɨɪɨɝɢ G[
ȿɫɥɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ Ɍɉ ɤɚɤ ɫɬɚɰɢɨɧɚɪɧɭɸ ɫɢɫɬɟɦɭ ɬɨ ɢɡɦɟɧɟɧɢɟ ɦɟɠɞɭɱɢɫɥɨɦɚɜɬɨɦɨɛɢɥɟɣ ɩɨɞɥɢɧɟɞɨɪɨɝɢG[ɡɚ ɜɪɟɦɹGWɞɨɥɠɧɨɛɵɬɶ ɪɚɜɧɨ ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ ɱɢɫɥɨɦ ɚɜɬɨɦɨɛɢɥɟɣ ɜɯɨɞɹɳɢɯ ɧɚ ɭɱɚɫɬɨɤ [ ɢ ɱɢɫɥɨɦ ɚɜɬɨɦɨɛɢɥɟɣ ɜɵɯɨɞɹɳɢɯ ɫ ɭɱɚɫɬɤɚ [ G[
ɉɭɫɬɶ [ – ɪɚɫɫɬɨɹɧɢɟ ɜɞɨɥɶ ɞɨɪɨɝɢ Ɋɚɫɫɦɨɬɪɢɦ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɭɱɚɫɬɨɤ ɞɨɪɨɝɢ G[ ɂɡɦɟɧɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ ɚɜɬɨɦɨɛɢɥɟɣ G. ɡɚ ɜɪɟɦɹ GW ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɨ ɤɚɤ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɩɪɢɛɵɜɚɸɳɢɦɢ ɚɜɬɨɦɨɛɢɥɹɦɢ ɜ ɬɨɱɤɭ [ ɢ ɭɛɵɜɚɸɳɢɦɢ ɢɡ ɬɨɱɤɢ [ G[
dK Ndt (N dN )dt , |
(1.3) |
15
ɝɞɟ G1 – ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɨɟ ɢɡɦɟɧɟɧɢɟ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚ ɭɱɚɫɬɤɟ G[ ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ ɢɡɦɟɧɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ ɚɜɬɨɦɨɛɢɥɟɣ G. ɦɨɠɧɨ
ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɢɡɦɟɧɟɧɢɟ ɩɥɨɬɧɨɫɬɢ T ɡɚ ɜɪɟɦɹ GW
dK qdx (q dq)dx . |
(1.4) |
ɉɪɢɪɚɜɧɹɟɦ ɜɵɪɚɠɟɧɢɹ .3 ɢ .4) |
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dNdt dqdx , |
(1.5) |
ɢ ɩɨɥɭɱɢɦ ©ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɚɜɬɨɦɨɛɢɥɟɣª |
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ɜɵɜɟɞɟɧɧɵɣ ɩɪɢ ɭɫɥɨɜɢɢ ɱɬɨ ɧɚ ɭɱɚɫɬɤɟ ɞɨɪɨɝɢ ɧɟɬ ɜɴɟɡɞɨɜ ɢ ɫɴɟɡɞɨɜ ɋɦɵɫɥ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɫɥɟɞɭɸɳɢɣ ɤɨɥɢɱɟɫɬɜɨ ɚɜɬɨɦɨɛɢɥɟɣ ɜɯɨɞɹɳɢɯ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ GW ɧɚ ɭɱɚɫɬɨɤ G[ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɚɜɬɨɦɨɛɢɥɟɣ ɜɵɯɨɞɹɳɢɯ ɫ ɷɬɨɝɨ ɭɱɚɫɬɤɚ
Ɋɚɫɫɦɨɬɪɢɦ ɫɜɹɡɶ ɦɟɠɞɭ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ Ɍɉ ɫɤɨɪɨɫɬɶɸ Y ɩɥɨɬɧɨɫɬɶɸ T ɉɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ Ɍɉ
Ȼɭɞɟɦ ɫɱɢɬɚɬɶ ɱɬɨ ɫɤɨɪɨɫɬɶ Y ɜ ɬɨɱɤɟ [ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɩɥɨɬɧɨɫɬɶɸ T ɜ [ v f q(x,t Ɉɩɪɟɞɟɥɢɦ Y¶ ɤɚɤ
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ɉɪɢɦɟɦ ɫɪɟɞɧɟɟ ɭɫɤɨɪɟɧɢɟ ɧɚɛɥɸɞɚɬɟɥɹ ɬɚɤɢɦ ɤɚɤɨɟ ɨɛɵɱɧɨ ɢɦɟɟɬ ɩɚɬɪɭɥɶɧɵɣ ɚɜɬɨɦɨɛɢɥɶ ɞɨɪɨɠɧɨɣ ɫɥɭɠɛɵ ɞɜɢɝɚɸɳɢɣɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ ɪɚɜɧɨɣ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ Y
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ȼɵɩɨɥɧɢɦ ɫɥɟɞɭɸɳɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
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ɋ ɭɱɟɬɨɦ ɩɨɥɭɱɢɦ
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ɍɱɢɬɵɜɚɹ ɱɬɨ N=Ȟ* ɢ ɫ ɭɱɟɬɨɦ ɜɵɪɚɠɟɧɢɹ .6 ɚ ɬɚɤɠɟ ɩɨɥɶɡɭɹɫɶ ɩɪɚɜɢɥɚɦɢ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɩɪɨɢɡɜɟɞɟɧɢɹ ɩɨɥɭɱɢɦ
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ɉɨɞɫɬɚɜɢɦ 11 ɜ ɜɵɪɚɠɟɧɢɟ .10 ɢ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ Ɍɉ
dv |
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ɝɞɟ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ v' 2 q ɦɨɠɧɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɜ ɫɥɭɱɚɟ ɞɢɧɚɦɢɤɢ ɠɢɞɤɨɫɬɟɣ Ⱦɥɹ ɤɥɚɫɫɢɱɟɫɤɨɣ ɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɭɪɚɜɧɟɧɢɟ 12 ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢ ɢɦɟɟɬ ɜɢɞ
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ɝɞɟ ɋ – ɧɟɨɬɪɢɰɚɬɟɥɶɧɚɹ ɤɨɧɫɬɚɧɬɚ ɫ ɪɚɡɦɟɪɧɨɫɬɶɸ ɫɤɨɪɨɫɬɢ Ɉɞɧɚɤɨ ɝɢɩɨɬɟɡɚ ɨ ɪɚɫɫɦɨɬɪɟɧɢɢ Ɍɉ ɚɧɚɥɨɝɢɱɧɨ ɤɥɚɫɫɢɱɟɫɤɨɣ
ɠɢɞɤɨɫɬɢ ɢɡɥɢɲɧɟ ɝɪɭɛɚ ɢ ɫɥɟɞɭɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɛɨɥɟɟ ɨɛɳɢɣ ɤɥɚɫɫ ɦɨɞɟɥɟɣ ɬɚɤɢɯ ɤɚɤ
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17
ɍɪɚɜɧɟɧɢɟ 13 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɥɭɱɚɸ ɤɨɝɞɚ Q -1,
ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɦɵ ɩɪɟɞɩɨɥɚɝɚɟɦ ɱɬɨ |
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7 ɜɵɪɚɡɢɦ v' |
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ɩɟɪɟɦɟɧɧɵɯ ɢ ɩɪɨɢɧɬɟɝɪɢɪɭɟɦ |
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ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ ɱɬɨ ɩɪɢ Q |
-1 (1.15 ɢɦɟɟɬ ɜɢɞ |
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ɧɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ T Tmax, |
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ɉɪɢɜɟɞɟɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɟ ɪɟɲɟɧɢɹ ɩɪɢ Q -1
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ɩɪɢ Qz-1
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ɝɞɟTmax – ɦɚɤɫɢɦɚɥɶɧɨɜɨɡɦɨɠɧɚɹɩɥɨɬɧɨɫɬɶɌɉɧɚɞɨɪɨɝɟ ɩɪɢɤɨɬɨɪɨɣ v=0.
Ɇɨɞɟɥɶ ɜɵɪɚɠɟɧɧɚɹ ɭɪɚɜɧɟɧɢɟɦ 18 ɛɵɥɚ ɜɩɟɪɜɵɟ ɩɨɥɭɱɟɧɚ Ƚɪɢɧɛɟɪɝɨɦɜ ɝ Ɋɟɡɭɥɶɬɚɬɵɪɚɫɱɟɬɨɜɩɨɞɚɧɧɨɣɦɨɞɟɥɢɞɨɫɬɚɬɨɱɧɨ ɯɨɪɨɲɨ ɫɯɨɞɹɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ ɩɥɨɬɧɨɫɬɟɣ ɩɨɬɨɤɚ ɨɬɥɢɱɧɵɯ ɨɬ ɧɭɥɹ ɪɢɫ ).
Ⱦɥɹ ɦɨɞɟɥɢ ɫ Qt ɨɛɨɡɧɚɱɢɦ ɱɟɪɟɡ Y ɫɤɨɪɨɫɬɶ ɩɪɢ T
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Ɇɨɞɟɥɶ ɩɪɟɞɫɬɚɜɥɟɧɧɚɹ ɧɚ ɪɢɫ 6 ɩɨɥɭɱɚɟɬɫɹ ɤɚɤ ɱɚɫɬɧɵɣ ɫɥɭɱɚɣɢɡ ɭɪɚɜɧɟɧɢɹ 20 ɩɪɢQ ɥɢɧɟɣɧɨ ɡɚɜɢɫɢɬɨɬ T ɢɧɚɡɵɜɚɟɬɫɹ ɦɨɞɟɥɶɸ Ƚɪɢɧɲɢɥɶɞɫɚ ɤɨɬɨɪɚɹ ɜɩɟɪɜɵɟ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɜ ɝ
V,
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Ɋɢɫ. 1.5 Ɇɨɞɟɥɶ Ƚɪɢɧɛɟɪɝɚ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ
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Ɋɢɫ 6. ɉɪɢɛɥɢɠɟɧɧɚɹ ɫɜɹɡɶ ɦɟɠɞɭ Y ɢ T |
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ɦɨɞɟɥɶ Ƚɪɢɧɲɢɥɶɞɫɚ |
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Ɋɚɫɫɦɨɬɪɢɦ ɜɡɚɢɦɨɫɜɹɡɶ ɦɟɠɞɭ Y T 1 ɪɢɫ ɉɨɞɫɬɚɜɢɦ
N=q Y ɜ ɭɪɚɜɧɟɧɢɹ 18 ɢ 20 ɢ ɩɨɥɭɱɢɦ
v
N qmax v e C .
Nq C ln§¨¨ qmax ·¸¸
©q ¹.
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© qmax ¹ |
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n=0 |
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n=-1 |
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(1.21)
(1.22)
(1.23)
(1.24)
q/qmax
1
Ɋɢɫ. 1.7 ȼɥɢɹɧɢɟ ɩɚɪɚɦɟɬɪɚ Q ɧɚ ɜɢɞ ɦɨɞɟɥɢ