Механика.Методика решения задач
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Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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ȽɅȺȼȺ 7 ɁȺɄɈɇɕ ɋɈɏɊȺɇȿɇɂə ɆɈɆȿɇɌȺ ɂɆɉɍɅɖɋȺ ɂ
ɆȿɏȺɇɂɑȿɋɄɈɃ ɗɇȿɊȽɂɂ. ȽɂɊɈɋɄɈɉɕ. ȽɂɊɈɋɄɈɉɂɑȿɋɄɂȿ ɋɂɅɕ
7.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ
Ɂɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ (ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ) ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ1 – ɦɨɦɟɧɬ ɢɦ-
ɩɭɥɶɫɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ L ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɫɨɯɪɚɧɹɟɬɫɹ, ɟɫɥɢ ɫɭɦɦɚ ɦɨɦɟɧɬɨɜ ɜɧɟɲɧɢɯ ɫɢɥ Mex ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɚɧɧɨɣ ɬɨɱɤɢ ɪɚɜɧɚ ɧɭɥɸ:
dL |
Mex |
0 ɢɥɢ dL 0 . |
(7.1) |
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dt |
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Ɂɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ (ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ) ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ – ɦɨɦɟɧɬ ɢɦɩɭɥɶ-
ɫɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ Ln ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɫɨɯɪɚɧɹɟɬɫɹ, ɟɫɥɢ ɫɭɦɦɚ ɦɨɦɟɧɬɨɜ ɜɧɟɲɧɢɯ ɫɢɥ M nex ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɚɧɧɨɣ ɨɫɢ ɪɚɜɧɚ ɧɭɥɸ:
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dLn |
M nex |
0 |
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dt |
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ɢɥɢ |
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dLn |
0 . |
(7.2) |
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Ⱦɥɹ ɤɨɧɟɱɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ ɡɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɨɜ ɢɦɩɭɥɶɫɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ ɢ ɨɫɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (7.1) ɢ (7.2) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
ǻL { L(t2 ) L(t1 ) 0 |
ɢɥɢ L(t1) L(t2 ) , |
(7.3) |
ǻLn { Ln (t2 ) Ln (t1 ) |
0 ɢɥɢ Ln (t1) Ln (t2 ) . |
(7.4) |
Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɨɜ ɢɦɩɭɥɶɫɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ ɢ ɨɫɢ ɹɜɥɹɸɬɫɹ ɩɪɹɦɵɦ ɫɥɟɞɫɬɜɢɟɦ ɡɚɤɨɧɨɜ ɢɯ ɢɡɦɟɧɟɧɢɣ (ɫɦ. (6.38) ɢ (6.39) ɜ ɩ. 6.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 6).
1 Ɉɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ (ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ) ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢ ɦɨɦɟɧɬɚ ɫɢɥɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ (ɨɫɢ), ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɢɪɨɜɤɚ ɡɚɤɨɧɚ ɢɡɦɟɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ (ɭɪɚɜɧɟɧɢɹ ɦɨɦɟɧɬɨɜ) ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ (ɨɫɢ) ɞɚɧɵ ɜ ɩ. 6.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 6.
232 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ2 ɜ ɫɥɭɱɚɟ ɟɝɨ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɪɚɜɧɚ:
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k |
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c 2 |
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¦miȣi |
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¦mi V |
>Ȧri @ |
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¦mi V |
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2V >Ȧri @ >Ȧri @ |
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mV |
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c |
1 |
¦mi |
c 2 |
(7.5) |
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mV >Ȧrɰɦ @ |
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>Ȧri @ . |
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Ɂɞɟɫɶ mi |
ɢ ȣi |
– ɦɚɫɫɵ ɢ ɫɤɨɪɨɫɬɢ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ, ɢɡ ɤɨɬɨɪɵɯ |
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ɫɨɫɬɨɢɬ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɟ ɬɟɥɨ, V – ɫɤɨɪɨɫɬɶ ɧɚɱɚɥɚ ɫɢɫɬɟɦɵ ɨɬ- |
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ɫɱɟɬɚ S', ɠɟɫɬɤɨ ɫɜɹɡɚɧɧɨɣ ɫ ɬɟɥɨɦ, Ȧ – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɫɢɫɬɟɦɵ |
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S', ric – |
ɪɚɞɢɭɫ-ɜɟɤɬɨɪɵ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ ɬɟɥɚ |
ɨɬɧɨɫɢɬɟɥɶɧɨ |
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ɫɢɫɬɟɦɵ S', rɰɦc – ɪɚɞɢɭɫ-ɜɟɤɬɨɪ ɰɟɧɬɪɚ ɦɚɫɫ (ɫɦ. Ƚɥɚɜɭ 3) ɬɟɥɚ ɨɬ-
ɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ S'.
ȿɫɥɢ ɧɚɱɚɥɨ ɨɬɫɱɟɬɚ ɫɢɫɬɟɦɵ S', ɫɜɹɡɚɧɧɨɣ ɫ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɵɦ ɬɟɥɨɦ, ɫɨɜɩɚɞɚɟɬ ɫ ɰɟɧɬɪɨɦ ɦɚɫɫ ɬɟɥɚ, ɬɨ ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɪɚɜɧɚ ɫɭɦɦɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɫɨ ɫɤɨɪɨɫɬɶɸ ɰɟɧɬɪɚ ɦɚɫɫ ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɜɨɤɪɭɝ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ:
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k 1 |
2 |
1 |
c 2 |
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mȣɰɦ |
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¦mi >Ȧri @ , |
(7.6) |
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2 |
2 |
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ɝɞɟ ȣɰɦ – ɫɤɨɪɨɫɬɶ ɰɟɧɬɪɚ ɦɚɫɫ ɬɟɥɚ.
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɪɚɳɚɸɳɟɝɨɫɹ ɬɟɥɚ ɜɨɤɪɭɝ ɧɟɩɨɞ-
ɜɢɠɧɨɣ ɨɫɢ: |
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E k |
1 |
JZ2 , |
(7.7) |
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ɝɞɟ J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ, Z – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɬɟɥɚ.
2 Ɉɩɪɟɞɟɥɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɞɚɧɵ ɜ ɩ. 3.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 3, ɚ ɨɩɪɟɞɟɥɟɧɢɟ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɜ ɩ. 6.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 6.
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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Ɋɚɛɨɬɚ ɜɧɟɲɧɢɯ ɫɢɥ ɩɪɢ ɩɨɜɨɪɨɬɟ ɬɟɥɚ ɜɨɤɪɭɝ ɨɫɢ:
M2 |
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GA M ndM , A12 ³M ndM , |
(7.8) |
M1 |
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ɝɞɟ Mn – ɦɨɦɟɧɬ ɫɢɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ (ɫɦ. ɩ. 6.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 6), M1 ɢ M2 – ɧɚɱɚɥɶɧɨɟ ɢ ɤɨɧɟɱɧɨɟ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɩɨɜɨɪɨɬɚ.
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɜ ɫɥɭɱɚɟ ɟɝɨ ɩɥɨɫɤɨɝɨ ɞɜɢɠɟɧɢɹ:
E |
k |
1 |
mV |
2 |
c |
1 |
JZ |
2 |
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(7.9) |
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mV >Ȧrɰɦ @ |
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Ɂɞɟɫɶ ɫɦɵɫɥ ɨɛɨɡɧɚɱɟɧɢɣ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ ɬɨɬ ɠɟ, ɱɬɨ ɢ ɜ (7.5)
ɢ (7.7).
ȿɫɥɢ ɧɚɱɚɥɨ ɨɬɫɱɟɬɚ ɫɢɫɬɟɦɵ S', ɫɜɹɡɚɧɧɨɣ ɫ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɵɦ ɬɟɥɨɦ, ɧɚɯɨɞɢɬɫɹ ɜ ɰɟɧɬɪɟ ɦɚɫɫ ɬɟɥɚ, ɬɨ ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɪɚɜɧɚ ɫɭɦɦɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɫɨ ɫɤɨɪɨɫɬɶɸ ɰɟɧɬɪɚ ɦɚɫɫ ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɜɨɤɪɭɝ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ, ɢ ɜ ɫɥɭɱɚɟ ɩɥɨɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɪɚɜɧɚ (ɬɟɨɪɟɦɚ Ʉɟɧɢɝɚ):
E k |
1 |
mX2 |
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J |
Z2 |
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(7.10) |
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ɰɦ |
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ɝɞɟ ȣɰɦ – ɫɤɨɪɨɫɬɶ ɰɟɧɬɪɚ ɦɚɫɫ ɬɟɥɚ, |
Jɰɦ – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ |
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ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɟɝɨ ɰɟɧɬɪ ɦɚɫɫ.
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɡɚɩɢɫɚɧ-
ɧɚɹ ɱɟɪɟɡ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ |
Jn ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ |
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ɜɪɚɳɟɧɢɹ3: |
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E k |
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J Z2 . |
(7.11) |
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Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɡɚɤɪɟɩɥɟɧɧɨɝɨ ɜ ɬɨɱɤɟ:
E k { |
1 |
¦miȣi2 |
1 |
¦mi >Ȧri @2 , |
(7.12) |
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3 Ɉɩɪɟɞɟɥɟɧɢɟ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ ɞɚɧɨ ɜ ɩ. 6.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 6.
234 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
ɝɞɟ ri – ɪɚɞɢɭɫ-ɜɟɤɬɨɪɵ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ, ɢɡ ɤɨɬɨɪɵɯ ɫɨɫɬɨɢɬ ɬɟɥɨ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɚɤɪɟɩɥɟɧɧɨɣ ɬɨɱɤɢ ɷɬɨɝɨ ɬɟɥɚ. ȿɫɥɢ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɫɨɨɬɧɨɲɟɧɢɟɦ >ab@2
E k |
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¦mi >Ȧri @2 |
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¦mi Z2ri2 Ȧri 2 |
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Ɂɞɟɫɶ JDE |
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¦mi GDE ri |
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– ɬɟɧɡɨɪ ɢɧɟɪɰɢɢ ɬɟɥɚ, ɯɚɪɚɤɬɟ- |
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ɪɢɡɭɸɳɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɦɚɫɫɵ ɬɟɥɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ; GDE –
ɫɢɦɜɨɥ Ʉɪɨɧɟɤɟɪɚ.
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɡɚɤɪɟɩ-
ɥɟɧɧɨɝɨ ɧɚ ɨɫɢ: |
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J Z2 |
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ɝɞɟ J n – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ.
ȼ ɞɚɧɧɨɣ ɝɥɚɜɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɫɢɫɬɟɦɵ, ɫɨɫɬɨɹɳɢɟ ɢɡ ɫɨɜɨɤɭɩɧɨɫɬɢ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɵɯ ɬɟɥ ɢ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ. ɗɬɢ ɫɢɫɬɟɦɵ ɹɜɥɹɸɬɫɹ ɱɚɫɬɧɵɦɢ ɫɥɭɱɚɹɦɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɞɥɹ ɤɨɬɨɪɨɣ ɜ Ƚɥɚɜɟ 3 ɫɮɨɪɦɭɥɢɪɨɜɚɧɵ ɡɚɤɨɧɵ ɢɡɦɟɧɟɧɢɹ ɢ ɫɨɯɪɚɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ.
Ɂɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ – ɢɡɦɟ-
ɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɪɚɜɧɨ ɪɚɛɨɬɟ ɜɧɭɬɪɟɧɧɢɯ
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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F np,in |
ɢ ɜɧɟɲɧɢɯ F np,ex ɧɟɩɨɬɟɧɰɢɚɥɶɧɵɯ ɫɢɥ4: |
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GAnp,in GAnp,ex GAnp , |
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ɢɥɢ ɞɥɹ ɤɨɧɟɱɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ |
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ǻAnp . |
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Ɂɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ – ɟɫɥɢ |
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ɪɚɛɨɬɚ ɜɫɟɯ ɧɟɩɨɬɟɧɰɢɚɥɶɧɵɯ ɫɢɥ ɪɚɜɧɚ ɧɭɥɸ, ɬɨ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɫɨɯɪɚɧɹɟɬɫɹ:
ǻE { E(t2 ) E(t1 ) 0 |
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E(t1 ) E(t2 ) . |
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Ƚɢɪɨɫɤɨɩɵ Ƚɢɪɨɫɤɨɩ – ɷɬɨ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɟ ɬɟɥɨ, ɜɪɚɳɚɸɳɟɟɫɹ
ɫ ɛɨɥɶɲɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Ȧ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ ɫɢɦɦɟɬɪɢɢ (ɫɦ.
ɪɢɫ. 7.1).
ȍdt dL
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mg
Ɋɢɫ. 7.1. Ƚɢɪɨɫɤɨɩ ɜ ɩɨɥɟ ɫɢɥ ɬɹɠɟɫɬɢ
ɉɪɟɰɟɫɫɢɹ ɝɢɪɨɫɤɨɩɚ – ɜɪɚɳɟɧɢɟ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɝɢɪɨɫɤɨɩɚ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ȍ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɦɨɦɟɧɬɚ ɜɧɟɲɧɢɯ ɫɢɥ ɧɚɪɹɞɭ ɫ ɟɝɨ ɫɨɛɫɬɜɟɧɧɵɦ ɜɪɚɳɟɧɢɟɦ ɜɨɤɪɭɝ ɨɫɢ ɫɢɦɦɟɬɪɢɢ (ɫɦ.
ɪɢɫ. 7.1).
4 Ɉɩɪɟɞɟɥɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ, ɜɧɭɬɪɟɧɧɢɯ ɢ ɜɧɟɲɧɢɯ ɧɟɩɨɬɟɧɰɢɚɥɶɧɵɯ ɫɢɥ ɞɚɧɵ ɜ ɩ. 3.1 Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 3.
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ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
Ɉɫɧɨɜɧɵɟ ɮɢɡɢɱɟɫɤɢɟ ɞɨɩɭɳɟɧɢɹ ɷɥɟɦɟɧɬɚɪɧɨɣ ɬɟɨɪɢɢ ɝɢɪɨɫɤɨɩɚ:
-ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɝɢɪɨɫɤɨɩɚ ɢ ɟɝɨ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɧɚɩɪɚɜɥɟɧɵ ɜɞɨɥɶ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɝɢɪɨɫɤɨɩɚ;
-ɜɟɥɢɱɢɧɚ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɝɢɪɨɫɤɨɩɚ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ Ȧ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɵ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɩɪɟɰɟɫ-
ɫɢɢ ȍ .
ȼ ɪɚɦɤɚɯ ɩɪɢɧɹɬɵɯ ɞɨɩɭɳɟɧɢɣ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɝɢɪɨɫɤɨɩɚ L ɪɚɜɟɧ
L J z Ȧ , |
(7.18) |
ɚ ɭɪɚɜɧɟɧɢɟ ɦɨɦɟɧɬɨɜ (6.38) ɨɬɧɨɫɢɬɟɥɶɧɨ ɟɝɨ ɧɟɩɨɞɜɢɠɧɨɣ ɬɨɱɤɢ O (ɫɦ. ɪɢɫ. 7.1) ɢɦɟɟɬ ɜɢɞ:
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ɝɞɟ Jz – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɝɢɪɨɫɤɨɩɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɜɨɟɣ ɨɫɢ ɫɢɦɦɟɬɪɢɢ, M – ɫɭɦɦɚ ɦɨɦɟɧɬɨɜ ɜɧɟɲɧɢɯ ɫɢɥ (ɜ ɬɨɦ ɱɢɫɥɟ ɫɢɥɵ ɬɹɠɟɫɬɢ), ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɝɢɪɨɫɤɨɩ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (7.19) ɨɫɶ ɝɢɪɨɫɤɨɩɚ ɜɦɟɫɬɟ ɫ ɦɨɦɟɧɬɨɦ L ɩɪɟɰɟɫɫɢɪɭɟɬ ɜɨɤɪɭɝ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ȍ .
ɇɚ ɪɢɫ. 7.1 ɜɢɞɧɨ, ɱɬɨ: |
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ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɟɰɟɫɫɢɹ ɝɢɪɨɫɤɨɩɚ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢ- |
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ɋ ɭɱɟɬɨɦ ɭɪɚɜɧɟɧɢɹ ɦɨɦɟɧɬɨɜ (7.19) ɞɥɹ ɝɢɪɨɫɤɨɩɚ ɩɨɥɭɱɢɦ:
M >ȍL@ J z >ȍȦ@. (7.23)
Ɂɚɦɟɬɢɦ, ɱɬɨ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɨɩɪɟɞɟɥɹɟɬ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ, ɚ ɧɟ ɭɫɤɨɪɟɧɢɟ ɩɪɟɰɟɫɫɢɢ, ɬ.ɟ. ɩɪɟɰɟɫɫɢɨɧɧɨɟ ɞɜɢɠɟɧɢɟ ɹɜɥɹɟɬɫɹ ɛɟɡɢɧɟɪɰɢɨɧɧɵɦ!
Ƚɢɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɢɥɵ – ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɤɪɟɩɥɟɧɢɟ (ɪɚɦɤɭ, ɩɨɞɲɢɩɧɢɤ, ɪɭɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɬɨɪɚ ɢ ɬ.ɞ.) ɧɟɫɜɨɛɨɞɧɨɝɨ ɝɢɪɨɫɤɨɩɚ ɩɪɢ ɜɵɧɭɠɞɟɧɧɨɦ ɜɪɚɳɟɧɢɢ ɨɫɢ (ɜɵɧɭɠɞɟɧɧɨɣ ɩɪɟɰɟɫɫɢɢ) ɝɢɪɨɫɤɨɩɚ.
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɬɶɢɦ ɡɚɤɨɧɨɦ ɇɶɸɬɨɧɚ ɧɚ ɤɪɟɩɥɟɧɢɟ |
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ɞɟɣɫɬɜɭɟɬ ɦɨɦɟɧɬ ɝɢɪɨɫɤɨɩɢɱɟɫɤɢɯ ɫɢɥ: |
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Mɝ M >ȍL@ |
J z >ȍȦ@. |
(7.24) |
ɉɪɚɜɢɥɨ ɇ.ȿ. ɀɭɤɨɜɫɤɨɝɨ – ɝɢɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɢɥɵ ɫɬɪɟɦɹɬɫɹ ɫɨɜɦɟɫɬɢɬɶ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɝɢɪɨɫɤɨɩɚ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɵɧɭɠɞɟɧɧɨɝɨ ɩɨɜɨɪɨɬɚ.
7.2. Ɉɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɞɚɱ ɢ ɦɟɬɨɞɵ ɢɯ ɪɟɲɟɧɢɹ
7.2.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ
Ȼɨɥɶɲɢɧɫɬɜɨ ɡɚɞɚɱ, ɨɬɧɨɫɹɳɢɯɫɹ ɤ ɬɟɦɟ "Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ. Ƚɢɪɨɫɤɨɩɵ. Ƚɢɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɢɥɵ" ɦɨɠɧɨ ɭɫɥɨɜɧɨ ɨɬɧɟɫɬɢ ɤ ɫɥɟɞɭɸɳɢɦ ɬɢɩɚɦ ɡɚɞɚɱ ɢɥɢ ɢɯ ɤɨɦɛɢɧɚɰɢɹɦ. Ɂɚɞɚɱɢ ɧɚ
1)ɡɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ (ɜ ɬɨɦ ɱɢɫɥɟ ɜɤɥɸɱɚɸɳɟɣ ɜ ɫɟɛɹ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɵɟ ɬɟɥɚ),
2)ɝɢɪɨɫɤɨɩɵ ɢ ɝɢɪɨɫɤɨɩɢɱɟɫɤɢɟ ɫɢɥɵ.
7.2.2.Ɉɛɳɚɹ ɫɯɟɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ
I.Ɉɩɪɟɞɟɥɢɬɶɫɹ ɫ ɦɨɞɟɥɹɦɢ ɦɚɬɟɪɢɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɢ ɹɜɥɟɧɢɣ.
1. ɇɚɪɢɫɨɜɚɬɶ ɱɟɪɬɟɠ, ɧɚ ɤɨɬɨɪɨɦ ɢɡɨɛɪɚɡɢɬɶ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɬɟɥɚ.
2. ȼɵɛɪɚɬɶ ɫɢɫɬɟɦɭ ɨɬɫɱɟɬɚ (ɢɡ ɫɨɨɛɪɚɠɟɧɢɣ ɭɞɨɛɫɬɜɚ), ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɣ ɛɭɞɭɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɡɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ (ɢɡɦɟɧɟɧɢɹ) ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɢ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɢɡɨɛɪɚɡɢɬɶ ɧɚ ɱɟɪɬɟɠɟ ɟɟ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ, ɚ ɬɚɤɠɟ ɬɨɱɤɭ (ɨɫɶ), ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɣ ɡɚɩɢɫɵɜɚɸɬɫɹ ɦɨɦɟɧɬɵ ɢɦɩɭɥɶɫɨɜ ɢ ɫɢɥ.
3. ɂɡɨɛɪɚɡɢɬɶ ɢ ɨɛɨɡɧɚɱɢɬɶ ɫɢɥɵ ɢ ɧɟɨɛɯɨɞɢɦɵɟ ɤɢɧɟɦɚɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɢɫɬɟɦɵ.
4. ȼɵɛɪɚɬɶ ɦɟɯɚɧɢɱɟɫɤɭɸ ɫɢɫɬɟɦɭ ɢ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɣ ɢɧɬɟɪɜɚɥ (ɧɚɱɚɥɶɧɵɣ ɢ ɤɨɧɟɱɧɵɣ ɦɨɦɟɧɬɵ) ɜɪɟɦɟɧɢ.
5. ȼɵɛɪɚɬɶ ɦɨɞɟɥɢ ɬɟɥ (ɟɫɥɢ ɷɬɨ ɧɟ ɫɞɟɥɚɧɨ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ)
ɢɪɚɫɫɦɨɬɪɟɬɶ ɨɫɨɛɟɧɧɨɫɬɢ ɢɯ ɞɜɢɠɟɧɢɹ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟ-
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ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
ɦɵɯ ɢɧɬɟɪɜɚɥɚɯ ɜɪɟɦɟɧɢ (ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɟɪɟɞ ɫɨɭɞɚɪɟɧɢɟɦ, ɫɪɚɡɭ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ, ɢ ɬ.ɞ.).
6.ɉɪɨɜɟɫɬɢ ɚɧɚɥɢɡ ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɬɟɥɚ ɫɢɫɬɟɦɵ ɫɢɥ ɢ ɢɯ ɦɨɦɟɧɬɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɵɛɪɚɧɧɨɣ ɬɨɱɤɢ (ɨɫɢ) ɜɪɚɳɟɧɢɹ.
II.Ɂɚɩɢɫɚɬɶ ɩɨɥɧɭɸ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɢɫɤɨɦɵɦ ɜɟɥɢɱɢɧɚɦ.
1.ȼɵɛɪɚɬɶ ɡɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ (ɢɡɦɟɧɟɧɢɹ) ɢ ɡɚɩɢɫɚɬɶ ɢɯ ɜ ɜɵɛɪɚɧɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɞɥɹ ɜɵɛɪɚɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢ ɜɵɛɪɚɧɧɵɯ ɢɧɬɟɪɜɚɥɨɜ ɜɪɟɦɟɧɢ ɜ ɪɚɦɤɚɯ ɜɵɛɪɚɧɧɨɣ ɦɨɞɟɥɢ ɞɜɢɠɟɧɢɹ ɬɟɥ ɫɢɫɬɟɦɵ.
2.Ɂɚɩɢɫɚɬɶ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɦɨɦɟɧɬɨɜ ɫɢɥ, ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɢ ɢɦɩɭɥɶɫɚ ɬɟɥ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɬɟɥ ɫ ɭɱɟɬɨɦ ɯɚɪɚɤɬɟɪɚ ɢɯ ɞɜɢɠɟɧɢɹ.
3.Ɂɚɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɹ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɜɹɡɢ.
4.ɂɫɩɨɥɶɡɨɜɚɬɶ ɪɟɡɭɥɶɬɚɬɵ ɪɚɧɟɟ ɪɟɲɟɧɧɵɯ ɡɚɞɚɱ ɢ ɨɫɨɛɵɟ ɭɫɥɨɜɢɹ ɡɚɞɚɱɢ.
III.ɉɨɥɭɱɢɬɶ ɢɫɤɨɦɵɣ ɪɟɡɭɥɶɬɚɬ ɜ ɚɧɚɥɢɬɢɱɟɫɤɨɦ ɢ ɱɢɫɥɟɧɧɨɦ ɜɢɞɚɯ.
1.Ɋɟɲɢɬɶ ɫɢɫɬɟɦɭ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ.
2.ɉɪɨɜɟɫɬɢ ɚɧɚɥɢɡ ɪɟɲɟɧɢɹ (ɩɪɨɜɟɪɢɬɶ ɪɚɡɦɟɪɧɨɫɬɶ ɢ ɥɢɲɧɢɟ ɤɨɪɧɢ, ɪɚɫɫɦɨɬɪɟɬɶ ɯɚɪɚɤɬɟɪɧɵɟ ɫɥɭɱɚɢ, ɭɫɬɚɧɨɜɢɬɶ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɢɦɨɫɬɢ).
3.ɉɨɥɭɱɢɬɶ ɱɢɫɥɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ.
7.3.ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ
7.3.1. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ
Ɂɚɞɚɱɚ 7.1
ȼɨɤɪɭɝ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɬɨɱɤɭ ɡɚɤɪɟɩɥɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ ɦɚɫɫɨɣ m ɢ ɞɥɢɧɨɣ l, ɦɨɠɟɬ ɜɪɚɳɚɬɶɫɹ ɛɟɡ ɬɪɟɧɢɹ ɨɞɧɨɪɨɞɧɵɣ ɫɬɟɪɠɟɧɶ ɦɚɫɫɨɣ M ɢ ɞɥɢɧɨɣ L t l, ɲɚɪɧɢɪɧɨ ɡɚɤɪɟɩɥɟɧɧɵɣ ɜ ɬɨɣ ɠɟ ɬɨɱɤɟ (ɫɦ. ɪɢɫ. 7.2). Ɇɚɹɬɧɢɤ ɨɬɩɭɫɤɚɸɬ ɢɡ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɩɨɥɨɠɟɧɢɹ. ɇɚɣɬɢ ɦɚɤɫɢɦɚɥɶɧɵɣ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɫɬɟɪɠɧɹ Dmax ɩɨɫɥɟ ɚɛɫɨɥɸɬɧɨ ɭɩɪɭɝɨɝɨ ɫɨɭɞɚɪɟɧɢɹ c ɦɚɹɬɧɢɤɨɦ.
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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Ɋɟɲɟɧɢɟ |
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I. ȼɵɛɟɪɟɦ ɥɚɛɨɪɚɬɨɪɧɭɸ ɢɧɟɪɰɢ- |
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ɚɥɶɧɭɸ ɫɢɫɬɟɦɭ ɨɬɫɱɟɬɚ, ɠɟɫɬɤɨ ɫɜɹɡɚɧ- |
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ɧɭɸ ɫ ɬɨɱɤɨɣ ɩɨɞɜɟɫɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ |
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ɦɚɹɬɧɢɤɚ ɢ ɫɬɟɪɠɧɹ. ɇɚɩɪɚɜɢɦ ɝɨɪɢɡɨɧ- |
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ɬɚɥɶɧɭɸ ɨɫɶ ɜɪɚɳɟɧɢɹ ɡɚ ɩɥɨɫɤɨɫɬɶ ɱɟɪ- |
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ɬɟɠɚ (ɫɦ. ɪɢɫ. 7.2). |
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ȼɵɛɟɪɟɦ ɱɟɬɵɪɟ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ: |
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Ɋɢɫ. 7.2 |
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t1 – ɦɨɦɟɧɬ ɧɚɱɚɥɚ ɞɜɢɠɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟ-
ɫɤɨɝɨ ɦɚɹɬɧɢɤɚ, t2 – ɦɨɦɟɧɬ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɟɪɟɞ ɫɨɭɞɚɪɟɧɢɟɦ ɦɚɹɬɧɢɤɚ ɫɨ ɫɬɟɪɠɧɟɦ, t3 – ɦɨɦɟɧɬ ɫɪɚɡɭ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ, t4 – ɦɨɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɨɬɤɥɨɧɟɧɢɸ ɫɬɟɪɠɧɹ. ȼ ɬɟɱɟɧɢɟ ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ (t1, t2) ɫɨɯɪɚɧɹɟɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ. ȼ ɩɪɨɦɟɠɭɬɤɟ ɜɪɟɦɟɧɢ (t2, t3) ɫɨɯɪɚɧɹɸɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɫɢɫɬɟɦɵ ɬɟɥ «ɦɚɹɬɧɢɤ + ɫɬɟɪɠɟɧɶ». ɂɦɩɭɥɶɫ ɫɢɫɬɟɦɵ ɬɟɥ ɜ ɷɬɨɦ ɩɪɨɦɟɠɭɬɤɟ ɧɟ ɫɨɯɪɚɧɹɟɬɫɹ, ɩɨɫɤɨɥɶɤɭ ɜ ɬɨɱɤɟ ɩɨɞɜɟɫɚ ɫɬɟɪɠɧɹ ɜɨ ɜɪɟɦɹ ɫɨɭɞɚɪɟɧɢɹ ɜɨɡɧɢɤɚɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɫɢɥɵ, ɢɦɩɭɥɶɫ ɤɨɬɨɪɵɯ ɨɬɥɢɱɟɧ ɨɬ ɧɭɥɹ. ȼ ɩɪɨɦɟɠɭɬɤɟ ɜɪɟɦɟɧɢ (t3, t4) ɫɨɯɪɚɧɹɟɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɬɟɪɠɧɹ ɜɫɥɟɞɫɬɜɢɟ ɨɬɫɭɬɫɬɜɢɹ ɫɢɥ ɬɪɟɧɢɹ.
ɉɨɬɟɧɰɢɚɥɶɧɵɟ ɷɧɟɪɝɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ ɢ ɫɬɟɪɠɧɹ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɪɚɜɧɵɦɢ ɧɭɥɸ ɩɪɢ ɢɯ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ.
II. Ɂɚɩɢɲɟɦ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ (7.17) ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ ɧɚ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ (t1, t2):
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Ɂɞɟɫɶ mgl – ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɦɚɹɬɧɢɤɚ ɜ ɟɝɨ ɢɫɯɨɞɧɨɦ ɝɨɪɢ-
ɡɨɧɬɚɥɶɧɨɦ ɩɨɥɨɠɟɧɢɢ (ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t1), |
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ɫɤɚɹ ɷɧɟɪɝɢɹ ɦɚɹɬɧɢɤɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɟɪɟɞ ɫɨɭɞɚɪɟɧɢɟɦ (ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t2), J1 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɦɚɹɬɧɢɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ, Z1 – ɟɝɨ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɟɪɟɞ ɫɨɭɞɚɪɟɧɢɟɦ.
Ⱦɥɹ ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ (t2, t3) ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ (7.4) ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ (7.17) ɞɥɹ ɫɢɫɬɟɦɵ ɬɟɥ «ɦɚ-
ɹɬɧɢɤ + ɫɬɟɪɠɟɧɶ» ɢɦɟɸɬ ɜɢɞ: |
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ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
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ɝɞɟ J2 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɫɬɟɪɠɧɹ, Z2 ɢ Z3 – ɭɝɥɨɜɵɟ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɫɬɟɪɠɧɹ ɢ ɦɚɹɬɧɢɤɚ ɫɪɚɡɭ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ.
Ɂɚɩɢɲɟɦ ɬɚɤɠɟ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ
(7.17) ɞɥɹ ɫɬɟɪɠɧɹ ɧɚ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ (t3, t4): |
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Ɇɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ɦɚɹɬɧɢɤɚ J1 ɢ ɫɬɟɪɠɧɹ J 2 |
ɨɬɧɨɫɢɬɟɥɶɧɨ |
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ɜɵɛɪɚɧɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ ɪɚɜɧɵ: |
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ml 2 , |
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III. Ɋɟɲɚɹ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (7.25) – (7.30) ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫ-
ɤɨɦɨɝɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɭɝɥɚ ɨɬɤɥɨɧɟɧɢɹ ɫɬɟɪɠɧɹ, ɩɨɥɭɱɚɟɦ: |
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arccos 1 |
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ɉɨɫɤɨɥɶɤɭ Dmax |
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ɧɟ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ S / 2 , ɬɨ ɧɚ ɫɨɨɬɧɨɲɟ- |
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ɧɢɹ ɦɚɫɫ M / m ɢ ɞɥɢɧ |
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L / l ɫɬɟɪɠɧɹ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ |
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ɧɚɤɥɚɞɵɜɚɟɬɫɹ ɭɫɥɨɜɢɟ: |
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¨3 ¨ ¸ ¸
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ɩɪɢ ɧɚɪɭɲɟɧɢɢ ɤɨɬɨɪɨɝɨ ɫɬɟɪɠɟɧɶ ɭɞɚɪɢɬɫɹ ɨ ɩɨɬɨɥɨɤ.
ɇɚ ɪɢɫ. 7.3 ɢɡɨɛɪɚɠɟɧɵ ɨɛɥɚɫɬɢ ɡɧɚɱɟɧɢɣ ɨɬɧɨɲɟɧɢɣ ɞɥɢɧ ɢ ɦɚɫɫ ɦɚɹɬɧɢɤɚ ɢ ɫɬɟɪɠɧɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɦɚɤɫɢɦɚɥɶɧɵɣ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɫɬɟɪɠɧɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɨɭɞɚɪɟɧɢɹ ɫ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɦɚɹɬɧɢɤɨɦ ɦɟɧɶɲɟ ɢɥɢ ɪɚɜɟɧ S / 2 . Ʉɪɢɜɚɹ, ɢɡɨɛɪɚɠɟɧɧɚɹ ɧɚ ɪɢɫ. 7.3 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɧɚɱɟɧɢɹɦ ɨɬɧɨɲɟɧɢɣ ɞɥɢɧ l / L ɢ ɦɚɫɫ m / M ɦɚɹɬɧɢɤɚ ɢ ɫɬɟɪɠɧɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɫɬɟɪɠɟɧɶ ɩɪɢɧɢɦɚɟɬ ɝɨɪɢɡɨɧɬɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ, ɧɟ ɫɨɭɞɚɪɹɹɫɶ ɫ ɩɨɬɨɥɤɨɦ. Ɉɛɥɚɫɬɶ ɡɧɚɱɟɧɢɣ ɨɬɧɨɲɟ-