Производственная безопасность основы производственной безопасности. Практикум
.pdfɈɩɪɟɞɟɥɟɧɢɟ ɩɨɠɚɪɨɨɩɚɫɧɨɣ ɤɚɬɟɝɨɪɢɢ ɩɨɦɟɳɟɧɢɹ ɨɫɭɳɟɫɬɜɥɹ ɟɬɫɹ ɩɭɬɟɦ ɫɪɚɜɧɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɞɟɥɶɧɨɣ ɜɪɟɦɟɧɧɨғɣ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡɤɢ ɞɚɥɟɟ ɩɨ ɬɟɤɫɬɭ ± ɩɨɠɚɪɧɚɹ ɧɚɝɪɭɡɤɚ ɧɚ ɥɸɛɨɦ ɢɡ ɭɱɚɫɬɤɨɜ ɫ ɜɟɥɢɱɢɧɨɣ ɭɞɟɥɶɧɨɣ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡɤɢ ɩɪɢɜɟɞɟɧɧɨɣ ɜ ɬɚɛɥ
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Ɍɚɛɥɢɰɚ 6.2 |
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ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɚɬɟɝɨɪɢɣ ɩɨɦɟɳɟɧɢɣ ȼ ±ȼ |
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Ʉɚɬɟɝɨɪɢɹ |
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ɍɞɟɥɶɧɚɹ ɩɨɠɚɪɧɚɹ |
ɋɩɨɫɨɛ ɪɚɡɦɟɳɟɧɢɹ |
ɩɨɦɟɳɟɧɢɹ |
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ɧɚɝɪɭɡɤɚ G ɧɚ ɭɱɚɫɬɤɟ |
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ɆȾɠ ā ɦ± |
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ȼ |
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Ȼɨɥɟɟ |
ɇɟ ɧɨɪɦɢɪɭɟɬɫɹ |
ȼ |
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Ɋɚɫɫɱɢɬɵɜɚɟɬɫɹ |
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ɫɦ ɩɪɢɦɟɱɚɧɢɟ |
ȼ |
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Ɋɚɫɫɱɢɬɵɜɚɟɬɫɹ |
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ɫɦ ɩɪɢɦɟɱɚɧɢɟ |
ȼ |
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ɇɚ ɥɸɛɨɦ ɭɱɚɫɬɤɟ ɩɨɥɚ ɩɨɦɟɳɟ |
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ɧɢɹ ɩɥɨɳɚɞɶɸ ɦ ɋɩɨɫɨɛ |
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ɪɚɡɦɟɳɟɧɢɹ ɭɱɚɫɬɤɨɜ ɩɨɠɚɪɧɨɣ |
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ɧɚɝɪɭɡɤɢ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ |
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ɫɦ ɩɪɢɦɟɱɚɧɢɟ |
ɉɪɢ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡɤɟ ɜɤɥɸɱɚɸɳɟɣ ɜ ɫɟɛɹ ɪɚɡɥɢɱɧɵɟ ɫɨɱɟɬɚɧɢɹɫɦɟɫɶ ɝɨɪɸɱɢɯ ɬɪɭɞɧɨɝɨɪɸɱɢɯ ɠɢɞɤɨɫɬɟɣ ɬɜɟɪɞɵɯ ɝɨɪɸɱɢɯ ɢ ɬɪɭɞɧɨɝɨɪɸɱɢɯ ɜɟɳɟɫɬɜ ɢ ɦɚɬɟɪɢɚɥɨɜ ɜ ɩɪɟɞɟɥɚɯ ɩɨɠɚɪɨɨɩɚɫɧɨɝɨ ɭɱɚɫɬɤɚ ɩɨɠɚɪɧɚɹ ɧɚɝɪɭɡɤɚ Q ɆȾɠ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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Q ¦n |
GiQɧɪi |
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i |
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ɝɞɟ Gi ± ɤɨɥɢɱɟɫɬɜɨ i ɝɨ ɦɚɬɟɪɢɚɥɚ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡɤɢ ɤɝ
Qɧɪ ± ɧɢɡɲɚɹ ɬɟɩɥɨɬɚ ɫɝɨɪɚɧɢɹ i ɝɨ ɦɚɬɟɪɢɚɥɚ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡ ɤɢ ɆȾɠ ā ɤɝ±
ȿɫɥɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡɤɢ ɬɪɟɛɭɟɬɫɹ ɭɱɟɬ ɬɨɥɶɤɨ ɜɟɳɟɫɬɜɚ ɜɵɲɟɞɲɟɝɨ ɢɡ ɚɩɩɚɪɚɬɚ ɩɪɢ ɚɜɚɪɢɢ ɬɨ G ɤɝ ɦɨɠɧɨ ɨɩɪɟ ɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ
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G VɠUɠ |
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ɝɞɟ Vɠ ± ɨɛɴɟɦ ɪɚɡɥɢɜɲɟɣɫɹ ɥɟɝɤɨɜɨɫɩɥɚɦɟɧɹɸɳɟɣɫɹ ɢɥɢ ɝɨɪɸɱɟɣ ɠɢɞɤɨɫɬɢ ɦ Uɠ ± ɩɥɨɬɧɨɫɬɶ ɥɟɝɤɨɜɨɫɩɥɚɦɟɧɹɸɳɟɣɫɹ ɢɥɢ ɝɨɪɸɱɟɣ ɠɢɞɤɨɫɬɢ ɤɝāɦ±
ɍɞɟɥɶɧɚɹ ɩɨɠɚɪɧɚɹ ɧɚɝɪɭɡɤɚ g ɆȾɠāɦ± ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬ ɧɨɲɟɧɢɹ
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g |
Q |
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ɝɞɟ Q ± ɩɨɠɚɪɧɚɹ ɧɚɝɪɭɡɤɚ S ± ɩɥɨɳɚɞɶ ɪɚɡɦɟɳɟɧɢɹ ɩɨɠɚɪɧɨɣ ɧɚɝɪɭɡɤɢ ɦ ɧɨ ɧɟ ɦɟɧɟɟɦ
ɉɨɪɹɞɨɤ ɪɚɫɱɟɬɚ
ɉɪɢ ɪɚɫɱɟɬɟ ɡɧɚɱɟɧɢɣ ɤɪɢɬɟɪɢɟɜ ɜɡɪɵɜɨɩɨɠɚɪɧɨɣ ɨɩɚɫɧɨɫɬɢ ɜ ɤɚ ɱɟɫɬɜɟ ɪɚɫɱɟɬɧɨɝɨ ɫɥɟɞɭɟɬ ɜɵɛɢɪɚɬɶ ɧɚɢɛɨɥɟɟ ɧɟɛɥɚɝɨɩɪɢɹɬɧɵɣ ɜɚɪɢ ɚɧɬ ɚɜɚɪɢɢ ɢɥɢ ɩɟɪɢɨɞ ɧɨɪɦɚɥɶɧɨɣ ɪɚɛɨɬɵ ɚɩɩɚɪɚɬɨɜ ɩɪɢ ɤɨɬɨɪɨɦ ɜɨ ɜɡɪɵɜɟ ɭɱɚɫɬɜɭɟɬ ɧɚɢɛɨɥɶɲɟɟ ɤɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜ ɢɥɢ ɦɚɬɟɪɢɚɥɨɜ ɧɚɢɛɨɥɟɟ ɨɩɚɫɧɵɯ ɜ ɨɬɧɨɲɟɧɢɢ ɩɨɫɥɟɞɫɬɜɢɣ ɜɡɪɵɜɚ Ɉɫɧɨɜɧɵɦ ɩɨɤɚ ɡɚɬɟɥɟɦ ɹɜɥɹɟɬɫɹ ɢɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ ɜɡɪɵɜɚ ɬ ɟ ɞɚɜɥɟɧɢɟ ɜɨɡɧɢɤɚ ɸɳɟɟ ɩɪɢ ɞɟɮɥɚɝɪɚɰɢɨɧɧɨɦ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɥɚɦɟɧɢ ɩɨ ɝɨɪɸɱɟɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ ɝɨɪɟɧɢɢ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɫɦɟɫɢ ɜ ɡɚɦɤɧɭɬɨɦ ɩɪɨɫɬɪɚɧ ɫɬɜɟ Ɋɚɫɱɟɬ ɢɡɛɵɬɨɱɧɨɝɨ ɞɚɜɥɟɧɢɹ ɜɡɪɵɜɚ 'ɪ ɤɉɚ ɞɥɹ ɥɟɝɤɨɜɨɫɩɥɚ ɦɟɧɹɸɳɢɯɫɹ ɢ ɝɨɪɸɱɢɯ ɠɢɞɤɨɫɬɟɣ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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'ɪ ɪ |
ɪ |
mZ |
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V U |
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ɋ |
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K |
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PD[ |
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ɩ |
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ɫɬ |
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ɫɜ |
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ɝɞɟ ɪPD[ ± ɦɚɤɫɢɦɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɝɚɡɨɜɨɡɞɭɲɧɨɣ ɢɥɢ ɩɚɪɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɜ ɡɚɦɤɧɭɬɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɪɢɧɢɦɚ ɟɬɫɹ ɪɚɜɧɨɣ ɤɉɚ ɪ ± ɧɚɱɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ ɤɉɚ m ± ɦɚɫɫɚ ɩɚɪɨɜ ɥɟɝɤɨɜɨɫɩɥɚɦɟɧɹɸɳɢɯɫɹ ɠɢɞɤɨɫɬɟɣ Ʌȼɀ ɢ ɝɨɪɸɱɢɯ ɠɢɞɤɨɫɬɟɣ Ƚɀ ɜɵɲɟɞɲɢɯ ɜ ɪɟɡɭɥɶɬɚɬɟ ɚɜɚɪɢɢ ɜ ɩɨ ɦɟɳɟɧɢɟ ɤɝ Z ± ɤɨɷɮɮɢɰɢɟɧɬ ɭɱɚɫɬɢɹ ɝɨɪɸɱɟɝɨ ɜɨ ɜɡɪɵɜɟ ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧ ɧɚ ɨɫɧɨɜɟ ɯɚɪɚɤɬɟɪɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɝɚɡɨɜ ɢ ɩɚɪɨɜ ɜ ɨɛɴɟɦɟ ɩɨɦɟɳɟɧɢɹ Vɫɜ ± ɫɜɨɛɨɞɧɵɣ ɨɛɴɟɦ ɩɨɦɟɳɟɧɢɹ ɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɨɛɴɟɦɨɦ ɩɨɦɟɳɟɧɢɹ ɢ ɨɛɴɟɦɨɦ ɡɚɧɢɦɚɟɦɵɦ ɬɟɯɧɨɥɨɝɢ ɱɟɫɤɢɦ ɨɛɨɪɭɞɨɜɚɧɢɟɦ ȿɫɥɢ ɫɜɨɛɨɞɧɵɣ ɨɛɴɟɦ ɩɨɦɟɳɟɧɢɹ ɨɩɪɟ ɞɟɥɢɬɶ ɧɟɜɨɡɦɨɠɧɨ ɬɨ ɟɝɨ ɞɨɩɭɫɤɚɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɭɫɥɨɜɧɨ ɪɚɜ ɧɵɦ ɝɟɨɦɟɬɪɢɱɟɫɤɨɝɨ ɨɛɴɟɦɚ ɩɨɦɟɳɟɧɢɹ
Uɩ ± ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ ɢɥɢ ɩɚɪɚ ɩɪɢ ɪɚɫɱɟɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t ɤɝāɦ± Cɫɬ ± ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɚɹ ɬɟɨɪɟɬɢɱɟɫɤɢ ɜɵɱɢɫɥɹɟɦɵɣ ɨɛɴɟɦ ɜɟ ɳɟɫɬɜɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɚɪɨɜ Ʌȼɀ ɢɥɢ Ƚɀ ɨɛɴɟɦɧ K ± ɤɨɷɮɮɢɰɢɟɧɬ ɭɱɢɬɵɜɚɸɳɢɣ ɧɟɝɟɪɦɟɬɢɱɧɨɫɬɶ ɩɨɦɟɳɟɧɢɹ ɢ ɧɟɚɞɢɚɛɚɬɢɱɧɨɫɬɶ ɩɪɨɰɟɫɫɚ ɝɨɪɟɧɢɹ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ ɬɪɟɦ
ɉɪɢ ɪɚɫɱɟɬɟ ɜɟɥɢɱɢɧɵ m ɢɫɯɨɞɹɬ ɢɡ ɫɥɟɞɭɸɳɢɯ ɩɪɟɞɩɨɫɵɥɨɤɉɪɨɢɫɯɨɞɢɬ ɪɚɫɱɟɬɧɚɹ ɚɜɚɪɢɹ ɨɞɧɨɝɨ ɢɡ ɚɩɩɚɪɚɬɨɜȼɫɟ ɫɨɞɟɪɠɢɦɨɟ ɚɩɩɚɪɚɬɚ ɩɨɫɬɭɩɚɟɬ ɜ ɩɨɦɟɳɟɧɢɟɉɪɨɢɫɯɨɞɢɬ ɨɞɧɨɜɪɟɦɟɧɧɚɹ ɭɬɟɱɤɚ ɜɟɳɟɫɬɜ ɢɡ ɬɪɭɛɨɩɪɨɜɨɞɨɜ
ɩɢɬɚɸɳɢɯ ɚɩɩɚɪɚɬɉɪɨɢɫɯɨɞɢɬ ɢɫɩɚɪɟɧɢɟ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɥɢɜɲɟɣɫɹ ɠɢɞɤɨɫɬɢ
ɉɥɨɳɚɞɶ ɢɫɩɚɪɟɧɢɹ F ɢ ɩɪɢ ɪɚɡɥɢɜɟ ɧɚ ɩɨɥ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɫɯɨɞɹ ɢɡ ɪɚɫɱɟɬɚ ɥ ɧɚ ɦ ɩɨɥɚ ɩɨɦɟɳɟɧɢɹ
Ɋɚɫɱɟɬɧɨɟ ɜɪɟɦɹ ɨɬɤɥɸɱɟɧɢɹ ɬɪɭɛɨɩɪɨɜɨɞɨɜ Tɚ ɪɚɜɧɹɟɬɫɹ ɫ ɩɪɢ ɪɭɱɧɨɦ ɨɬɤɥɸɱɟɧɢɢ
Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ ɠɢɞɤɨɫɬɢ T ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɨɣ ɜɪɟ ɦɟɧɢ ɟɟ ɩɨɥɧɨɝɨ ɢɫɩɚɪɟɧɢɹ ɧɨ ɧɟ ɛɨɥɟɟ ɫ
Ɇɚɫɫɚ ɩɚɪɨɜ ɠɢɞɤɨɫɬɢ m ɤɝ ɩɨɫɬɭɩɢɜɲɢɯ ɜ ɩɨɦɟɳɟɧɢɟ ɨɩɪɟɞɟ ɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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m JFɢT |
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ɝɞɟ J ± ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ ɤɝāɫ± āɦ± Fɢ ± ɩɥɨɳɚɞɶ ɢɫɩɚɪɟɧɢɹ ɦ ɨɩɪɟɞɟɥɹɟɦɚɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩ ɩɪɟɞɩɨɫɵɥɨɤ T ± ɞɥɢɬɟɥɶɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ ɫ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩ ɩɪɟɞɩɨɫɵɥɨɤ
ɂɧɬɟɧɫɢɜɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ J ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɫɩɪɚɜɨɱɧɵɦ ɢ ɷɤɫɩɟ ɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ Ⱦɥɹ ɧɟɧɚɝɪɟɬɵɯ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ ɨɤɪɭɠɚ ɸɳɟɣ ɫɪɟɞɵ Ʌȼɀ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɚɧɧɵɯ ɞɨɩɭɫɤɚɟɬɫɹ ɪɚɫɫɱɢɬɵɜɚɬɶ J ɩR ɮɨɪɦɭɥɟ
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J M p |
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ɝɞɟ Ɇ – ɦɨɥɹɪɧɚɹ ɦɚɫɫɚ ɤɝāɦɨɥɶ± ɪɧ ± ɞɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ ɩɪɢ ɪɚɫɱɟɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɠɢɞɤɨɫɬɢ t ɨɩɪɟɞɟɥɹɟɦɨɟ ɩɨ ɫɩɪɚɜɨɱɧɵɦ ɞɚɧɧɵɦ ɤɉɚ
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɟ ɪɧ ɫɧɚɱɚɥɚ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɩɚɪɚɦɟɬɪ OJɪɧ ɩɨ ɫɥɟ ɱɟɝɨ ɫɬɚɧɨɜɢɬɫɹ ɜɨɡɦɨɠɧɵɦ ɩɨ ɧɨɦɨɝɪɚɦɦɟ ɪɢɫ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ɞɚɜɥɟɧɢɹ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ Ʌȼɀ ɢɥɢ Ƚɀ
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OJɪ A |
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ɂɡ ɬɚɛɥ ɧɚɯɨɞɹɬɫɹ ɡɧɚɱɟɧɢɹ ɤɨɧɫɬɚɧɬ Ⱥɧɬɭɚɧɚ Ⱥ ȼ ɢ ɋȺ
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Ɋɢɫ Ɂɚɜɢɫɢɦɨɫɬɶ ɞɚɜɥɟɧɢɹ ɪɧ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ Ʌȼɀ ɚ |
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ɢɥɢ Ƚɀ ɛ ɨɬ ɩɚɪɚɦɟɬɪɚ OJɪɧ |
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ɉɥɨɳɚɞɶ ɢɫɩɚɪɟɧɢɹ Fɢ ɧɚɯɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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Fɢ |
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ɝɞɟ Vɠ ± ɨɛɴɟɦ Ʌȼɀ ɢɥɢ Ƚɀ ɜɵɲɟɞɲɟɣ ɢɡ ɬɪɭɛɨɩɪɨɜɨɞɚ ɞɨ ɟɝɨ |
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ɨɬɤɥɸɱɟɧɢɹ Ɋɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɝɞɟ Vɚ ± ɨɛɴɟɦ ɚɩɩɚɪɚɬɚ ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɬɫɹ ɝɨɪɸɱɟɟ ɜɟɳɟɫɬɜɨ ɦ q ± ɪɚɫɯɨɞ ɝɨɪɸɱɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ ɦ āɫ± Tɚ ± ɪɚɫɱɟɬɧɨɟ ɜɪɟɦɹ ɨɬɤɥɸɱɟɧɢɹ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɫ Ɉɩɪɟɞɟɥɹɟɬ ɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩ ɩɪɟɞɩɨɫɵɥɨɤ r ± ɪɚɞɢɭɫ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɦ L ± ɫɭɦɦɚɪɧɚɹ ɞɥɢɧɚ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɦ
ȿɫɥɢ ɩɥɨɳɚɞɶ ɩɨɦɟɳɟɧɢɹ F ɦɟɧɶɲɟ ɪɚɫɫɱɢɬɚɧɧɨɣ ɩɥɨɳɚɞɢ ɢɫɩɚ ɪɟɧɢɹ ɬɨ ɩɥɨɳɚɞɶ ɢɫɩɚɪɟɧɢɹ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɨɣ ɩɥɨɳɚɞɢ ɩɨɦɟɳɟ ɧɢɹ Fɢ F
ɋɪɟɞɧɹɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɚɪɨɜ Ʌȼɀ ɢɥɢ Ƚɀ CFɪ ɨɛɴɟɦɧ ɜ ɩɨ
ɦɟɳɟɧɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɝɞɟ m ± ɦɚɫɫɚ ɩɚɪɨɜ Ʌȼɀ ɢɥɢ Ƚɀ ɩɨɫɬɭɩɢɜɲɟɝɨ ɜ ɩɨɦɟɳɟɧɢɟ ɤɝ Uɩ ± ɩɥɨɬɧɨɫɬɶ Ʌȼɀ ɢɥɢ Ƚɀ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t ɤɝāɦ± Vɫɜ ± ɫɜɨɛɨɞɧɵɣ ɨɛɴɟɦ ɩɨɦɟɳɟɧɢɹ ɦ
ȿɫɥɢ ɡɧɚɱɟɧɢɟ Cɫɪ ɛɨɥɶɲɟ ɩɪɨɢɡɜɟɞɟɧɢɹ ɋɇɄɉɊ ɡɞɟɫɶ
©ɇɄɉɊª ± ɧɢɠɧɢɣ ɤɨɧɰɟɧɬɪɚɰɢɨɧɧɵɣ ɩɪɟɞɟɥ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɥɚ ɦɟɧɢ ɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɭɱɚɫɬɢɹ ɩɚɪɨɜ Ʌȼɀ ɢɥɢ Ƚɀ Z ɫɱɢɬɚɬɶ ɪɚɜ ɧɵɦ ɂɧɚɱɟ ɡɧɚɹ ɩɚɪɚɦɟɬɪ ; ɫɬɚɧɨɜɢɬɫɹ ɜɨɡɦɨɠɧɵɦ ɩɨɥɭɱɢɬɶ ɡɧɚɱɟɧɢɟ Z ɪɚɫɱɟɬɧɵɦ ɩɭɬɟɦ ɩɨ ɧɨɦɨɝɪɚɦɦɟ ɪɢɫ
Ɂɧɚɱɟɧɢɹ ; ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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ɋɧ |
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ɟɫɥɢ ɋ d ɋ |
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ɟɫɥɢ ɋ ! ɋ |
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ɝɞɟ ɩɚɪɚɦɟɬɪ Cɧ ɨɛɴɟɦɧ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ |
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ɡɞɟɫɶ ɪɧ ± ɞɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ Ʌȼɀ ɢɥɢ Ƚɀ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t ɤɉɚ ɋ ɨɛɴɟɦɧ ± ɜɟɥɢɱɢɧɚ ɡɚɞɚɜɚɟɦɚɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ
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ɫɬ |
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ɡɞɟɫɶ ɋɫɬ ± ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɝɨɪɸɱɢɯ ɝɚɡɨɜ ȽȽ ɢɥɢ ɩɚɪɨɜ Ʌȼɀ ɢ Ƚɀ ɨɛɴɟɦɧ
ɋɬɟɯɢɨɦɟɬɪɢɱɟɫɤɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ Ʌȼɀ ɢ Ƚɀ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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ɝɞɟ E ± ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɤɢɫɥɨɪɨɞɚ ɜ ɪɟɚɤɰɢɢ ɫɝɨɪɚ ɧɢɹ
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ɡɞɟɫɶ nɋ n+ nɈ n; ± ɱɢɫɥɨ ɚɬɨɦɨɜ ɋ ɇ Ɉ ɢ ɝɚɥɨɢɞɨɜ ɜ ɦɨɥɟɤɭɥɟ ɝɨ ɪɸɱɟɝɨ
ɉɨ ɡɧɚɱɟɧɢɸ ; ɢɫɩɨɥɶɡɭɹ ɧɨɦɨɝɪɚɦɦɭ ɫɦ ɪɢɫ ɨɩɪɟɞɟɥɹɟɦ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ Z ɭɱɚɫɬɢɹ ɩɚɪɨɜ Ʌȼɀ ɢɥɢ Ƚɀ ɜɨ ɜɡɪɵɜɟ
ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ ɢɥɢ ɩɚɪɚ ɩɪɢ ɪɚɫɱɟɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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ɝɞɟ t ± ɪɚɫɱɟɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɋ ȼ ɤɚɱɟɫɬɜɟ ɪɚɫɱɟɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɥɟɞɭɟɬ ɩɪɢɧɢɦɚɬɶ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ ɜɨɡɞɭ ɯɚ ɜ ɞɚɧɧɨɦ ɩɨɦɟɳɟɧɢɢ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɥɢɦɚɬɢɱɟɫɤɨɣ ɡɨɧɟ
Ɋɢɫ Ƚɪɚɮɢɤ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ Z ɭɱɢɬɵɜɚɸɳɟɝɨ ɭɱɚɫɬɢɟ ɩɚɪɨɜ Ʌȼɀ ɜɨ ɜɡɪɵɜɟ
ɉɪɢɦɟɪ ɉɪɨɢɡɜɟɫɬɢ ɨɩɪɟɞɟɥɟɧɢɟ ɤɚɬɟɝɨɪɢɢ ɩɨɦɟɳɟɧɢɹ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ
ɬɨɩɥɢɜɧɨɝɨ ɛɚɤɚ ɪɟɡɟɪɜɧɨɣ ɞɢɡɟɥɶɧɨɣ ɷɥɟɤɬɪɨɫɬɚɧɰɢɢ ɭɧɢɮɢɰɢɪɨ ɜɚɧɧɨɣ ɤɨɦɩɨɧɨɜɤɢ ȼ ɩɨɦɟɳɟɧɢɢ ɧɚɯɨɞɢɬɫɹ ɬɨɩɥɢɜɧɵɣ ɛɚɤ ɫ ɞɢ ɡɟɥɶɧɵɦ ɬɨɩɥɢɜɨɦ ɦɚɪɤɢ ȽɈɋɌ ± ɨɛɴɟɦɨɦ VD ɦ Ɋɚɡɦɟɪɵ ɩɨɦɟɳɟɧɢɹ LîBîH î î ɦ Ɉɛɴɟɦ ɩɨɦɟɳɟɧɢɹ
Vɩ ɦ ɋɜɨɛɨɞɧɵɣ ɨɛɴɟɦ ɩɨɦɟɳɟɧɢɹ VFɜ ā ɦ ɉɥɨɳɚɞɶ ɩɨɦɟɳɟɧɢɹ F ɦ ɋɭɦɦɚɪɧɚɹ ɞɥɢɧɚ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɞɢɚɦɟɬɪɨɦ d ɦɦ ɦ r ɦ ɨɝɪɚɧɢɱɟɧɧɚɹ ɡɚɞɜɢɠ ɤɚɦɢ ɪɭɱɧɵɦɢ ɭɫɬɚɧɨɜɥɟɧɧɵɦɢ ɧɚ ɩɨɞɜɨɞɹɳɟɦ ɢ ɨɬɜɨɞɹɳɟɦ ɭɱɚɫɬɤɟ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɫɨɫɬɚɜɥɹɟɬ L ɦ Ɋɚɫɯɨɞ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩ ɥɢɜɚ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ q ɥāɫ± ɦ āɫ± Ɇɨɥɹɪɧɚɹ ɦɚɫɫɚ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɦɚɪɤɢ Ɇ ɤɝāɤɦɨɥɶ± Ȼɪɭɬɬɨ ɮɨɪɦɭɥɚ
& + ɉɥɨɬɧɨɫɬɶ ɠɢɞɤɨɫɬɢ ɩɪɢ |
ɬɟɦɩɟɪɚɬɭɪɟ |
t ɋ |
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Uɠ ɤɝāɦ± |
Ʉɨɧɫɬɚɧɬɵ ɭɪɚɜɧɟɧɢɹ |
Ⱥɧɬɭɚɧɚ Ⱥ |
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ȼ ɋȺ |
Ɍɟɦɩɟɪɚɬɭɪɚ ɜɫɩɵɲɤɢ tɜɫɩ! ɋ ɇɢɡɲɚɹ |
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ɬɟɩɥɨɬɚ ɫɝɨɪɚɧɢɹ Qɧɪ ā Ⱦɠāɤɝ± ɆȾɠāɤɝ± ɇɢɠɧɢɣ
ɤɨɧɰɟɧɬɪɚɰɢɨɧɧɵɣ ɩɪɟɞɟɥ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɥɚɦɟɧɢ ɋɇɄɉɊ ɨɛɴɟɦɧ Ɍɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ tɪ ɋ
Ɋɟɲɟɧɢɟ
ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɢɡɛɵɬɨɱɧɨɝɨ ɞɚɜɥɟɧɢɹ ɜɡɪɵɜɚ ɜ ɤɚɱɟɫɬɜɟ ɪɚɫ ɱɟɬɧɨɝɨ ɜɚɪɢɚɧɬɚ ɚɜɚɪɢɢ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɡɝɟɪɦɟɬɢɡɚɰɢɹ ɬɨɩɥɢɜɧɨɝɨ ɛɚɤɚ ɢ ɜɵɯɨɞ ɢɡ ɧɟɝɨ ɢ ɩɨɞɜɨɞɹɳɢɯ ɢ ɨɬɜɨɞɹɳɢɯ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɞɢ ɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɜ ɨɛɴɟɦ ɩɨɦɟɳɟɧɢɹ
ɉɥɨɬɧɨɫɬɶ ɩɚɪɨɜ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɩɪɢ tɪ ɋ ɪɚɜɧɚ
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Ɋɚɫɱɟɬɧɨɟ ɜɪɟɦɹ ɨɬɤɥɸɱɟɧɢɹ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɩɨ ɩ ɩɪɟɞɩɨɫɵɥɨɤ Ɍɚ ɫ ɞɥɢɬɟɥɶɧɨɫɬɶɢɫɩɚɪɟɧɢɹɩɨɩ ɩɪɟɞɩɨɫɵɥɨɤɌ ɫ
Ɉɛɴɟɦ Vɠ ɢ ɩɥɨɳɚɞɶ ɪɚɡɥɢɜɚ Fɢ ɩɨɫɬɭɩɢɜɲɟɝɨ ɩɪɢ ɪɚɫɱɟɬɧɨɣ ɚɜɚɪɢɢ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɨɥɨɠɟ ɧɢɹɦɢ ɩ ɩɪɟɞɩɨɫɵɥɨɤ
Vɠ VD qɌɚ Sr L ā ā āɦ ɥ
Fɢ ā ɦ
ɉɨɫɤɨɥɶɤɭ ɩɥɨɳɚɞɶ ɩɨɦɟɳɟɧɢɹ F ɦ ɦɟɧɶɲɟ ɪɚɫɫɱɢɬɚɧɧɨɣ ɩɥɨɳɚɞɢ ɪɚɡɥɢɜɚ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ Fɢ ɦ ɬɨ ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɪɢɧɢɦɚɟɦ Fɢ F ɦ
Ɉɩɪɟɞɟɥɹɟɦ ɞɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɪɧ ɩɪɢ ɪɚɫɱɟɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ tɪ ɋ
OJɪɧ ± ±
Ɉɬɤɭɞɚ ɩɨ ɧɨɦɨɝɪɚɦɦɟ ɫɦ ɪɢɫ ɧɚɯɨɞɢɦ ɪɧ ɤɉɚɂɧɬɟɧɫɢɜɧɨɫɬɶ ɢɫɩɚɪɟɧɢɹ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ J ɫɨɫɬɚɜɢɬ
J ± ā ā ā ā ± ɤɝāɦ± āɫ±
Ɇɚɫɫɚ ɩɚɪɨɜ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɩɨɫɬɭɩɢɜɲɢɯ ɜ ɩɨɦɟɳɟɧɢɟ ɛɭɞɟɬ ɪɚɜɧɚ
m ā ± ā ā ɤɝ
Ɉɩɪɟɞɟɥɟɧɢɟ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɚɪɨɜ ɞɢɡɟɥɶ ɧɨɝɨ ɬɨɩɥɢɜɚ ɋɫɬ ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ ɢɫɯɨɞɹ ɢɡ ɯɢɦɢɱɟɫɤɨɣ ɛɪɭɬɬɨ ɮɨɪɦɭɥɵ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɫɨɫɬɚɜɢɬ
E
ɋɫɬ ā ɨɛɴɟɦɧ
Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɱɚɫɬɢɹ ɩɚɪɨɜ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɜɨ ɜɡɪɵɜɟ
ɋɪɟɞɧɹɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɚɪɨɜ ɞɢɡɟɥɶɧɨɝɨ ɬɨɩɥɢɜɚ ɋɫɪ ɜ ɩɨɦɟ ɳɟɧɢɢ ɫɨɫɬɚɜɢɬ
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ɨɛɴɟɦɧ |
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Fɪ |
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ɋɫɪ ɨɛɴɟɦɧ āɋɇɄɉɊ ā ɨɛɴɟɦɧ ɫɥɟɞɨ ɜɚɬɟɥɶɧɨ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ Z ɪɚɫɱɟɬɧɵɦ
ɦɟɬɨɞɨɦɁɧɚɱɟɧɢɟ ɋɧ ɛɭɞɟɬ ɪɚɜɧɨ
ɋɧ ā ɨɛɴɟɦɧɁɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ɋ ɛɭɞɟɬ ɪɚɜɧɨ
ɋ ā ɨɛɴɟɦɧ
ɉɨɫɤɨɥɶɤɭ ɋɧ ɋ ɨɛɴɟɦɧ ɬɨ ɪɚɫɫɱɢɬɵɜɚ ɟɦ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ;
ɏ ɋɋɧ
ɋɨɝɥɚɫɧɨ ɧɨɦɨɝɪɚɦɦɟ ɱɟɪɬɟɠɚ ɫɦ ɪɢɫ ɩɪɢ ɡɧɚɱɟɧɢɢ ɏ ɨɩɪɟɞɟɥɹɟɦ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɱɚɫɬɢɹ ɩɚɪɨɜ ɞɢɡɟɥɶ ɧɨɝɨ ɬɨɩɥɢɜɚ ɜɨ ɜɡɪɵɜɟ =
ɂɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ ɜɡɪɵɜɚ 'p ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ ɫɨɫɬɚ ɜɢɬ
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ɤɉɚ |
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Ɋɚɫɱɟɬɧɨɟ ɢɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ ɜɡɪɵɜɚ ɦɟɧɟɟ ɤɉɚ ɉɨɦɟɳɟ ɧɢɟ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɬɨɩɥɢɜɧɨɝɨ ɛɚɤɚ ɪɟɡɟɪɜɧɨɣ ɞɢɡɟɥɶɧɨɣ ɷɥɟɤɬɪɨ ɫɬɚɧɰɢɢ ɭɧɢɮɢɰɢɪɨɜɚɧɧɨɣ ɤɨɦɩɨɧɨɜɤɢ ɧɟ ɨɬɧɨɫɢɬɫɹ ɤ ɤɚɬɟɝɨɪɢɹɦ Ⱥ ɢ Ȼ ɋɨɝɥɚɫɧɨ ɬɚɛɥ ɩɪɨɜɟɞɟɦ ɩɪɨɜɟɪɤɭ ɩɪɢɧɚɞɥɟɠɧɨɫɬɢ ɩɨɦɟɳɟ ɧɢɹ ɤ ɤɚɬɟɝɨɪɢɹɦ ȼ ±ȼ
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ ɨɩɪɟɞɟɥɢɦ ɩɨɠɚɪɧɭɸ ɧɚɝɪɭɡɤɭ Q ɢ ɭɞɟɥɶɧɭɸ ɩɨɠɚɪɧɭɸ ɧɚɝɪɭɡɤɭ g
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G VɠUɠ ā ɤɝ |
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Q |
G Qɪ |
ā ɆȾɠ |
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ɧ |
S F ɦ |
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ɆȾɠāɦ± |
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ɍɞɟɥɶɧɚɹ ɩɨɠɚɪɧɚɹ ɧɚɝɪɭɡɤɚ ɛɨɥɟɟ ɆȾɠāɦ± ɉɨɦɟɳɟɧɢɟ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɬɨɩɥɢɜɧɨɝɨ ɛɚɤɚ ɪɟɡɟɪɜɧɨɣ ɞɢɡɟɥɶɧɨɣ ɷɥɟɤɬɪɨɫɬɚɧ ɰɢɢ ɭɧɢɮɢɰɢɪɨɜɚɧɧɨɣ ɤɨɦɩɨɧɨɜɤɢ ɫɨɝɥɚɫɧɨ ɬɚɛɥ ɨɬɧɨɫɢɬɫɹ ɤ ɤɚɬɟɝɨɪɢɢ ȼ
ȼɚɪɢɚɧɬɵ ɡɚɞɚɧɢɣ ɞɚɧɵ ɜ ɬɚɛɥ
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Ɍɚɛɥɢɰɚ 6.3 |
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ɜɟɳɟɫɬɜɧɟɤɨɬɨɪɵɯɨɩɚɫɧɨɫɬɢɩɨɠɚɪɧɨɣɩɨɤɚɡɚɬɟɥɟɣɁɧɚɱɟɧɢɹ |
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ɇɢɠɧɢɣ ɤɨɧ |
Ʉɨɧɫɬɚɧɬɵ ɭɪɚɜɧɟɧɢɹ |
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ɇɢɡɲɚɹ |
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Ɍɟɦɩɟ |
ɉɥɨɬɧɨɫɬɶ |
ɰɟɧɬɪɚ |
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Ⱥɧɬɭɚɧɚ |
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ɏɚɪɚɤ |
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ɏɢɦɢɢɱɟ |
Ɇɨɥɹɪɧɚɹ |
ɰɢɨɧɧɵɣ ɩɪɟ |
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ɬɟɪɢ |
ɬɟɩɥɨɬɚ |
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ȼɟɳɟɫɬɜɨ |
ɪɚɬɭɪɚ |
ɜɟɳɟɫɬɜɚ |
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ɫɝɨɪɚɧɢɹ |
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ɫɤɚɹ |
ɦɚɫɫɚɆ |
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± |
ɞɟɥ ɪɚɫɩɪɨ |
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ɫɬɢɤɚ |
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ɮɨɪɦɭɥɚ |
ɤɝāɤɦɨɥɶ± |
ɜɫɩɵɲ |
ɤɝāɦ |
ɫɬɪɚɧɟɧɢɹ |
Ⱥ |
ȼ |
ɋ |
Ⱥ |
ɜɟɳɟ |
Qɪ |
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ɤɢtɋ |
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ɩɥɚɦɟɧɢCɧ |
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ɫɬɜɚ |
ɧ |
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ɆȾɠāɤɝ± |
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ɨɛɴɟɦɧ |
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Ȼɟɧɡɢɧ ɚɜɢɚ |
ɋ ɇ |
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± |
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Ʌȼɀ |
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ɰɢɨɧɧɵɣ Ȼ |
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Ⱥɦɢɥɚɰɟɬɚɬ |
ɋ ɇ Ɉ |
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Ʌȼɀ |
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Ⱥɦɢɥɟɧ |
ɋ ɇ |
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± |
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Ʌȼɀ |
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ɍɚɣɬ ɫɩɢɪɢɬ |
ɋ ɇ |
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! |
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Ʌȼɀ |
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Ⱥɰɟɬɨɧ |
ɋ ɇ Ɉ |
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± |
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Ʌȼɀ |
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ɧȽɟɤɫɚɧ |
ɋ ɇ |
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± |
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Ʌȼɀ |
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Ƚɥɢɰɟɪɢɧ |
ɋ ɇ Ɉ |
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Ƚɀ |
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Ɇɟɬɢɥɨɜɵɣ |
ɋɇ Ɉ |
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Ʌȼɀ |
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ɫɩɢɪɬ |
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ɗɬɢɥɟɧɝɥɢɤɨɥɶ |
& + 2 |
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Ƚɀ |
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ɗɬɢɥɨɜɵɣ |
& + 2 |
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Ʌȼɀ |
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ɫɩɢɪɬ |
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ɋɬɢɪɨɥ |
& + |
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Ʌȼɀ |
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ɧ-Ɉɤɬɚɧ |
& + |
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Ʌȼɀ |
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Ʉɟɪɨɫɢɧ |
ɋ ɇ |
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! |
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Ʌȼɀ |
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ɨɫɜɟɬɢɬɟɥɶɧɵɣ |
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Ȼɟɧɡɢɧ Ⱥɂ |
ɋ ɇ |
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± |
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Ʌȼɀ |
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