ɆɈɋɄɈȼɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ ɢɦɟɧɢ Ɇ.ȼ. ɅɈɆɈɇɈɋɈȼȺ Ɇɟɯɚɧɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɮɚɤɭɥɶɬɟɬ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɞɜɢɠɟɧɢɣ ɱɟɥɨɜɟɤɚ ɜ ɧɨɪɦɟ ɢ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɜɢɞɚɯ ɩɚɬɨɥɨɝɢɢ. ɩɨɞ ɪɟɞɚɤɰɢɟɣ ɩɪɨɮɟɫɫɨɪɚ ɂ.ȼ.ɇɨɜɨɠɢɥɨɜɚ ɢ ɞɨɰɟɧɬɚ ɉ.Ⱥ.Ʉɪɭɱɢɧɢɧɚ
Ɇɨɫɤɜɚ 2005 ɝɨɞ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɞɜɢɠɟɧɢɣ ɱɟɥɨɜɟɤɚ ɜ ɧɨɪɦɟ ɢ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɜɢɞɚɯ ɩɚɬɨɥɨɝɢɢ. ɩɨɞ ɪɟɞ. ɂ.ȼ.ɇɨɜɨɠɢɥɨɜɚ ɢ ɉ.Ⱥ.Ʉɪɭɱɢɧɢɧɚ– Ɇ.: ɂɡɞ. ɆȽɍ, 2005 – 64 ɫ.
ȼ ɫɛɨɪɧɢɤ ɜɤɥɸɱɟɧɵ ɪɚɛɨɬɵ ɩɨ ɮɢɡɢɨɥɨɝɢɢ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ, ɜɵɩɨɥɧɟɧɧɵɟ ɧɚ ɤɚɮɟɞɪɟ ɩɪɢɤɥɚɞɧɨɣ ɦɟɯɚɧɢɤɢ ɢ ɭɩɪɚɜɥɟɧɢɹ ɆȽɍ ɜ 2002-2004 ɝɨɞɚɯ. ɂɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɜ ɫɥɟɞɭɸɳɢɯ ɧɚɩɪɚɜɥɟɧɢɹɯ: ɍɬɨɱɧɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɞɥɹ cɝɢɛɚɬɟɥɶɧɨɪɚɡɝɢɛɚɬɟɥɶɧɵɯ ɞɜɢɠɟɧɢɣ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ ɱɟɥɨɜɟɤɚ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ. ɍɬɨɱɧɟɧɢɟ ɦɨɞɟɥɟɣ ɩɨɞɞɟɪɠɚɧɢɹ ɩɨɡɵ ɫ ɩɨɦɨɳɶɸ ɨɛɪɚɬɧɵɯ ɫɜɹɡɟɣ ɨɬ ɢɡɜɟɫɬɧɵɯ ɢɡ ɥɢɬɟɪɚɬɭɪɵ ɚɮɮɟɪɟɧɬɧɵɯ ɞɚɬɱɢɤɨɜ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɞɜɢɠɟɧɢɹ ɜ ɚɥɝɨɪɢɬɦɚɯ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ ɩɪɢ ɛɢɨɦɟɯɚɧɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɩɨɫɬɪɨɟɧɧɵɯ ɦɨɞɟɥɟɣ ɩɪɢ ɚɧɚɥɢɡɟ ɩɨɡɵ ɛɨɥɶɧɨɝɨ ɫ ɧɟɤɨɬɨɪɵɦɢ ɬɢɩɚɦɢ ɧɚɪɭɲɟɧɢɣ, ɧɚɛɥɸɞɚɟɦɵɦɢ ɩɪɢ ɞɟɬɫɤɨɦ ɰɟɪɟɛɪɚɥɶɧɨɦ ɩɚɪɚɥɢɱɟ.
© Ɇɟɯɚɧɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɆȽɍ, 2005 ɝ.
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ɮɚɤɭɥɶɬɟɬ
ɋɨɞɟɪɠɚɧɢɟ ɉɪɟɞɢɫɥɨɜɢɟ…………………………………………..………………..4 Ɍɪɟɯɡɜɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɞɥɹ ɡɚɞɚɱɢ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ. ɇɨɜɨɠɢɥɨɜ ɂ. ȼ., Ɍɟɪɟɯɨɜ Ⱥ. ȼ., Ɂɚɛɟɥɢɧ Ⱥ. ȼ., Ʌɟɜɢɤ ɘ. ɋ., ɒɥɵɤɨɜ ȼ. ɘ., Ʉɚɡɟɧɧɢɤɨɜ Ɉ. ȼ..…………………………………….. 7 Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ ɩɪɢ ɦɟɞɥɟɧɧɵɯ ɜɨɡɦɭɳɟɧɢɹɯ ɨɫɧɨɜɚɧɢɹ Ɍɟɪɟɯɨɜ Ⱥ. ȼ. ………………………………….……………………… 21 Ɉ ɜɨɡɦɨɠɧɨɫɬɢ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɚɧɚɥɢɡɚ ɞɜɢɠɟɧɢɣ ɢ ɫɬɚɛɢɥɨɝɪɚɮɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɵ… Ʉɪɭɱɢɧɢɧ ɉ.Ⱥ., Ɇɢɲɚɧɨɜ Ⱥ.ɘ., ɋɚɟɧɤɨ Ⱦ.Ƚ ……………………… 28 Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɧɚɪɭɲɟɧɢɣ ɩɨɡɵ ɛɨɥɶɧɨɵɯ ɩɪɢ rectus-ɫɢɧɞɪɨɦɟ ɢ hamstring-ɫɢɧɞɪɨɦɟ Ʉɪɭɱɢɧɢɧ ɉ.Ⱥ., ɀɭɪɚɜɥɟɜ Ⱥ.Ɇ.,ɏɚɤɢɦɨɜ Ⱥ.ɂ ………………….…… 54
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ɉɪɟɞɢɫɥɨɜɢɟ ɇɚɫɬɨɹɳɢɣ ɫɛɨɪɧɢɤ ɩɨɞɜɨɞɢɬ ɢɬɨɝ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɨ ɮɢɡɢɨɥɨɝɢɢ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ, ɩɪɨɜɨɞɢɦɵɯ ɧɚ ɤɚɮɟɞɪɟ ɩɪɢɤɥɚɞɧɨɣ ɦɟɯɚɧɢɤɢ ɢ ɭɩɪɚɜɥɟɧɢɹ ɆȽɍ ɡɚ ɩɨɫɥɟɞɧɢɟ ɬɪɢ ɝɨɞɚ. ɂɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɜ ɫɥɟɞɭɸɳɢɯ ɧɚɩɪɚɜɥɟɧɢɹɯ: x ɍɬɨɱɧɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɞɥɹ cɝɢɛɚɬɟɥɶɧɨ-ɪɚɡɝɢɛɚɬɟɥɶɧɵɯ ɞɜɢɠɟɧɢɣ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ ɱɟɥɨɜɟɤɚ ɜ ɫɚɝɝɢɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ. x ɍɬɨɱɧɟɧɢɟ ɦɨɞɟɥɟɣ ɩɨɞɞɟɪɠɚɧɢɹ ɩɨɡɵ ɫ ɩɨɦɨɳɶɸ ɨɛɪɚɬɧɵɯ ɫɜɹɡɟɣ ɨɬ ɢɡɜɟɫɬɧɵɯ ɢɡ ɥɢɬɟɪɚɬɭɪɵ ɚɮɮɟɪɟɧɬɧɵɯ ɞɚɬɱɢɤɨɜ. x ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɩɨɫɬɪɨɟɧɧɵɯ ɦɨɞɟɥɟɣ ɩɪɢ ɚɧɚɥɢɡɟ ɩɨɡɵ ɛɨɥɶɧɨɝɨ ɫ ɧɟɤɨɬɨɪɵɦɢ ɬɢɩɚɦɢ ɧɚɪɭɲɟɧɢɣ, ɧɚɛɥɸɞɚɟɦɵɦɢ ɩɪɢ ɞɟɬɫɤɨɦ ɰɟɪɟɛɪɚɥɶɧɨɦ ɩɚɪɚɥɢɱɟ. ȼ ɫɛɨɪɧɢɤ ɜɤɥɸɱɟɧɵ ɱɟɬɵɪɟ ɪɚɛɨɬɵ, ɨɬɪɚɠɚɸɳɢɟ ɨɫɧɨɜɧɵɟ ɞɨɫɬɢɠɟɧɢɹ ɜ ɭɤɚɡɚɧɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ. ȼ ɩɟɪɜɨɣ ɪɚɛɨɬɟ ɩɪɟɞɩɪɢɧɹɬɚ ɩɨɩɵɬɤɚ ɩɨɫɬɪɨɢɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɥɚ ɛɵ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ ɜɛɥɢɡɢ ɜɟɪɬɢɤɚɥɢ ɧɚ ɨɫɧɨɜɟ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɢ ɱɟɥɨɜɟɤɚ. ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɩɨɞɞɟɪɠɚɧɢɟ ɩɨɡɵ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɩɨɫɬɪɨɟɧɧɨɣ ɦɨɞɟɥɢ ɩɨɤɚɡɚɥɨ, ɱɬɨ ɨɧɢ ɫɨɝɥɚɫɭɸɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɧɚɛɥɸɞɚɟɦɵɦɢ ɦɚɤɫɢɦɭɦɚɦɢ ɜ ɫɩɟɤɬɪɟ ɫɬɚɛɢɥɨɝɪɚɦɦɵ ɫɩɨɤɨɣɧɨ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ. ɗɬɨɬ ɪɟɡɭɥɶɬɚɬ ɩɨɞɬɜɟɪɠɞɟɧ ɫɟɪɢɟɣ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɜ ɯɨɞɟ ɤɨɬɨɪɵɯ ɨɩɪɟɞɟɥɹɥɢɫɶ ɢ ɫɪɚɜɧɢɜɚɥɢɫɶ ɫɩɟɤɬɪɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɬɚɛɢɥɨɝɪɚɦɦɵ ɱɟɥɨɜɟɤɚ ɤɚɤ ɩɪɢ ɫɜɨɛɨɞɧɨɦ ɫɬɨɹɧɢɢ, ɬɚɤ ɢ ɜ ɭɫɥɨɜɢɹɯ ɨɝɪɚɧɢɱɟɧɧɨɣ ɩɨɞɜɢɠɧɨɫɬɢ ɜɫɟɯ ɫɭɫɬɚɜɨɜ ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ (ɷɤɫɩɟɪɢɦɟɧɬɵ ɩɪɨɜɨɞɢɥɢɫɶ ɫɨɜɦɟɫɬɧɨ ɫ ɫɨɬɪɭɞɧɢɤɚɦɢ ɥɚɛɨɪɚɬɨɪɢɢ ʋ9 ɂɉɉɂ). ɉɨɫɬɪɨɟɧɚ ɭɩɪɨɳɟɧɧɚɹ ɦɨɞɟɥɶ, ɨɩɢɫɵɜɚɸɳɚɹ ɞɜɢɠɟɧɢɹ ɬɪɟɯɡɜɟɧɧɢɤɚ ɧɚ ɧɢɡɲɟɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɟ. ɉɪɟɞɥɨɠɟɧɧɚɹ ɦɨɞɟɥɶ ɨɩɢɫɵɜɚɟɬ ɢɡɦɟɧɟɧɢɹ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ, ɤɨɥɟɧɧɨɝɨ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɝɨ ɫɭɫɬɚɜɧɵɯ ɭɝɥɨɜ ɩɪɢ ɦɚɥɵɯ ɨɬɤɥɨɧɟɧɢɹɯ ɨɬ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ. Ɉɧɚ ɭɬɨɱɧɟɧɹɟɬ ɦɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɬɨ-
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ɝɨ ɦɚɹɬɧɢɤɚ, ɬɪɚɞɢɰɢɨɧɧɨ ɢɫɩɨɥɶɡɭɟɦɭɸ ɩɪɢ ɚɧɚɥɢɡɟ ɜɨɩɪɨɫɨɜ ɫɜɹɡɚɧɧɵɯ ɫɨ ɫɬɚɛɢɥɢɡɚɰɢɟɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ. ȼɬɨɪɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɩɨɩɵɬɤɟ ɨɩɢɫɚɧɢɹ ɷɮɮɟɤɬɨɜ, ɩɨɥɭɱɟɧɧɵɯ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ ɩɨ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ ɧɚ ɦɟɞɥɟɧɧɨ ɧɚɤɥɨɧɹɟɦɨɦ ɨɫɧɨɜɚɧɢɢ. Ɂɚɞɚɱɚ ɭɩɪɚɜɥɟɧɢɹ ɫɬɚɜɢɬɫɹ ɤɚɤ ɡɚɞɚɱɚ ɩɨɫɬɪɨɟɧɢɹ ɚɞɚɩɬɢɜɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɜ ɭɫɥɨɜɢɹɯ ɧɟɢɡɜɟɫɬɧɨɝɨ ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ ɜɨɡɦɭɳɟɧɢɹ. ɉɪɢɦɟɧɟɧɢɟ ɦɟɬɨɞɚ, ɚɧɚɥɨɝɢɱɧɨɝɨ ɦɟɬɨɞɭ ɫɤɨɪɨɫɬɧɨɝɨ ɝɪɚɞɢɟɧɬɚ, ɩɨɡɜɨɥɹɟɬ ɩɨɫɬɪɨɢɬɶ ɦɨɞɟɥɶ ɭɞɟɪɠɚɧɢɹ ɱɟɥɨɜɟɤɨɦ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ, ɨɩɢɫɵɜɚɸɳɭɸ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɹɜɥɟɧɢɹ. ɋɬɪɨɢɬɫɹ ɭɩɪɨɳɟɧɧɚɹ ɦɨɞɟɥɶ, ɡɚɞɚɜɚɟɦɚɹ ɥɢɧɟɣɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ, ɨɩɢɫɵɜɚɸɳɚɹ ɦɟɞɥɟɧɧɵɟ, ɧɢɡɤɨɱɚɫɬɨɬɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɫɬɚɛɢɥɢɡɚɰɢɢ ɞɜɢɠɟɧɢɹ. ɗɬɚ ɦɨɞɟɥɶ ɩɨɡɜɨɥɹɟɬ ɨɩɢɫɚɬɶ ɤɚɱɟɫɬɜɟɧɧɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɫɭɳɢɟ ɞɜɢɠɟɧɢɹɦ ɧɚ ɭɤɚɡɚɧɧɵɯ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧɚɯ, ɨɰɟɧɢɬɶ ɩɚɪɚɦɟɬɪɵ ɫɢɫɬɟɦɵ ɢ ɩɪɨɜɟɫɬɢ ɩɥɚɧɢɪɨɜɚɧɢɟ ɞɚɥɶɧɟɣɲɢɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ. Ɉɩɵɬ ɭɱɚɫɬɢɹ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɛɢɨɦɟɯɚɧɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɩɨɤɚɡɵɜɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɪɚɡɪɚɛɨɬɤɢ ɦɟɬɨɞɨɜ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɩɨɥɭɱɚɟɦɨɣ ɩɪɢ ɢɡɦɟɪɟɧɢɹɯ ɢɧɮɨɪɦɚɰɢɢ. Ɍɪɚɞɢɰɢɨɧɧɵɣ ɫɩɨɫɨɛ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɦɧɨɝɨɤɪɚɬɧɨɦ ɩɨɜɬɨɪɟɧɢɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɞɜɢɠɟɧɢɹ ɢ ɩɨɫɥɟɞɭɸɳɟɦ ɨɫɪɟɞɧɟɧɢɢ ɪɟɡɭɥɶɬɚɬɨɜ ɢɡɦɟɪɟɧɢɣ ɩɨ ɚɧɫɚɦɛɥɸ ɪɟɚɥɢɡɚɰɢɣ. Ɍɚɤɨɣ ɫɩɨɫɨɛ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɬɪɭɞɧɢɬɟɥɶɧɵɦ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɚɧɚɥɢɡɚ ɞɜɢɠɟɧɢɹ ɛɨɥɶɧɵɯ, ɜ ɨɫɨɛɟɧɧɨɫɬɢ ɞɟɬɟɣ. Ʉ ɬɨɦɭ ɠɟ ɬɚɤɚɹ ɩɪɨɰɟɞɭɪɚ ɷɮɮɟɤɬɢɜɧɚ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚɢɛɨɥɟɟ ɨɛɳɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɜɵɹɜɥɟɧɢɹ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɨɬɞɟɥɶɧɨɣ ɪɟɚɥɢɡɚɰɢɢ ɭɤɚɡɚɧɧɵɣ ɫɩɨɫɨɛ ɧɟɩɪɢɝɨɞɟɧ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɜ ɬɪɟɬɶɟɣ ɪɚɛɨɬɟ ɫɛɨɪɧɢɤɚ ɨɛɫɭɠɞɚɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɭɬɨɱɧɟɧɢɹ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɩɭɬɟɦ ɤɨɦɩɥɟɤɫɢɪɨɜɚɧɢɹ ɩɨɤɚɡɚɧɢɣ ɪɚɡɧɨɪɨɞɧɵɯ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɞɚɬɱɢɤɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɞɜɢɠɟɧɢɹ. ɉɪɢɜɨɞɹɬɫɹ ɩɪɨɫɬɟɣɲɢɟ ɚɥɝɨɪɢɬɦɵ ɤɨɦɩɥɟɤɫɢɪɨɜɚɧɢɹ ɞɜɭɦɟɪɧɨɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɚɧɚɥɢɡɚ ɢ ɫɬɚɛɢɥɨɦɟɬɪɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɵ. Ɉɛɫɭɠɞɚɸɬɫɹ ɜɨɡɦɨɠɧɵɟ ɜɚɪɢɚɧɬɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɫɬɚɛɢɥɨɦɟɬɪɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɵ ɞɥɹ ɭɬɨɱɧɟɧɢɹ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɚɧɚɥɢɡɚ. ȼ ɡɚɤɥɸɱɢɬɟɥɶɧɨɣ ɪɚɛɨɬɟ ɫɛɨɪɧɢɤɚ ɪɚɫɫɦɨɬɪɟɧ ɩɪɢɦɟɪ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨɡɵ ɛɨɥɶɧɵɯ ɫ ɫɢɦɩɬɨɦɨɤɨɦɩɥɟɤɫɚɦɢ rectus-ɫɢɧɞɪɨɦ ɢ hamstring-ɫɢɧɞɪɨɦ. ɗɬɢ ɛɨɥɶɧɵɟ ɨɬɧɨɫɹɬɫɹ ɤ ɝɪɭɩɩɟ ɛɨɥɶɧɵɯ ɫ ɡɚɛɨɥɟɜɚɧɢɹɦɢ ɞɟɬɫɤɨɝɨ ɰɟɪɟɛɪɚɥɶɧɨɝɨ ɩɚɪɚɥɢɱɚ. Ɇɨɬɨɪɢɤɚ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ ɞɥɹ ɧɢɯ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɩɨɜɵɲɟɧɧɵɦ ɬɨɧɭɫɨɦ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ. ɉɨɫɬɪɨɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɨɩɢɫɵɜɚɟɬ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɣ ɜɚɪɢɚɧɬ ɫɨɯɪɚɧɟɧɢɹ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɭ ɬɚɤɢɯ ɛɨɥɶɧɵɯ: ɛɥɢɡɤɨɟ ɤ ɜɟɪɬɢɤɚɥɶɧɨɦɭ ɩɨɥɨɠɟɧɢɟ ɬɭɥɨɜɢɳɚ ɧɚ ɩɨɥɭɫɨɝɧɭɬɵɯ ɤɨɧɟɱɧɨɫɬɹɯ. ɉɨɡɚ ɛɨɥɶɧɨɝɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɦɢɧɢɦɢɡɚɰɢɢ ɮɭɧɤɰɢɨɧɚɥɚ ɧɚ 5
ɦɧɨɝɨɨɛɪɚɡɢɢ. Ɇɧɨɝɨɨɛɪɚɡɢɟ ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ ɪɚɜɧɨɜɟɫɢɹ ɢ ɭɪɚɜɧɟɧɢɹɦɢ ɫɟɪɜɨɫɜɹɡɟɣ. ɉɨɫɥɟɞɧɢɟ ɦɨɞɟɥɢɪɭɸɬ ɪɚɛɨɬɭ ɧɟɪɜɧɨɣ ɫɢɫɬɟɦɵ ɩɨ «ɜɟɪɬɢɤɚɥɢɡɚɰɢɢ» ɩɨɡɵ. ɋɪɚɜɧɟɧɢɹ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɤɥɢɧɢɱɟɫɤɢɯ ɧɚɛɥɸɞɟɧɢɣ ɩɨɤɚɡɚɥɨ, ɱɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɨɩɢɫɵɜɚɟɬ ɢɫɯɨɞɧɭɸ ɩɨɡɭ ɛɨɥɶɧɨɝɨ ɫ ɬɪɨɣɧɵɦ ɫɝɢɛɚɧɢɟɦ ɜ ɫɭɫɬɚɜɚɯ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ. Ɋɚɛɨɬɚ ɜɵɩɨɥɧɟɧɚ ɩɪɢ ɮɢɧɚɧɫɨɜɨɣ ɩɨɞɞɟɪɠɤɟ ɊɎɎɂ (Ƚɪɚɧɬ ʋ 02-01-00774) ɢ ɩɪɨɝɪɚɦɦɵ ɍɧɢɜɟɪɫɢɬɟɬɵ Ɋɨɫɫɢɢ (ɞɨɝɨɜɨɪ ɍɊ.04.03.064). Ɂɚɦɟɱɚɧɢɹ ɢ ɩɪɟɞɥɨɠɟɧɢɹ ɩɪɢɫɵɥɚɬɶ ɩɨ ɚɞɪɟɫɭ: 119992 Ɇɨɫɤɜɚ, ɆȽɍ, ɦɟɯɚɧɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɮɚɤɭɥɶɬɟɬ, ɤɚɮɟɞɪɚ ɩɪɢɤɥɚɞɧɨɣ ɦɟɯɚɧɢɤɢ ɢ ɭɩɪɚɜɥɟɧɢɹ ɢɥɢ ɷɥɟɤɬɪɨɧɧɨɦɭ ɚɞɪɟɫɭ
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6
Ɍɪɟɯɡɜɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɞɥɹ ɡɚɞɚɱɢ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ ɂ. ȼ. ɇɨɜɨɠɢɥɨɜ, Ⱥ. ȼ. Ɍɟɪɟɯɨɜ, Ⱥ. ȼ. Ɂɚɛɟɥɢɧ, ɆȽɍ ɢɦ. Ɇ.ȼ.Ʌɨɦɨɧɨɫɨɜɚ
ɘ. ɋ. Ʌɟɜɢɤ, ȼ. ɘ. ɒɥɵɤɨɜ, Ɉ. ȼ. Ʉɚɡɟɧɧɢɤɨɜ ɂɉɉɂ ɊȺɇ ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɜɨɩɪɨɫɨɜ, ɫɜɹɡɚɧɧɵɯ ɫɨ ɫɬɚɛɢɥɢɡɚɰɢɟɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ, ɬɪɚɞɢɰɢɨɧɧɨ ɩɪɢɦɟɧɹɟɬɫɹ ɦɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ [1,2]. Ɇɨɞɟɥɶ ɩɨɞɪɚɡɭɦɟɜɚɟɬ, ɱɬɨ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɭɤɚɡɚɧɧɨɣ ɡɚɞɚɱɢ ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɵɦ ɩɨɤɚɡɚɬɟɥɟɦ ɹɜɥɹɟɬɫɹ ɨɬɤɥɨɧɟɧɢɟ ɰɟɧɬɪɚ ɦɚɫɫ ɱɟɥɨɜɟɤɚ ɨɬ ɜɟɪɬɢɤɚɥɢ. ɋɨɝɥɚɫɧɨ ɦɨɞɟɥɢ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ, ɬɟɥɨ ɱɟɥɨɜɟɤɚ ɡɚɦɟɧɹɟɬɫɹ ɠɟɫɬɤɢɦ ɫɬɟɪɠɧɟɦ, ɩɪɨɯɨɞɹɳɢɦ ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ ɱɟɥɨɜɟɤɚ ɢ ɨɫɶ ɜɪɚɳɟɧɢɹ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɨɞɟɥɶ ɧɟ ɭɱɢɬɵɜɚɟɬ ɩɨɞɜɢɠɧɨɫɬɶ ɜ ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ. Ɉɝɪɚɧɢɱɟɧɧɨɫɬɶ ɬɚɤɨɝɨ ɩɨɞɯɨɞɚ ɛɵɥɚ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɚ ɞɨɫɬɚɬɨɱɧɨ ɞɚɜɧɨ [3], ɬɟɦ ɧɟ ɦɟɧɟɟ, ɦɨɞɟɥɶ ɩɪɨɞɨɥɠɚɸɬ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɛɥɚɝɨɞɚɪɹ ɟɟ ɩɪɨɫɬɨɬɟ ɢ ɧɚɝɥɹɞɧɨɫɬɢ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɦɨɞɟɥɢ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ ɛɵɥ ɜɵɞɜɢɧɭɬ ɢ ɩɪɨɜɟɪɟɧ ɪɹɞ ɩɪɢɧɰɢɩɢɚɥɶɧɵɯ ɝɢɩɨɬɟɡ ɨ ɦɟɯɚɧɢɡɦɚɯ ɪɚɛɨɬɵ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɱɟɥɨɜɟɤɚ [4-6]. ɇɟɩɪɢɦɟɧɢɦɨɫɬɶ ɭɤɚɡɚɧɧɨɣ ɦɨɞɟɥɢ ɞɥɹ ɚɧɚɥɢɡɚ ɞɜɢɠɟɧɢɣ ɱɟɥɨɜɟɤɚ ɧɚ ɪɟɡɤɨ ɜɨɡɦɭɳɚɟɦɨɦ ɨɫɧɨɜɚɧɢɢ [3] ɩɨɫɬɚɜɢɥɚ ɢɫɫɥɟɞɨɜɚɬɟɥɟɣ ɩɟɪɟɞ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɢɫɩɨɥɶɡɨɜɚɬɶ ɛɨɥɟɟ ɫɥɨɠɧɭɸ ɦɨɞɟɥɶ, ɭɱɢɬɵɜɚɸɳɭɸ ɩɨɞɜɢɠɧɨɫɬɶ ɜ ɬɪɟɯ ɫɭɫɬɚɜɚɯ: ɝɨɥɟɧɨɫɬɨɩɧɨɦ, ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ (ɫɦ. Ɇɟɬɨɞɵ) [7,8]. Ɉɛɵɱɧɨ, ɜ ɪɚɛɨɬɚɯ, ɢɫɩɨɥɶɡɭɸɳɢɯ ɬɪɟɯɡɜɟɧɧɭɸ ɦɨɞɟɥɶ, ɦɵɲɟɱɧɵɟ ɭɫɢɥɢɹ ɡɚɦɟɧɹɸɬɫɹ ɭɩɪɭɝɢɦɢ ɦɨɦɟɧɬɚɦɢ ɜ ɫɭɫɬɚɜɚɯ. Ɍɚɤɨɣ ɩɨɞɯɨɞ, ɨɬɱɚɫɬɢ, ɧɟɤɨɪɪɟɤɬɟɧ, ɩɨɫɤɨɥɶɤɭ, ɜɨ-ɩɟɪɜɵɯ, ɦɵɲɰɵ ɩɨ ɫɜɨɟɣ ɩɪɢɪɨɞɟ ɦɨɝɭɬ ɨɤɚɡɵɜɚɬɶ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɫɬɹɝɢɜɚɸɳɢɟ ɭɫɢɥɢɹ, ɜɨ-ɜɬɨɪɵɯ, ɡɧɚɱɢɬɟɥɶɧɚɹ ɱɚɫɬɶ ɦɵɲɰ ɹɜɥɹɟɬɫɹ ɞɜɭɫɭɫɬɚɜɧɵɦɢ. ɉɨɞɪɨɛɧɟɟ ɨɛ ɷɬɢɯ ɩɪɨɛɥɟɦɚɯ ɫɦ. [9]. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɪɟɞɥɚɝɚɟɬɫɹ ɬɪɟɯɡɜɟɧɧɚɹ ɦɨɞɟɥɶ, ɭɱɢɬɵɜɚɸɳɚɹ ɨɫɧɨɜɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɫɬɪɨɟɧɢɹ ɫɤɟɥɟɬɧɨ-ɦɵɲɟɱɧɨɝɨ ɚɩɩɚɪɚɬɚ. ɉɪɨɜɟɞɟɧɨ ɫɪɚɜɧɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɱɢɫɥɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɢɡ [1]. Ɉɩɢɫɚɧ ɪɟɡɭɥɶɬɚɬ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɩɨɡɜɨɥɹɸɳɢɯ ɫɪɚɜɧɢɬɶ ɤɨɥɟɛɚɧɢɹ ɱɟɥɨɜɟɤɚ ɩɪɢ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɜ ɞɜɭɯ ɭɫɥɨɜɢɹɯ: ɩɪɢ ɫɩɨɤɨɣɧɨɦ ɫɬɨɹɧɢɢ (ɋɋ) ɢ ɩɪɢ ɫɬɨɹɧɢɢ ɫ ɨɝɪɚɧɢɱɟɧɧɨɣ ɩɨɞɜɢɠɧɨɫɬɶɸ (Ɉɉ) ɜ ɤɨɥɟɧɧɨɦ 7
ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ. Ɋɟɡɭɥɶɬɚɬɵ ɫɨɩɨɫɬɚɜɥɹɸɬɫɹ ɫ ɞɚɧɧɵɦɢ ɦɨɞɟɥɢ. ɋ ɩɨɦɨɳɶɸ ɦɟɬɨɞɨɜ ɪɚɡɞɟɥɟɧɢɹ ɞɜɢɠɟɧɢɹ [10] ɫɬɪɨɢɬɫɹ ɩɪɢɛɥɢɠɟɧɧɚɹ ɦɨɞɟɥɶ ɫ ɨɞɧɨɣ ɧɟɡɚɜɢɫɢɦɨɣ ɩɟɪɟɦɟɧɧɨɣ, ɨɛɥɚɞɚɸɳɚɹ ɩɪɨɫɬɨɬɨɣ ɢ ɧɚɝɥɹɞɧɨɫɬɶɸ ɦɨɞɟɥɢ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ ɢ ɭɱɢɬɵɜɚɸɳɚɹ ɩɨɞɜɢɠɧɨɫɬɶ ɜ ɬɪɟɯ ɫɭɫɬɚɜɚɯ. ɉɪɨɜɨɞɢɬɫɹ ɫɪɚɜɧɟɧɢɟ ɩɨɥɧɨɣ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɢ, ɩɪɢɛɥɢɠɟɧɧɨɣ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɢ ɢ ɦɨɞɟɥɢ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ. ȼɵɹɜɥɹɟɬɫɹ ɪɨɥɶ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɜ ɭɩɪɚɜɥɟɧɢɢ ɞɜɢɠɟɧɢɹɦɢ ɱɟɥɨɜɟɤɚ ɩɪɢ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ. ȼɚɠɧɨɫɬɶ ɢɫɫɥɟɞɨɜɚɧɢɹ ɷɬɨɝɨ ɜɨɩɪɨɫɚ ɩɨɞɱɟɪɤɢɜɚɥɚɫɶ ɇ. Ⱥ. Ȼɟɪɧɲɬɟɣɧɨɦ [12]. ȼ ɪɚɛɨɬɟ ɜɵɫɤɚɡɵɜɚɟɬɫɹ ɝɢɩɨɬɟɡɚ ɨ ɫɜɹɡɢ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɤɨɥɟɛɚɧɢɣ ɫ ɞɜɢɝɚɬɟɥɶɧɵɦɢ ɫɢɧɟɪɝɢɹɦɢ ɩɨ Ȼɟɪɧɲɬɟɣɧɭ [11]. Ɇɟɬɨɞɵ Ɇɟɬɨɞɵ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɜɢɠɟɧɢɣ ɬɟɥɚ ɱɟɥɨɜɟɤɚ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɪɟɞɥɚɝɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɪɟɯɡɜɟɧɧɭɸ ɫɢɫɬɟɦɭ, C3 ɡɜɟɧɶɹ ɤɨɬɨɪɨɣ ɫɨɟɞɢɧɟɧɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɨɫɧɨɜɚɧɢɟɦ ɢ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɩɨɫɪɟɞɫɬɜɨɦ ɬɨɱɟɱɧɵɯ ɲɚɪɧɢɪɨɜ (ɪɢɫɭɧɨɤ 1). Ɍɚɤɚɹ ɦɨ\3 ɞɟɥɶ ɩɪɢɦɟɧɢɦɚ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɫɬɨO3 ɩɚ ɧɟ ɨɬɪɵɜɚɟɬɫɹ ɨɬ ɡɟɦɥɢ, ɪɭɤɢ ɢ ɝɨɥɨɜɚ ɧɟɩɨɞɜɢɠɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɪɩɭɫɚ, ɭɝɥɵ ɜ \2 C2 ɨɞɧɨɢɦɟɧɧɵɯ ɫɭɫɬɚɜɚɯ ɨɛɟɢɯ ɧɨɝ ɫɨɜɩɚɞɚɸɬ. ɉɨɞɨɛɧɚɹ ɦɨɞɟɥɶ ɱɟɥɨɜɟɱɟɫɤɨɝɨ ɬɟɥɚ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɟɬɫɹ [3,7,8,12-14]. ɆɚɫɫO2 ɢɧɟɪɰɢɨɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɡɜɟɧɶɟɜ ɩɪɢɧɢɦɚɸɬɫɹ ɪɚɜɧɵɦɢ ɦɚɫɫ-ɢɧɟɪɰɢɨɧɧɵɦ ɯɚC1 ɪɚɤɬɟɪɢɫɬɢɤɚɦ ɥɟɜɨɣ ɢ ɩɪɚɜɨɣ ɝɨɥɟɧɢ, ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɤɚɤ ɨɞɧɨ ɬɟɥɨ - ɞɥɹ ɧɢɠɧɟɝɨ \1 ɡɜɟɧɚ, ɥɟɜɨɝɨ ɢ ɩɪɚɜɨɝɨ ɛɟɞɪɚ, ɪɚɫɫɦɚɬɪɢO1 ɜɚɟɦɵɯ ɤɚɤ ɨɞɧɨ ɬɟɥɨ - ɞɥɹ ɫɪɟɞɧɟɝɨ ɡɜɟɧɚ, ɤɨɪɩɭɫɚ, ɝɨɥɨɜɵ ɢ ɪɭɤ, ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɤɚɤ ɨɞɧɨ ɬɟɥɨ - ɞɥɹ ɜɟɪɯɧɟɝɨ ɡɜɟɧɚ. Ⱦɥɢɧɵ Ɋɢɫɭɧɨɤ 1. Ɍɪɟɯɡɜɟɧɶɟɜ ɛɟɪɭɬɫɹ ɪɚɜɧɵɦɢ ɪɚɫɫɬɨɹɧɢɹɦ ɨɬ ɡɜɟɧɧɚɹ ɫɢɫɬɟɦɚ ɨɫɢ ɜɪɚɳɟɧɢɹ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ ɞɨ ɞɥɹ ɨɩɢɫɚɧɢɹ ɨɫɢ ɤɨɥɟɧɧɨɝɨ ɫɭɫɬɚɜɚ, ɨɬ ɨɫɢ ɤɨɥɟɧɧɨɝɨ ɞɨ ɬɟɥɚ ɱɟɥɨɜɟɤɚ. ɨɫɢ ɬɚɡɨɛɟɞɪɟɧɧɨɝɨ, ɨɬ ɨɫɢ ɬɚɡɨɛɟɞɪɟɧɧɨɝɨ ɫɭɫɬɚɜɚ ɞɨ ɰɟɧɬɪɚ ɦɚɫɫ ɜɟɪɯɧɟɝɨ ɡɜɟɧɚ, - ɞɥɹ ɧɢɠɧɟɝɨ, ɫɪɟɞɧɟɝɨ ɢ ɜɟɪɯɧɟɝɨ ɡɜɟɧɶɟɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɰɟɧɬɪɵ ɦɚɫɫ ɡɜɟɧɶɟɜ ( C1 , C2 , C3 ) ɥɟɠɚɬ ɧɚ ɡɜɟɧɶɹɯ. ɂɫɩɨɥɶɡɭɟɦɵɟ
8
ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɡɧɚɱɟɧɢɹ ɦɚɫɫ-ɢɧɟɪɰɢɨɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢ ɞɥɢɧ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 1 [15]. Ɇɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ( J 1 , J 2 , J 3 ) ɭɤɚɡɚɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɨɜ ɦɚɫɫ. ɉɨɥɨɠɟɧɢɟ ɨɩɢɫɚɧɧɨɣ ɫɢɫɬɟɦɵ ɦɨɠɟɬ ɛɵɬɶ ɡɚɞɚɧɨ ɬɪɟɦɹ ɨɛɨɛɳɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ. ȼ ɤɚɱɟɫɬɜɟ ɬɚɤɨɜɵɯ ɛɟɪɭɬɫɹ ɫɭɫɬɚɜɧɵɟ ɭɝɥɵ \ 1 , \ 2 , \ 3 (ɪɢɫɭɧɨɤ 1). ɋɨɝɥɚɫɧɨ[1], ɜ ɤɚɱɟɫɬɜɟ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɩɨɥɨɠɟɧɢɟ ɫɢɫɬɟɦɵ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɹɦ ɭɝɥɨɜ (\ 10 , \ 2 0 , \ 3 0 ), ɩɪɢɜɟɞɟɧɧɵɦ ɜ ɬɚɛɥɢɰɟ 2. Ɍɚɛɥɢɰɚ 1. m2 m1
12ɤɝ O1O2
18ɤɝ
0.50 ɦ Ɍɚɛɥɢɰɚ 2.
\ 10
\ 20
83q 2q Ɍɚɛɥɢɰɚ 3.
m3
J1
50ɤɝ O2O3
1.1ɤɝ ɦ O1C1
0.45 ɦ
0.25 ɦ
J2 2
J3
1.4ɤɝ ɦ O2C2
2
0.23 ɦ
2.1ɤɝ ɦ 2 O3C3 0.18 ɦ
\ 30 5q
D3
E3
V0
V1
V2
a3
b3
R2
r2
s0
s1
s2
66q
66q
46q
8q
90q
10ɫɦ
13ɫɦ
6ɫɦ
4ɫɦ
6ɫɦ
36ɫɦ
3ɫɦ
ɋɢɫɬɟɦɚ ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ ɢ ɩɪɨɬɢɜɨɞɟɣɫɬɜɭɸɳɢɯ ɟɣ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ. ȼ ɦɨɞɟɥɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɬɨɥɶɤɨ ɞɜɭɫɭɫɬɚɜɧɵɟ ɦɵɲɰɵ. ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɭɱɚɫɬɜɭɸɬ ɬɪɢ ɝɪɭɩɩɵ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ: ɝɪɭɩɩɚ ɡɚɞɧɢɯ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰɵ ɝɨɥɟɧɢ (ɞɚɥɟɟ ɨɛɨɡɧɚɱɚɟɬɫɹ ɢɧɞɟɤɫɨɦ "1"), ɝɪɭɩɩɚ ɩɟɪɟɞɧɢɯ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ (ɢɧɞɟɤɫ "2"), ɝɪɭɩɩɚ ɡɚɞɧɢɯ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ (ɢɧɞɟɤɫ "3"). Ɂɞɟɫɶ ɢɫɩɨɥɶɡɭɟɬɫɹ ɬɟɪɦɢɧɨɥɨɝɢɹ ɢɡ [16].
9
Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɦɵɲɰ ɢɫɩɨɥɶɡɭɟɬɫɹ "ɧɢɬɹɧɚɹ ɦɨɞɟɥɶ" [17], ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɣ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɦɵɲɰɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɦɟɧɟɧɚ ɧɢɬɶɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɞɥɢɧɵ ɢ ɧɚɬɹɠɟɧɢɹ, ɫɨɟɞɢɧɹɸɳɟɣ ɬɨɱɤɢ ɤɪɟɩɥɟɧɢɹ ɦɵɲɰɵ ɤ ɫɤɟɥɟɬɭ (ɪɢɫɭɧɤɢ 2Ⱥ, 2Ȼ). Ⱦɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɝɪɭɩɩ ɦɵɲɰ ɩɪɢɧɹɬɚ ɫɯɟɦɚ ɤɪɟɩɥɟɧɢɹ ɢɡ [12,13], ɩɪɢɜɟɞɟɧɧɚɹ ɧɚ ɪɢɫɭɧɤɚɯ a3 2Ⱥ, 2Ȼ. ȼ ɬɚɛɥɢɰɟ 3 ɭɤɚɡɚD3 ɧɵ ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɦɨɞɟɥɢ ɡɧɚɱɟɧɢɹ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ O 3 E3 ɩɚɪɚɦɟɬɪɨɜ, ɩɨɥɭɱɟɧɧɵɯ V2 ɩɨ [18]. ɍɤɚɡɚɧɧɚɹ ɫɯɟɦɚ s2 b3 ɭɫɩɟɲɧɨ ɩɪɢɦɟɧɹɥɚɫɶ ɩɪɢ O2 ɪɟɲɟɧɢɢ ɪɚɡɥɢɱɧɵɯ ɡɚɞɚɱ A2 [8,12-14]. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɦɵA3 A1 2 V1 ɲɟɱɧɵɯ ɭɫɢɥɢɣ ɩɪɢɧɹɬɚ 3 r R 1 2 2 O -ɦɨɞɟɥɶ Ɏɟɥɶɞɦɚɧɚ (ɝɢs1 ɩɨɬɟɡɚ ɪɚɜɧɨɜɟɫɧɨɣ ɬɨɱɤɢ) O2 [19]. ɋɨɝɥɚɫɧɨ ɷɬɨɣ ɦɨɞɟɥɢ, ɫɬɚɬɢɱɟɫɤɢɟ ɭɫɢɥɢɹ, ɪɚɡɜɢɜɚɟɦɵɟ ɦɵɲɰɚɦɢ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɟɤɭɳɟɣ O1 V0 ɞɥɢɧɨɣ ɦɵɲɰɵ ɢ ɡɧɚɱɟɧɢs0 ɟɦ ɭɩɪɚɜɥɹɸɳɟɝɨ ɩɚɪɚɦɟɬɪɚ O , ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ Ȼ Ⱥ ɩɨɪɨɝɭ ɫɬɪɟɬɱ-ɪɟɮɥɟɤɫɚ. (ɪɢɫɭɧɨɤ 3). ɉɪɢɦɟɧɢɦɨɫɬɶ Ɋɢɫɭɧɨɤ 2. ɉɪɢɧɹɬɚɹ ɫɯɟɦɚ ɦɵɲɰ. O -ɦɨɞɟɥɢ Ɏɟɥɶɞɦɚɧɚ ɞɥɹ Ɇɵɲɰɵ ɨɛɨɡɧɚɱɟɧɵ ɱɚɫɬɵɦ ɩɭɧɤɚɧɚɥɢɡɚ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɬɢɪɨɦ. ɱɟɥɨɜɟɤɚ ɨɛɫɭɠɞɚɟɬɫɹ ɜ [20]. ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɟɪɬɢɤɚɥɶɧɚɹ ɩɨɡɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɥɨɠɟɧɢɸ ɪɚɜɧɨɜɟɫɢɹ ɫɢɫɬɟɦɵ, ɡɚɞɚɜɚɟɦɨɦɭ ɩɨɫɬɨɹɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɭɩɪɚɜɥɹɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ O ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɝɪɭɩɩ ɦɵɲɰ. ɉɪɨɜɨɞɢɬɫɹ ɥɢɧɟɚɪɢɡɚɰɢɹ ɡɚɜɢɫɢɦɨɫɬɢ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ ɨɬ ɞɥɢɧɵ ɦɵɲɰɵ A ɢ ɭɩɪɚɜɥɹɸɳɟɝɨ ɩɚɪɚɦɟɬɪɚ O ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɪɚɜɧɨɜɟɫɧɨɣ ɞɥɢɧɵ A 0 (ɪɢɫɭɧɨɤ 3). Ʌɢɧɟɚɪɢɡɨɜɚɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɢɦɟɟɬ ɜɢɞ: (1) F A, O F A 0 , O0 K GA PGA GO ɝɞɟ K - ɩɨɫɬɨɹɧɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɢɦɟɸɳɢɣ ɪɚɡɦɟɪɧɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɠɟɫɬɤɨɫɬɢ, P - ɩɨɫɬɨɹɧɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ
10
ɤɨɷɮɮɢɰɢɟɧɬ, ɢɦɟɸɳɢɣ ɪɚɡɦɟɪɧɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɟɦɩɮɢɪɨɜɚɧɢɹ. Ʌɢɧɟɚɪɢɡɚɰɢɹ ɤɨɪɪɟɤɬɧɚ ɩɪɢ F 0 F A 0 , O0 ! 0 . Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɫɱɢɬɚɟɬɫɹ, ɱɬɨ ɠɟɫɬɤɨɫɬɢ ɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɞɟɦɩɮɢɪɨɜɚɧɢɹ ɜɫɟɯ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɦɵɲɰ ɪɚɜF ɧɵ ɦɟɠɞɭ ɫɨɛɨɣ: K1 K 2 K 3 N
P1 P 2 P 3 P ɋ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟF0 ɧɢɣ Ʌɚɝɪɚɧɠɚ 2-ɝɨ ɪɨɞɚ ɜɵɜɨɞɹɬɫɹ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɫɢɫɬɟɦɵ. ɉɟɪɟɫɱɟɬ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ ɜ ɨɛɨɛA A0 ɳɟɧɧɵɟ ɫɢɥɵ ɨɫɭɳɟɫɬɜɥɹɥɫɹ ɦɟɬɨɞɨɦ, ɨɩɢɫɚɧɧɵɦ O ɜ [12]. ɉɪɨɜɨɞɢɬɫɹ ɥɢɧɟɚɪɢɡɚɰɢɹ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɊɢɫɭɧɨɤ 3. Ɇɨɞɟɥɶ Ɏɟɥɶɞɦɚɧɚ ɧɟɧɢɣ. Ⱦɥɹ ɥɢɧɟɚɪɢɡɨɜɚɧ(ɩɭɧɤɬɢɪ) ɢ ɟɟ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɧɨɣ ɫɢɫɬɟɦɵ ɪɟɲɚɟɬɫɹ ɡɚ(ɫɩɥɨɲɧɚɹ ɥɢɧɢɹ). ɞɚɱɚ ɧɚ ɧɚɯɨɠɞɟɧɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ ɱɢɫɟɥ ɩɪɢɦɟɧɹɸɬɫɹ ɫɬɚɧɞɚɪɬɧɵɟ ɮɭɧɤɰɢɢ ɫɪɟɞɵ MATLAB. ɋɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ ɨɤɚɡɵɜɚɸɬɫɹ ɫɢɥɶɧɨ ɪɚɡɧɟɫɟɧɧɵɦɢ. ȼɟɥɢɱɢɧɚ N ɜɵɛɢɪɚɟɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɢɡɲɚɹ ɫɨɛɫɬɜɟɧɧɚɹ ɱɚɫɬɨɬɚ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɹɥɚɫɶ 0.3~0.4 Ƚɰ, ɱɬɨ, ɫɨɝɥɚɫɧɨ [1], ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɫɧɨɜɧɨɣ ɱɚɫɬɨɬɟ ɤɨɥɟɛɚɧɢɣ ɱɟɥɨɜɟɤɚ (ɩɨɞɪɨɛɧɟɟ ɫɦ. ɞɚɥɟɟ ɪɚɡɞɟɥ «ɨɫɧɨɜɧɵɟ ɤɨɥɟɛɚɧɢɹ»). Ɇɟɬɨɞɚɦɢ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɨɩɢɫɚɧɧɵɦɢ ɜ [21], ɫɬɪɨɢɬɫɹ ɩɪɢɛɥɢɠɟɧɧɚɹ ɦɨɞɟɥɶ ɞɥɹ ɦɟɞɥɟɧɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɞɜɢɠɟɧɢɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɫɬɪɨɢɬɫɹ ɦɨɞɟɥɶ, ɩɨɥɭɱɚɸɳɚɹɫɹ ɢɡ ɢɫɯɨɞɧɨɣ ɩɭɬɟɦ ɧɚɥɨɠɟɧɢɹ ɫɜɹɡɟɣ (2) \2 \3 0, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɮɢɤɫɚɰɢɢ ɭɝɥɨɜ ɜ ɤɨɥɟɧɟ ɢ ɛɟɞɪɟ. Ⱦɥɹ ɢɫɯɨɞɧɨɣ ɦɨɞɟɥɢ ɜ ɫɢɥɭ ɮɨɪɦɭɥɵ (1) ɜɵɱɢɫɥɹɸɬɫɹ ɭɫɢɥɢɹ ɜ ɢɤɪɨɧɨɠɧɨɣ ɦɵɲɰɟ (ɝɪɭɩɩɚ ɡɚɞɧɢɯ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰɵ ɝɨɥɟɧɢ) ɜ ɩɪɨɰɟɫɫɟ ɤɨɥɟɛɚɧɢɣ. ɉɨɪɹɞɨɤ ɩɪɨɜɟɞɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢ ɦɟɬɨɞɵ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ. ȼ ɷɤɫɩɟɪɢɦɟɧɬɟ ɩɪɢɧɢɦɚɥɢ ɭɱɚɫɬɢɟ 9 ɱɟɥɨɜɟɤ ɦɭɠɫɤɨɝɨ ɩɨɥɚ ɜ ɜɨɡɪɚɫɬɟ ɨɬ 15 ɞɨ 50 ɥɟɬ. ȼɫɟ ɢɫɩɵɬɭɟɦɵɟ ɛɵɥɢ ɩɪɨɢɧɮɨɪɦɢɪɨɜɚɧɵ ɨ ɩɨɪɹɞɤɟ ɩɪɨɜɟɞɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢ ɞɚɥɢ ɫɜɨɟ ɫɨɝɥɚɫɢɟ ɧɚ ɭɱɚɫɬɢɟ
11
ɜ ɧɟɦ. ȼ ɯɨɞɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɪɟɝɢɫɬɪɢɪɨɜɚɥɢɫɶ ɩɨɤɚɡɚɧɢɹ ɫɬɚɛɢɥɨɝɪɚɮɚ. ɑɚɫɬɨɬɚ ɫɴɟɦɚ ɫɢɝɧɚɥɚ - 50 Ƚɰ. ɗɤɫɩɟɪɢɦɟɧɬ ɩɪɨɯɨɞɢɥ ɜ ɞɜɭɯ ɭɫɥɨɜɢɹɯ. 1) ɍɫɥɨɜɢɟ ɫɩɨɤɨɣɧɨɝɨ ɫɬɨɹɧɢɹ (ɋɋ). ɂɫɩɵɬɭɟɦɵɣ ɫɬɨɢɬ ɧɚ ɫɬɚɛɢɥɨɝɪɚɮɟ ɫ ɡɚɤɪɵɬɵɦɢ ɝɥɚɡɚɦɢ ɜ ɬɟɱɟɧɢɟ ɬɪɟɯ ɦɢɧɭɬ ɜ ɩɪɢɜɵɱɧɨɣ ɫɬɨɣɤɟ. Ɋɭɤɢ ɢɫɩɵɬɭɟɦɨɝɨ ɩɪɢɜɹɡɚɧɵ ɤ ɤɨɪɩɭɫɭ ɪɟɦɧɟɦ. 2) ɍɫɥɨɜɢɟ ɨɝɪɚɧɢɱɟɧɧɨɣ ɩɨɞɜɢɠɧɨɫɬɢ (Ɉɉ). ɂɫɩɵɬɭɟɦɵɣ ɫɬɨɢɬ ɧɚ ɫɬɚɛɢɥɨɝɪɚɮɟ ɫ ɡɚɤɪɵɬɵɦɢ ɝɥɚɡɚɦɢ ɜ ɬɟɱɟɧɢɟ ɬɪɟɯ ɦɢɧɭɬ. ɉɨɞɜɢɠɧɨɫɬɶ ɜ ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ ɨɝɪɚɧɢɱɟɧɚ ɩɨɫɪɟɞɫɬɜɨɦ ɬɪɟɯ ɞɟɪɟɜɹɧɧɵɯ ɩɥɚɧɨɤ, ɞɜɟ ɢɡ ɤɨɬɨɪɵɯ ɤɪɟɩɹɬɫɹ ɪɟɦɧɹɦɢ ɤ ɧɨɝɚɦ ɢ ɤɨɪɩɭɫɭ ɫɨ ɫɬɨɪɨɧɵ ɠɢɜɨɬɚ, ɬɪɟɬɶɹ ɤɪɟɩɢɬɫɹ ɤ ɤɨɪɩɭɫɭ ɫɨ ɫɬɨɪɨɧɵ ɫɩɢɧɵ ɢ ɡɚɬɵɥɤɭ. ɂɫɩɵɬɭɟɦɵɯ ɩɪɨɫɢɥɢ ɫɨɨɛɳɚɬɶ ɜ ɫɥɭɱɚɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɱɭɜɫɬɜɚ ɞɢɫɤɨɦɮɨɪɬɚ ɢɥɢ ɛɨɥɟɜɵɯ ɨɳɭɳɟɧɢɣ. ɉɪɨɜɨɞɢɥɫɹ ɫɩɟɤɬɪɚɥɶɧɵɣ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɞɚɧɧɵɯ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ ȼɟɥɱɚ (ɞɥɹ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ) ɢ ɦɟɬɨɞɚ ɤɨɪɪɟɥɹɰɢɣ (ɞɥɹ ɧɢɡɤɢɯ). ɉɪɢɦɟɪ ɫɩɟɤɬɪɚɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɨɥɭɱɟɧɧɨɣ ɦɟɬɨɞɨɦ ɤɨɪɪɟɥɹɰɢɣ, ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫɭɧɤɟ 4. ɋɨɝɥɚɫɧɨ [1], ɱɚɫɬɨɬɭ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɟɪɜɨɦɭ ɩɢɤɭ ɫɩɟɤɬɪɚ, ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɱɚɫɬɨɬɨɣ ɨɫɧɨɜɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɚ ɤɨɥɟɛɚɧɢɹ ɧɚ ɷɬɨɣ ɱɚɫɬɨɬɟ - ɨɫɧɨɜɧɵɦɢ ɤɨɥɟɛɚɧɢɹɦɢ. Ɋɟɡɭɥɶɬɚɬɵ Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɉɨɫɬɪɨɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ, ɨɩɢɫɵɜɚɸɳɚɹ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ ɜɛɥɢɡɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ. ȼ ɫɢɥɭ ɩɨɥɭɱɟɧɧɨɣ ɦɨɞɟɥɢ, ɨɩɪɟɞɟɥɟɧɵ ɡɧɚɱɟɧɢɹ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɨɥɨɠɟɧɢɟ, ɡɚɞɚɜɚɟɦɨɟ ɭɝɥɚɦɢ ɢɡ ɬɚɛɥɢɰɵ 2, ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɨ ɩɨɥɨɠɟɧɢɸ ɪɚɜɧɨɜɟɫɢɹ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ. ɉɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɨɤɚɡɵɜɚɸɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ (ɬɚɛɥɢɰɚ 4), ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɥɢɧɟɚɪɢɡɨɜɚɬɶ O -ɦɨɞɟɥɶ Ɏɟɥɶɞɦɚɧɚ. ɉɪɨɜɨɞɢɬɫɹ ɥɢɧɟɚɪɢɡɚɰɢɹ ɭɪɚɜɧɟɧɢɣ ɩɨɫɬɪɨɟɧɧɨɣ ɦɨɞɟɥɢ ɜɛɥɢɡɢ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ. ȼ ɥɢɧɟɣɧɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢɦɟɸɬ ɜɢɞ: AG\ PNLT LG\ (NLT L G )G\ NLGO (3) ɡɞɟɫɶ G\
G\
G\ 2 G\ 3
T
1
- ɨɬɤɥɨɧɟɧɢɹ ɭɝɥɨɜ ɨɬ ɩɨɥɨɠɟɧɢɹ
ɪɚɜɧɨɜɟɫɢɹ, GO GO1 GO 2 GO 3 - ɨɬɤɥɨɧɟɧɢɹ ɡɧɚɱɟɧɢɣ ɭɩɪɚɜɥɹɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ, ɨɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɨɥɨɠɟɧɢɸ ɪɚɜɧɨɜɟɫɢɹ. Ɇɚɬɪɢɰɵ A , G , L ɢɦɟɸɬ ɜɢɞ. T
12
§ J1 m1c12 m2 L12 m3 L12 ¨ 0 S T ¨ m2c2 m3 L2 L1 cos\ 2 ¨¨ 0 0 m c L cos( \ \ ) 3 3 1 2 3 ©
A
G
m2c2 m3 L2 L1 cos\ 20 2
J 2 m2c2 m3 L2 m3c3 L2 cos\ 3
2
0
0
· § ( m1c1 m2 L1 m3 L1 ) g sin\ 10 0 0 ¸ ¨ 0 0 ¸S ST ¨ 0 ( m2 c 2 m3 L2 ) g sin(\ 1 \ 2 ) 0 0 0 0 ¸ ¨¨ 0 0 m3c3 g sin(\ 1 \ 2 \ 3 ) ¸¹ © s2 § · 0 0 0 0 L1 sin(\ 2 V 2 ) s1 sin(\ 1 V 0 V 1 ) ¨ s 0 sin(\ 1 V 0 V 1 ) ¸ L1 s1 ¨ ¸ 0 ¨ 0 R2 a3 cos(\ 3 D 3 ) ¸ ¨ ¸ 0 0 r2 b3 cos(\ 3 E 3 ) ¸ ¨ ¨ ¸ © ¹
L
0
m3c3 L1 cos(\ 2 \ 3 ) · ¸ 0 ¸S m3c3 L2 cos\ 3 ¸¸ 2 J 3 m3c3 ¹
ɝɞɟ ɩɪɢɧɹɬɵ ɨɛɨɡɧɚɱɟɧɢɹ: L1 O1O2 , L2 O2 O3 , c1
O1C1 , c2
O2 C 2 , c3
O3C3
§1 0 0 · ¨ ¸ ¨1 1 0 ¸ ¨1 1 1 ¸ © ¹
S
Ɇɨɞɟɥɶ, ɨɩɢɫɵɜɚɟɦɚɹ (3), ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ ɋɋ ɷɤɫɩɟɪɢɦɟɧɬɚ. Ⱦɚɥɟɟ ɟɟ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɶɸ. ɋɨɝɥɚɫɧɨ ɦɟɬɨɞɚɦ ɢɡ [10] ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɜɫɩɨɦɨɝɚɬɟɥɶɧɚɹ ɫɢɫɬɟɦɚ: AG\ (NLT L G )G\ 0 (4) ɩɨɥɭɱɚɟɦɚɹ ɢɡ (3) ɩɪɢ P 0 , ɞɥ 0 . Ⱦɥɹ ɫɢɫɬɟɦɵ (4) ɪɟɲɚɟɬɫɹ ɡɚɞɚɱɚ ɨ ɧɚɯɨɠɞɟɧɢɢ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɢ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɤɨɥɟɛɚɧɢɣ. ɉɚɪɚɦɟɬɪ N ɜɵɛɢɪɚɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ [1] ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɢɡɲɚɹ ɫɨɛɫɬɜɟɧɧɚɹ ɱɚɫɬɨɬɚ ɪɚɜɧɹɥɚɫɶ 0.4 Ƚɰ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɫɧɨɜɧɵɦ ɤɨɥɟɛɚɧɢɹɦ ɫɩɨɤɨɣɧɨ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ (ɫɦ. ɪɚɡɞɟɥ «ɨɫɧɨɜɧɵɟ ɤɨɥɟɛɚɧɢɹ»). Ɉɬɫɸɞɚ:
N | 8u 10 5 ɇ ɦ ɉɨɥɭɱɟɧɧɵɟ ɫɨɛɫɬɜɟɧɧɵɟ ɜɟɤɬɨɪɵ vi , ɫɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ f i ɢ ɡɧɚɱɟɧɢɹ ɪɚɜɧɨɜɟɫɧɵɯ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ Fi 0 ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ Ɍɚɛɥɢɰɚ 4. 0 F1 4
0.3 10 ɇ
F2
0 4
0.4 Ƚɰ
T
^0.3
f2
f3
3.2 Ƚɰ
9.0 Ƚɰ
f1
1.2 10 ɇ
v2 0.5 0.5`
0 4
1.5 10 ɇ
T
v1
^0.7
F3
v3
0.7 0.6`
T
^0.4
0.5 0.8`
Ɂɧɚɱɢɬɟɥɶɧɨɟ ɪɚɡɧɟɫɟɧɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɩɨɡɜɨɥɹɟɬ ɩɨɫɬɪɨɢɬɶ ɩɪɢɛɥɢɠɟɧɧɭɸ ɦɨɞɟɥɶ, ɨɩɢɫɵɜɚɸɳɭɸ ɞɜɢɠɟɧɢɹ ɫ ɯɚɪɚɤɬɟɪɧɵɦɢ ɜɪɟɦɟɧɚɦɢ ɩɨɪɹɞɤɚ ɩɟɪɢɨɞɨɜ ɧɢɡɲɢɯ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚ13
ɧɢɣ. ɉɪɢɦɟɧɟɧɢɟ ɦɟɬɨɞɨɜ ɢɡ [21] ɤ ɫɢɫɬɟɦɟ (3) ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɩɪɢɛɥɢɠɟɧɧɭɸ ɦɨɞɟɥɶ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɟɬɫɹ ɨɞɧɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɢ ɞɜɭɦɹ ɚɥɝɟɛɪɚɢɱɟɫɤɢɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ: ~ ~ ~ I G\1 RG\ 1 KG\ 1 n ɞɥ (5) G\ 2 a 2 G\ 1 G\ 3 a 3G\ 1 Ɂɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɭɪɚɜɧɟɧɢɹ (5), ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 5. Ⱦɚɥɟɟ ɦɨɞɟɥɶ, ɨɩɢɫɵɜɚɟɦɭɸ (5), ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɩɪɢɛɥɢɠɟɧɧɨɣ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɶɸ. Ɍɚɛɥɢɰɚ 5. ~ ~ I K 35ɤɝ ɦ 2 194 ɇ
a2
a3
n
0. 7
0. 7
^ 1.7
0.8 0.8`u 104 ɇ ɦ
ɉɨɫɦɨɬɪɢɦ, ɤɚɤ ɢɡɦɟɧɢɬɫɹ ɩɨɜɟɞɟɧɢɟ ɫɢɫɬɟɦɵ (3) ɩɨɫɥɟ ɧɚɥɨɠɟɧɢɹ ɫɜɹɡɢ (2). Ɍɚɤɚɹ ɦɨɞɟɥɶ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ Ɉɉ ɷɤɫɩɟɪɢɦɟɧɬɚ. IG\1 RG\ 1 KG\ 1 nGO1
G\ 2 G\ 3
(6)
0
0 Ɂɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɭɪɚɜɧɟɧɢɹ (6) ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 6. Ⱦɚɥɟɟ, ɦɨɞɟɥɶ ɨɩɢɫɵɜɚɟɦɭɸ (6), ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɦɨɞɟɥɶɸ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ. Ɍɚɛɥɢɰɚ 6.
I 35ɤɝ ɦ 2
K 194 ɇ
n 3u 104 ɇ ɦ
ȼ ɬɚɛɥɢɰɟ 7 ɩɪɢɜɟɞɟɧɵ ɫɜɨɞɧɵɟ ɞɚɧɧɵɟ ɩɨ ɫɨɛɫɬɜɟɧɧɵɦ ɱɚɫɬɨɬɚɦ ɞɥɹ ɫɢɫɬɟɦ (3), (5), (6) ɩɪɢ įȜ=0. Ɍɚɛɥɢɰɚ 7. Ɇɨɞɟɥɢ ɬɪɟɯɡɜɟɧɧɚɹ ɩɪɢɛɥɢɠɟɧɧɚɹ ɬɪɟɯɡɜɟɧɧɚɹ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ
14
ɋɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ ɧɢɡɲɚɹ ɫɪɟɞɧɹɹ 0.4 Ƚɰ 3 Ƚɰ 0.4 Ƚɰ 0.6 Ƚɰ -
ɜɵɫɲɚɹ 9 Ƚɰ -
Ɉɫɧɨɜɧɵɟ ɤɨɥɟɛɚɧɢɹ ȼ [1] ɧɚ ɨɫɧɨɜɚɧɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥɨ ɡɚɦɟɱɟɧɨ, ɱɬɨ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɫɬɚɛɢɥɨɝɪɚɦɦɟ ɫɩɨɤɨɣɧɨ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ ɩɪɢɫɭɬɫɬɜɭɸɬ ɤɨɥɟɛɚɧɢɹ ɧɚ ɱɚɫɬɨɬɟ ɩɪɢɦɟɪɧɨ 0.4 Ƚɰ. ɗɬɢ ɤɨɥɟɛɚɧɢɹ ɜɫɥɟɞ ɡɚ Ƚɭɪɮɢɧɤɟɥɟɦ [1] ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɨɫɧɨɜɧɵɦɢ ɤɨɥɟɛɚɧɢɹɦɢ. ȼ [22] ɜɵɫɤɚɡɚɧɨ ɩɪɟɞɩɨɥɨɠɟɊɢɫɭɧɨɤ 4. ɋɩɟɤɬɪɚɥɶɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɢɫɩɵɬɭɟɦɨɝɨ Ⱦȼ. ɀɢɪɧɢɟ, ɱɬɨ ɨɫɧɨɜɧɵɟ ɤɨɥɟɛɚɧɢɹ ɧɚɹ ɥɢɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ ɨɩɪɟɞɟɥɹɸɬɫɹ ɠɟɫɬɤɨɫɬɶɸ ɋɋ, ɬɨɧɤɚɹ - ɭɫɥɨɜɢɸ Ɉɉ. ɉɭɧɤɬɢɦɵɲɰ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɷɬɨɝɨ ɪɨɦ ɨɛɨɡɧɚɱɟɧɵ ɩɢɤɢ, ɫɨɨɬɜɟɬɫɬɩɚɪɚɦɟɬɪ ɠɟɫɬɤɨɫɬɢ N ɜ (4) ɜɭɸɳɢɟ ɨɫɧɨɜɧɵɦ ɤɨɥɟɛɚɧɢɹɦ. ɜɵɛɢɪɚɥɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɢɡɲɚɹ ɫɨɛɫɬɜɟɧɧɚɹ ɱɚɫɬɨɬɚ ɫɢɫɬɟɦɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɚ ɱɚɫɬɨɬɟ ɨɫɧɨɜɧɵɯ ɤɨɥɟɛɚɧɢɣ. Ȼɵɥɚ ɩɪɨɜɟɞɟɧɚ ɫɟɪɢɹ ɷɤɫɩɟɪɢɦɟɧɬɨɜ. ɉɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ ɞɥɹ ɤɚɠɞɨɝɨ ɢɫɩɵɬɭɟɦɨɝɨ ɦɟɬɨɞɨɦ ɫɬɪɨɢɥɢɫɶ ɞɜɟ ɫɩɟɤɬɪɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: ɞɥɹ ɭɫɥɨɜɢɹ ɋɋ ɢ ɞɥɹ ɭɫɥɨɜɢɹ Ɉɉ. ɉɪɢɦɟɪ ɫɩɟɤɬɪɚɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫɭɧɤɟ 4. ɉɨ ɫɩɟɤɬɪɚɥɶɧɵɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɨɩɪɟɞɟɥɹɥɢɫɶ ɱɚɫɬɨɬɵ ɨɫɧɨɜɧɵɯ ɤɨɥɟɛɚɧɢɣ (ɬɚɛɥɢɰɚ 8). Ɍɚɛɥɢɰɚ 8. ɂɋɉɕɌɍȿɆɕȿ ȺɁ ȺɌ ȼȻ ɋɋ 0.35 0.35 0.55 Ɉɉ 0.7 0.4 0.65 ɑɚɫɬɨɬɵ ɩɪɢɜɟɞɟɧɵ ɜ Ƚɟɪɰɚɯ. ɍɫɥɨɜɢɹ
Ⱦȼ 0.35 0.65
ȾɄ 0.3 0.4
ȾɌ 0.5 0.65
ɉɄ 0.25 0.4
ɉɌ 0.5 0.65
ɘɅ 0.25 0.35
ɫɪɟɞɧɟɟ 0.35 0.55
ɂɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɜɢɞɧɨ, ɱɬɨ: - ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɫɬɚɛɢɥɨɝɪɚɦɦɟ ɩɪɢɫɭɬɫɬɜɭɸɬ ɤɨɥɟɛɚɧɢɹ ɧɚ ɱɚɫɬɨɬɟ ɜ ɫɪɟɞɧɟɦ 0.4 Ƚɰ. 15
ɩɪɢ ɨɝɪɚɧɢɱɟɧɢɢ ɩɨɞɜɢɠɧɨɫɬɢ ɜ ɫɭɫɬɚɜɚɯ ɱɚɫɬɨɬɚ ɨɫɧɨɜɧɵɯ ɤɨɥɟɛɚɧɢɣ ɫɦɟɳɚɟɬɫɹ ɜ ɫɪɟɞɧɟɦ ɞɨ 0.6 Ƚɰ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɦɨɞɟɥɢ (3), (5), (6) ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɨɩɢɫɵɜɚɸɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɬɦɟɱɟɧɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɨɫɧɨɜɧɨɣ ɱɚɫɬɨɬɵ ɩɨɫɥɟ ɧɚɥɨɠɟɧɢɹ ɫɜɹɡɟɣ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɬɚɛɥɢɰɵ 7, ɬɪɟɯɡɜɟɧɧɚɹ ɦɨɞɟɥɶ (ɭɫɥɨɜɢɟ ɋɋ), ɭ ɤɨɬɨɪɨɣ ɧɢɡɲɚɹ ɱɚɫɬɨɬɚ ɪɚɜɧɹɟɬɫɹ ɩɪɢɦɟɪɧɨ 0.4 Ƚɰ, ɩɨɫɥɟ ɧɚɥɨɠɟɧɢɹ ɫɜɹɡɢ (2) ɩɟɪɟɯɨɞɢɬ ɜ ɦɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɊɢɫɭɧɨɤ 5. ɋɩɟɤɬɪɚɥɶɧɚɹ ɯɚɪɚɤɬɟɪɢɬɨɝɨ ɦɚɹɬɧɢɤɚ (ɭɫɥɨɜɢɟ ɫɬɢɤɚ ɢɫɩɵɬɭɟɦɨɝɨ ȺɁ. ɀɢɪɧɚɹ ɥɢɧɢɹ Ɉɉ), ɭ ɤɨɬɨɪɨɣ ɧɢɡɲɚɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ ɋɋ, ɬɨɧɤɚɹ ɱɚɫɬɨɬɚ ɪɚɜɧɚ ɩɪɢɦɟɪɧɨ ɭɫɥɨɜɢɸ Ɉɉ. ɉɭɧɤɬɢɪɨɦ ɨɛɨɡɧɚɱɟɧ ɩɢɤ, 0.6 Ƚɰ. ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɦ -
ɤɨɥɟɛɚɧɢɹɦ.
ȼɵɫɨɤɨɱɚɫɬɨɬɧɵɟ ɤɨɥɟɛɚɧɢɹ ȼ [1] ɩɪɢɜɟɞɟɧɵ ɞɚɧɧɵɟ ɨ ɧɚɥɢɱɢɢ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɫɬɚɛɢɥɨɝɪɚɦɦɟ ɫɩɨɤɨɣɧɨ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ ɤɨɥɟɛɚɧɢɣ ɫ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɨɣ (7-12 Ƚɰ) ɢ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɨɣ (ɜ ɞɟɫɹɬɤɢ ɪɚɡ ɦɟɧɶɲɟ, ɱɟɦ ɭ ɨɫɧɨɜɧɵɯ ɤɨɥɟɛɚɧɢɣ). Ⱥɧɚɥɢɡ ɷɥɟɤɬɪɨɦɢɨɝɪɚɦɦɵ (ɗɆȽ) ɢɤɪɨɧɨɠɧɨɣ ɦɵɲɰɵ [1] ɩɨɤɚɡɚɥ, ɱɬɨ ɜ ɗɆȽ ɩɪɢɫɭɬɫɬɜɭɸɬ ɜɫɩɵɲɤɢ ɚɤɬɢɜɧɨɫɬɢ, ɢɦɟɸɳɢɟ ɱɚɫɬɨɬɭ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɫɨɜɦɟɫɬɧɨɝɨ ɚɧɚɥɢɡɚ ɗɆȽ ɢ ɫɬɚɛɢɥɨɝɪɚɦɦɵ ɜ [1] ɫɞɟɥɚɧɨ ɡɚɤɥɸɱɟɧɢɟ ɨ ɤɨɪɪɟɥɢɪɨɜɚɧɧɨɫɬɢ ɦɚɤɫɢɦɭɦɨɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ (ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɦɟɳɟɧɢɸ ɰɟɧɬɪɚ ɞɚɜɥɟɧɢɹ ɜɩɟɪɟɞ) ɢ ɜɫɩɵɲɟɤ ɚɤɬɢɜɧɨɫɬɢ ɗɆȽ. ɇɚ ɜɤɥɚɞɤɟ ɩɪɢɜɟɞɟɧ ɪɢɫɭɧɨɤ I ɢɡ [1], ɢɥɥɸɫɬɪɢɪɭɸɳɢɣ ɨɩɢɫɚɧɧɵɟ ɹɜɥɟɧɢɹ. ɇɚɦɢ ɩɪɨɜɟɞɟɧɚ ɫɟɪɢɹ ɷɤɫɩɟɪɢɦɟɧɬɨɜ. Ⱥɧɚɥɢɡɢɪɨɜɚɥɢɫɶ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɟ (5-12 Ƚɰ) ɨɛɥɚɫɬɢ ɫɩɟɤɬɪɚ ɢɫɩɵɬɭɟɦɵɯ ɜ ɭɫɥɨɜɢɹɯ ɋɋ ɢ Ɉɉ. ɉɪɢɦɟɪɵ ɫɩɟɤɬɪɚɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫɭɧɤɟ 5. ȼ ɬɚɛɥɢɰɟ 9 ɩɪɢɜɟɞɟɧɵ ɱɚɫɬɨɬɵ ɡɚɦɟɬɧɵɯ ɩɢɤɨɜ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ. ɉɪɨɱɟɪɤ ɨɡɧɚɱɚɟɬ ɨɬɫɭɬɫɬɜɢɟ ɬɚɤɢɯ ɩɢɤɨɜ. ɍ ɜɫɟɯ ɢɫɩɵɬɭɟɦɵɯ, ɤɪɨɦɟ ɨɬɦɟɱɟɧɧɵɯ ɡɜɟɡɞɨɱɤɨɣ, ɜɟɥɢɱɢɧɚ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɩɢɤɨɜ ɜ ɭɫɥɨɜɢɢ ɋɋ ɜ ɞɜɚ ɢ ɛɨɥɟɟ ɪɚɡɚ ɜɵɲɟ, ɱɟɦ ɜ ɭɫɥɨɜɢɢ Ɉɉ.
16
Ɍɚɛɥɢɰɚ 9. ɂɋɉɕɌɍȿɆɕȿ ȺɁ ȺɌ ȼȻ* Ⱦȼ ȾɄ ȾɌ ɉɄ ɉɌ ɘɅ* ɫɪɟɞɧɟɟ ɋɋ 8 8 7 6 6.5 7.5 7 Ɉɉ 6.5 7 7 7.5 7 ɑɚɫɬɨɬɵ ɩɪɢɜɟɞɟɧɵ ɜ Ƚɟɪɰɚɯ. * ɍ ɷɬɢɯ ɢɫɩɵɬɭɟɦɵɯ ɜɟɥɢɱɢɧɚ ɩɢɤɚ ɜ ɭɫɥɨɜɢɢ ɋɋ ɦɟɧɶɲɟ ɱɟɦ ɜ Ɉɉ. ɍɫɥɨɜɢɹ
ɂɡ ɩɪɢɜɟɞɟɧɧɵɯ ɞɚɧɧɵɯ ɫɥɟɞɭɟɬ: - ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɫɬɚɛɢɥɨɝɪɚɦɦɟ ɩɪɢɫɭɬɫɬɜɭɸɬ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɟ ɤɨɥɟɛɚɧɢɹ. - ɦɚɤɫɢɦɭɦɚɦ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɫɩɵɲɤɚɦ ɚɤɬɢɜɧɨɫɬɢ ɜ ɗɆȽ. - ɚɦɩɥɢɬɭɞɚ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ ɫɬɚɧɨɜɢɬɫɹ ɡɚɦɟɬɧɨ ɦɟɧɶɲɟ ɩɨɫɥɟ ɡɚɤɪɟɩɥɟɧɢɹ ɤɨɥɟɧɧɨɝɨ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɝɨ ɫɭɫɬɚɜɨɜ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɬɚɛɥɢɰɵ 7, ɜɵɫɲɚɹ ɫɨɛɫɬɜɟɧɧɚɹ ɱɚɫɬɨɬɚ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɢ ɪɚɜɧɚ 9 Ƚɰ, ɬ.ɟ. ɥɟɠɢɬ ɜ ɭɤɚɡɚɧɧɨɦ ɜ [1] ɞɢɚɩɚɡɨɧɟ ɢ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɢɡ ɬɚɛɥɢɰɵ 9. ɋɨɛɫɬɜɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ ɩɪɢɜɨɞɹɬ ɤ ɤɨɥɟɛɚɧɢɹɦ ɞɥɢɧɵ ɢɤɪɨɧɨɠɧɨɣ ɦɵɲɰɵ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (1), ɩɪɢɜɨɞɢɬ ɤ ɤɨɥɟɛɚɧɢɹɦ ɪɚɡɜɢɜɚɟɦɨɣ ɦɵɲɰɟɣ ɭɫɢɥɢɣ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɗɆȽ. ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɫɬɚɛɢɥɨɝɪɚɦɦɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɦɨɦɟɧɬɭ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ [12]. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɨɪɪɟɥɢɪɨɜɚɧɧɨɫɬɶ ɗɆȽ ɢ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɦɨɞɟɥɶɸ Ɏɟɥɶɞɦɚɧɚ. Ɉɝɪɚɧɢɱɟɧɢɸ ɩɨɞɜɢɠɧɨɫɬɢ ɫɭɫɬɚɜɨɜ (ɭɫɥɨɜɢɟ Ɉɉ) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɬɚɛɥɢɰɵ 7, ɦɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ ɢɦɟɟɬ ɨɞɧɭ ɱɚɫɬɨɬɭ ɩɪɢɦɟɪɧɨ 0.6 Ƚɰ. ɋɨɝɥɚɫɧɨ ɦɨɞɟɥɢ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ, ɜ ɭɫɥɨɜɢɢ Ɉɉ ɧɟ ɞɨɥɠɧɵ ɧɚɛɥɸɞɚɬɶɫɹ ɩɢɤɢ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ. ɉɨɫɤɨɥɶɤɭ ɜ ɯɨɞɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɧɟɥɶɡɹ ɩɨɥɧɨɫɬɶɸ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɫɭɫɬɚɜɵ, ɷɬɢ ɩɢɤɢ ɫɨɯɪɚɧɹɸɬɫɹ, ɧɨ ɢɯ ɜɟɥɢɱɢɧɚ ɡɚɦɟɬɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɭ ɛɨɥɶɲɢɧɫɬɜɚ ɢɫɩɵɬɭɟɦɵɯ. Ɉɛɫɭɠɞɟɧɢɟ ɋɪɚɜɧɟɧɢɟ ɦɨɞɟɥɟɣ ɇɚ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɦɟɯɚɧɢɡɦɨɜ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɟɬɫɹ ɦɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɪɟɞɥɨɠɟɧɵ ɞɜɟ ɦɨɞɟɥɢ: ɬɪɟɯɡɜɟɧɧɚɹ ɦɨɞɟɥɶ ɢ ɩɪɢɛɥɢɠɟɧɧɚɹ ɬɪɟɯɡɜɟɧɧɚɹ ɦɨɞɟɥɶ. ɋɪɚɜɧɢɦ ɬɪɢ ɭɤɚɡɚɧɧɵɟ ɦɨɞɟɥɢ. 17
Ɇɨɞɟɥɶ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ ɜɵɫɨɤɨɣ ɧɚɝɥɹɞɧɨɫɬɶɸ ɢ ɩɪɨɫɬɨɬɨɣ. Ɉɧɚ ɨɩɢɫɵɜɚɟɬɫɹ ɨɞɧɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ. Ɇɨɞɟɥɶ ɧɟɩɪɢɦɟɧɢɦɚ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɦɟɞɥɟɧɧɵɯ ɞɜɢɠɟɧɢɣ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɨɡɦɭɳɟɧɢɣ ɢɦɟɸɳɢɯ ɦɚɥɵɟ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ [3]. Ɇɨɞɟɥɶ ɧɟ ɩɨɡɜɨɥɹɟɬ ɪɚɡɥɢɱɚɬɶ ɫɬɟɩɟɧɶ ɭɱɚɫɬɢɹ ɪɚɡɥɢɱɧɵɯ ɦɵɲɰ ɜ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɬɟɥɚ ɱɟɥɨɜɟɤɚ. Ɍɪɟɯɡɜɟɧɧɚɹ ɦɨɞɟɥɶ ɨɩɢɫɵɜɚɟɬ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ ɫ ɭɱɟɬɨɦ ɩɨɞɜɢɠɧɨɫɬɢ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ, ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ. Ɇɨɞɟɥɶ ɩɨɡɜɨɥɹɟɬ ɨɩɢɫɚɬɶ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɜ ɫɩɟɤɬɪɟ ɫɩɨɤɨɣɧɨ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ. Ɇɨɞɟɥɶ ɩɪɢɦɟɧɢɦɚ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɜɢɠɟɧɢɣ, ɢɦɟɸɳɢɯ ɲɢɪɨɤɢɣ ɞɢɚɩɚɡɨɧ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧ (ɨɬ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɫɟɤɭɧɞɵ ɞɨ ɫɟɤɭɧɞ). Ɇɨɞɟɥɶ ɩɨɡɜɨɥɹɟɬ ɪɚɡɥɢɱɚɬɶ ɫɬɟɩɟɧɶ ɭɱɚɫɬɢɹ ɪɚɡɥɢɱɧɵɯ ɦɵɲɰ ɜ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɬɟɥɚ ɱɟɥɨɜɟɤɚ. Ɇɨɞɟɥɶ ɨɩɢɫɵɜɚɟɬɫɹ ɫɢɫɬɟɦɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɲɟɫɬɨɝɨ ɩɨɪɹɞɤɚ. ȼɵɫɨɤɢɣ ɩɨɪɹɞɨɤ ɭɪɚɜɧɟɧɢɣ ɦɨɞɟɥɢ ɡɚɬɪɭɞɧɹɟɬ ɟɟ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ. ɉɪɢɛɥɢɠɟɧɧɚɹ ɬɪɟɯɡɜɟɧɧɚɹ ɦɨɞɟɥɶ ɹɜɥɹɟɬɫɹ ɩɪɨɫɬɨɣ ɢ ɧɚɝɥɹɞɧɨɣ. Ɉɧɚ ɨɩɢɫɵɜɚɟɬɫɹ ɨɞɧɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɢ ɞɜɭɦɹ ɥɢɧɟɣɧɵɦɢ ɚɥɝɟɛɪɚɢɱɟɫɤɢɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ. Ɇɨɞɟɥɶ ɩɨɡɜɨɥɹɟɬ ɭɱɟɫɬɶ ɢɡɦɟɧɟɧɢɟ ɭɝɥɨɜ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ, ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɪɢ ɫɬɨɹɧɢɢ ɢ ɪɚɡɥɢɱɚɬɶ ɫɬɟɩɟɧɶ ɭɱɚɫɬɢɹ ɪɚɡɥɢɱɧɵɯ ɦɵɲɰ ɜ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɬɟɥɚ ɱɟɥɨɜɟɤɚ. Ɇɨɞɟɥɶ ɩɪɢɦɟɧɢɦɚ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɦɟɞɥɟɧɧɵɯ ɞɜɢɠɟɧɢɣ ɧɚ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧɚɯ ɩɨɪɹɞɤɚ ɫɟɤɭɧɞ. Ɉ ɫɜɹɡɢ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɢ ɫɢɧɟɪɝɢɣ Ɉɛɳɟɟ ɪɟɲɟɧɢɟ ɫɢɫɬɟɦɵ (4) ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɤɚɤ ɫɭɦɦɚ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ. Ʉɚɱɟɫɬɜɟɧɧɵɣ ɜɢɞ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɤɨɥɟɛɚɧɢɣ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫɭɧɤɟ 6. ȼ ɫɢɥɭ ɫɢɫɬɟɦɵ (4), ɩɪɨɢɡɜɨɥɶɧɨɟ ɦɚɥɨɟ ɨɬɤɥɨɧɟɧɢɟ ɱɟɥɨɜɟɤɚ ɨɬ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɤɚɤ ɫɭɩɟɪɩɨɡɢɰɢɹ ɨɬɤɥɨɧɟɧɢɣ ɩɨ ɫɨɛɫɬɜɟɧɧɵɦ ɮɨɪɦɚɦ [8]. Ɇɨɠɧɨ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɞɜɢɝɚɬɟɥɶɧɵɟ ɫɢɧɟɪɝɢɢ ɩɨ Ȼɟɪɧɲɬɟɣɧɭ [11] ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɫɨɛɫɬɜɟɧɧɵɦ ɮɨɪɦɚɦ ɤɨɥɟɛɚɧɢɣ. ɂɧɚɱɟ ɝɨɜɨɪɹ, ɧɟɪɜɧɚɹ ɫɢɫɬɟɦɚ "ɤɨɧɫɬɪɭɢɪɭɟɬ" ɩɪɨɢɡɜɨɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɢɡ ɨɬɤɥɨɧɟɧɢɣ 18
ɧɢɡɲɚɹ
ɫɪɟɞɧɹɹ
ɜɵɫɲɚɹ
Ɋɢɫɭɧɨɤ 6. Ƚɪɚɮɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɤɨɥɟɛɚɧɢɣ ɬɪɟɯɡɜɟɧɧɨɣ ɦɨɞɟɥɢ.
ɩɨ ɫɨɛɫɬɜɟɧɧɵɦ ɮɨɪɦɚɦ. ɋɨɨɛɪɚɠɟɧɢɹ ɨ ɫɜɹɡɢ ɞɜɢɝɚɬɟɥɶɧɵɯ ɫɢɧɟɪɝɢɣ ɢ ɫɨɛɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɨɩɢɫɵɜɚɸɳɟɣ ɬɟɥɨ ɱɟɥɨɜɟɤɚ, ɜɵɫɤɚɡɵɜɚɥɢɫɶ ɪɚɧɟɟ ɜ [7]. ȼ ɷɬɨɣ ɫɬɚɬɶɟ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɢ ɫɨɛɫɬɜɟɧɧɵɟ ɮɨɪɦɵ, ɜɨɡɧɢɤɚɸɳɢɟ ɥɢɲɶ ɡɚ ɫɱɟɬ ɫɢɥɵ ɬɹɠɟɫɬɢ – ɛɟɡ ɭɱɟɬɚ ɦɵɲɟɱɧɵɯ ɜɨɡɞɟɣɫɬɜɢɣ ȼɵɜɨɞɵ ȼ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɩɨɫɬɪɨɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ, ɭɱɢɬɵɜɚɸɳɚɹ ɨɫɨɛɟɧɧɨɫɬɢ ɫɤɟɥɟɬɧɨ-ɦɵɲɟɱɧɨɝɨ ɚɩɩɚɪɚɬɚ. ɉɪɨɜɟɞɟɧɚ ɫɟɪɢɹ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɜ ɯɨɞɟ ɤɨɬɨɪɨɣ ɚɧɚɥɢɡɢɪɨɜɚɥɨɫɶ ɜɥɢɹɧɢɟ ɨɝɪɚɧɢɱɟɧɢɹ ɩɨɞɜɢɠɧɨɫɬɢ ɜ ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɧɚ ɱɚɫɬɨɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ. ɉɨɫɬɪɨɟɧɚ ɩɪɢɛɥɢɠɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ, ɨɛɥɚɞɚɸɳɚɹ ɩɪɨɫɬɨɬɨɣ ɦɨɞɟɥɢ ɩɟɪɟɜɟɪɧɭɬɨɝɨ ɦɚɹɬɧɢɤɚ ɢ ɭɱɢɬɵɜɚɸɳɚɹ ɩɨɞɜɢɠɧɨɫɬɶ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ, ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ. ȼɵɫɤɚɡɚɧɚ ɝɢɩɨɬɟɡɚ ɨ ɫɜɹɡɢ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɤɨɥɟɛɚɧɢɣ ɢ ɫɢɧɟɪɝɢɣ ɩɨ Ȼɟɪɧɲɬɟɣɧɭ. Ɋɚɛɨɬɚ ɨɫɭɳɟɫɬɜɥɟɧɚ ɩɪɢ ɩɨɞɞɟɪɠɤɟ ɊɎɎɂ (ɝɪɚɧɬ 02-0448234). Ʌɢɬɟɪɚɬɭɪɚ 1. 2.
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Ƚɭɪɮɢɧɤɟɥɶ ȼ. ɋ., Ʉɨɰ ə. Ɇ., ɒɢɤ Ɇ. Ʌ. Ɋɟɝɭɥɹɰɢɹ ɩɨɡɵ ɱɟɥɨɜɟɤɚ. - Ɇ. ɇɚɭɤɚ, 1965. Winter D. A., Patla A. E., Rietdyk S., Ishac M. G. Ankle muscle stiffness in the control of balance during quiet standing.// J Neurophysiology, 85(6), 2001. Horak F. B., Nashner L. M. Central programming of postural movements: adaptation to altered support surface configurations.// J Neurophysiology, 62, 1986. Collins J. J., De Luca C. J. Open-loop and close-loop control of posture: a random walk analysis of center-of-pressure trajectories.// Experimental Brain Research 95, 1993. Gurfinkel V. S., Ivanenko Yu. P., Levik Yu. S., Babakova I. A. Kinesthetic reference for human orthograde posture.// Neuroscience, 68(1), 1995. Morasso P. G., Baratto L., Capra R., Spada G. Internal models in the control of posture.// Neural Networks 12, 1999. Alexandrov A. V., Frolov A. A., Horak F. B., Carlson-Kuhta P., Park S. Strategies of feedback equilibrium control during human upright standing.// J Biomechanics, in press. 19
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Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ ɩɪɢ ɦɟɞɥɟɧɧɵɯ ɜɨɡɦɭɳɟɧɢɹɯ ɨɫɧɨɜɚɧɢɹ.
Ⱥ. ȼ. Ɍɟɪɟɯɨɜ ɆȽɍ ɢɦ. Ɇ.ȼ.Ʌɨɦɨɧɨɫɨɜɚ Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɞɚɱɚ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ ɜ ɫɚɝɝɢɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ. Ⱥɧɚɥɢɡ ɫɩɟɤɬɪɚ ɷɬɨɝɨ ɞɜɢɠɟɧɢɹ ɨɛɧɚɪɭɠɢɜɚɟɬ ɩɪɢɫɭɬɫɬɜɢɟ ɧɢɡɤɨɱɚɫɬɨɬɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ (ɧɢɠɟ 0.2Ƚɰ) [1]. ȼ [2] ɩɪɢɜɟɞɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɩɨɡɜɨɥɹɸɳɢɯ ɜɵɞɟɥɢɬɶ ɞɜɢɠɟɧɢɹ ɫ ɛɨɥɶɲɢɦɢ ɯɚɪɚɤɬɟɪɧɵɦɢ ɜɪɟɦɟɧɚɦɢ (ɩɨɪɹɞɤɚ ɞɟɫɹɬɤɨɜ ɫɟɤɭɧɞ). ȼ [3] ɜɵɫɤɚɡɚɧɨ ɩɪɟɞɩɨɥɨɠɟɧɢɟ, ɱɬɨ ɫɬɚɛɢɥɢɡɚɰɢɹ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ ɨɪɝɚɧɢɡɨɜɚɧɚ ɢɟɪɚɪɯɢɱɟɫɤɢ ɢ ɨɛɪɚɡɨɜɚɧɚ, ɩɨ ɦɟɧɶɲɟɣ ɦɟɪɟ, ɞɜɭɦɹ ɭɪɨɜɧɹɦɢ: ɩɟɪɜɵɣ ɨɬɜɟɱɚɟɬ ɡɚ ɡɚɞɚɧɢɟ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ, ɜ ɤɨɬɨɪɨɣ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɨɰɟɫɫ ɫɬɚɛɢɥɢɡɚɰɢɢ, ɜɬɨɪɨɣ ɪɟɚɥɢɡɭɟɬ ɩɪɨɰɟɫɫ ɫɬɚɛɢɥɢɡɚɰɢɢ. ɋɨɝɥɚɫɧɨ [2], ɧɢɡɤɨɱɚɫɬɨɬɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɞɜɢɠɟɧɢɹ ɦɨɝɭɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɪɚɛɨɬɟ ɩɟɪɜɨɝɨ ɭɪɨɜɧɹ ɫɬɚɛɢɥɢɡɚɰɢɢ. ɇɢɠɟ ɩɪɟɞɥɚɝɚɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ, ɩɨɡɜɨɥɹɸɳɚɹ ɨɩɢɫɚɬɶ ɭɤɚɡɚɧɧɵɟ ɧɢɡɤɨɱɚɫɬɨɬɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɞɜɢɠɟɧɢɹ ɢ ɭɱɢɬɵɜɚɸɳɚɹ ɩɪɟɞɥɨɠɟɧɧɭɸ ɜ [3] ɫɬɪɭɤɬɭɪɭ ɭɩɪɚɜɥɟɧɢɹ ɫɬɚɛɢɥɢɡɚɰɢɟɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ. Ɉɩɢɫɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɗɤɫɩɟɪɢɦɟɧɬ, ɨɩɢɫɚɧɧɵɣ ɜ ɪɚɛɨɬɟ [2] ɫɨɫɬɨɢɬ ɜ ɫɥɟɞɭɸɳɟɦ. ɂɫɩɵɬɭɟɦɵɣ ɫɬɨɢɬ ɫ ɡɚɤɪɵɬɵɦɢ ɝɥɚɡɚɦɢ ɧɚ ɢɡɧɚɱɚɥɶɧɨ ɧɟɩɨɞɜɢɠɧɨɣ ɩɥɚɬɮɨɪɦɟ (ɪɢɫɭɧɨɤ 1). ɉɥɚɬɮɨɪɦɚ ɧɚɤɥɨɧɹɟɬɫɹ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɥɢɛɨ ɪɚɜɧɨɦɟɪɧɨ ɧɚ 1q ɡɚ 20 ɫɟɤɭɧɞ, ɥɢɛɨ ɩɨ ɫɢɧɭɫɨɢɞɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɚɦɩɥɢɬɭɞɨɣ 1.5q ɢ ɩɟɪɢɨɞɨɦ 160 ɫɟɤɭɧɞ. ɂɡɦɟɪɹɟɬɫɹ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɤɨɪɩɭɫɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɥɚɬɮɨɪɦɵ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɪɬɢɤɚɥɢ ɩɨ ɥɢɧɟɣɧɵɦ ɫɦɟɳɟɧɢɹɦ ɯɚɪɚɤɬɟɪɧɵɯ ɬɨɱɟɤ ɝɪɭɞɢ ɢ ɝɨɥɟɧɢ. Ⱥɧɚɥɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɩɨɤɚɡɵɜɚɟɬ: 1) ȼ ɫɥɭɱɚɟ ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɜɨɡɦɭɳɟɧɢɹ
Ɋɢɫɭɧɨɤ 1. ɍɫɥɨɜɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ (ɪɢɫɭɧɨɤ ɢɡ [2]). 21
ɱɟɥɨɜɟɤ ɨɬɤɥɨɧɹɟɬɫɹ ɨɬ ɜɟɪɬɢɤɚɥɢ ɩɨ ɡɚɤɨɧɭ, ɛɥɢɡɤɨɦɭ ɤ ɫɢɧɭɫɨɢɞɚɥɶɧɨɦɭ, ɫ ɬɨɣ ɠɟ ɱɚɫɬɨɬɨɣ, ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ ɩɨ ɚɦɩɥɢɬɭɞɟ ɜ ɩɪɟɞɟɥɚɯ 0.5-2.0 ɢ ɫ ɨɬɫɬɚɜɚɧɢɟɦ ɩɨ ɮɚɡɟ ɜ ɩɪɟɞɟɥɚɯ 270q 330q . Ʉɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɢ ɮɚɡɨɜɵɣ ɫɞɜɢɝ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɵɦɢ ɞɥɹ ɤɚɠɞɨɝɨ ɢɫɩɵɬɭɟɦɨɝɨ. 2) ȼ ɫɥɭɱɚɟ ɪɚɜɧɨɦɟɪɧɨɝɨ ɧɚɤɥɨɧɚ ɩɥɚɬɮɨɪɦɵ ɧɚɛɥɸɞɚɥɢɫɶ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ, ɛɥɢɡɤɢɟ ɤ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɦ ɫ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɨɤɨɥɨ 10 ɫ (ɪɢɫɭɧɨɤ 3). ȼ [2] ɜɵɫɤɚɡɚɧɨ ɩɪɟɞɩɨɥɨɠɟɧɢɟ, ɱɬɨ ɧɚɛɥɸɞɚɟɦɵɟ ɮɚɡɨɜɵɟ ɫɞɜɢɝɢ ɢ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɨɛɴɹɫɧɹɸɬɫɹ ɛɨɥɶɲɢɦɢ ɩɨɫɬɨɹɧɧɵɦɢ ɜɪɟɦɟɧɢ, ɩɪɢɫɭɳɢɦɢ ɭɪɨɜɧɸ ɩɨɫɬɪɨɟɧɢɹ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ. ȼ ɫɬɚɬɶɟ ɜɵɫɤɚɡɚɧɨ ɬɚɤɠɟ ɩɪɟɞɩɨɥɨɠɟɧɢɟ, ɱɬɨ ɜ ɨɩɢɫɚɧɧɨɦ ɷɤɫɩɟɪɢɦɟɧɬɟ ɟɞɢɧɫɬɜɟɧɧɨɣ ɞɨɫɬɭɩɧɨɣ ɞɥɹ ɨɛɨɢɯ ɭɪɨɜɧɟɣ ɚɮɮɟɪɟɧɬɧɨɣ ɢɧɮɨɪɦɚɰɢɟɣ ɹɜɥɹɟɬɫɹ ɩɪɨɩɪɢɨɰɟɩɬɢɜɧɚɹ (ɢɧɮɨɪɦɚɰɢɹ ɨɬ ɦɵɲɟɱɧɵɯ, ɫɭɯɨɠɢɥɶɧɵɯ, ɫɭɫɬɚɜɧɵɯ ɪɟɰɟɩɬɨɪɨɜ ɢ ɨɬ ɪɟɰɟɩɬɨɪɨɜ ɞɚɜɥɟɧɢɹ ɫɬɨɩɵ). Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ Ɍɟɥɨ ɱɟɥɨɜɟɤɚ ɦɨɞɟɥɢɪɭɟɬɫɹ ɠɟɫɬɤɢɦ ɫɬɟɪɠɧɟɦ, ɫɨɜɟɪɲɚɸɳɢɦ ɩɥɨɫɤɢɟ ɜɪɚɳɟɧɢɹ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ (ɪɢɫɭɧɨɤ 2). Ɂɞɟɫɶ T - ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɩɪɹɦɨɣ, ɫɨɟɞɢɧɹɸɳɟɣ ɰɟɧɬɪ ɦɚɫɫ ɬɟɥɚ ɫ ɫɭɫɬɚɜɨɦ, ɨɬ ɜɟɪɬɢɤɚɥɢ, D - ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɫɧɨɜɚɧɢɹ, E - ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɬɟɥɚ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɧɨɜɚɧɢɹ. Ɍɨɝɞɚ T E D . ȼ ɫɢɥɭ ɦɚɥɨɫɬɢ ɭɝɥɨɜ ( D , E , T ), ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɥɢɧɟɣɧɨɟ ɩɪɢɛɥɢɠɟɧɢɟ Ɋɢɫɭɧɨɤ 2. Ɇɨɞɟɥɶ ɬɟɥɚ ɩɨ ɷɬɢɦ ɭɝɥɚɦ. ɱɟɥɨɜɟɤɚ (ɪɢɫɭɧɨɤ ɢɡ [2]). ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ ɫɬɚɛɢɥɢɡɢɪɭɟɬɫɹ ɡɚ ɫɱɟɬ ɦɨɦɟɧɬɚ M , ɫɨɡɞɚɜɚɟɦɨɝɨ ɦɵɲɰɚɦɢ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ. ɋɬɨɩɚ ɫɱɢɬɚɟɬɫɹ ɧɟɩɨɞɜɢɠɧɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɥɚɬɮɨɪɦɵ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɨɞɟɥɶ Ɏɟɥɶɞɦɚɧɚ [4], ɱɬɨ ɜ ɫɥɭɱɚɟ ɦɚɥɵɯ ɭɝɥɨɜ ɞɚɟɬ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ:
M K( E u ) RE
22
ɝɞɟ K - ɤɨɷɮɮɢɰɢɟɧɬ ɠɟɫɬɤɨɫɬɢ, R - ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ, u ɭɩɪɚɜɥɹɸɳɢɣ ɩɚɪɚɦɟɬɪ. Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ:
IE
mghE - K( E u ) - RE mghD ID
(1)
ɡɞɟɫɶ I - ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ ɱɟɥɨɜɟɤɚ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɝɨɥɟɧɨɫɬɨɩɧɵɟ ɫɭɫɬɚɜɵ, m - ɦɚɫɫɚ ɱɟɥɨɜɟɤɚ, h - ɜɵɫɨɬɚ ɰɟɧɬɪɚ ɦɚɫɫ. Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɪɟɚɥɢɡɚɰɢɹ ɜɬɨɪɨɝɨ ɭɪɨɜɧɹ ɫɬɚɛɢɥɢɡɚɰɢɢ, ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɦɨɦɟɧɬɚ ɭɩɪɭɝɨ-ɜɹɡɤɢɯ ɫɢɥ. Ɍɨɝɞɚ, ɩɨɬɪɟɛɭɟɦ K ! mgh ɢ R ! 0 . Ɂɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ K ɢ R ɜɵɛɢɪɚɸɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɨɛɳɟɟ ɪɟɲɟɧɢɟ ɫɢɫɬɟɦɵ (1) ɢɦɟɥɨ ɫɥɚɛɨɡɚɬɭɯɚɸɳɢɣ ɤɨɥɟɛɚɬɟɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɫ ɱɚɫɬɨɬɨɣ 0.3 Ƚɰ. ɋɨɝɥɚɫɧɨ [1] ɷɬɚ ɱɚɫɬɨɬɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɫɧɨɜɧɵɦ ɤɨɥɟɛɚɧɢɹɦ ɫɩɨɤɨɣɧɨ ɫɬɨɹɳɟɝɨ ɱɟɥɨɜɟɤɚ. ɉɪɟɞɩɨɥɨɠɢɦ ɬɚɤɠɟ, ɱɬɨ ɜ ɩɟɪɜɨɦ ɭɪɨɜɧɟ ɫɬɚɛɢɥɢɡɚɰɢɢ ɮɨɪɦɢɪɭɟɬɫɹ ɭɩɪɚɜɥɟɧɢɟ u , ɞɨɫɬɚɜɥɹɸɳɟɟ ɨɰɟɧɤɭ D~ ɨɬɤɥɨɧɟɧɢɹ ɩɥɚɬɮɨɪɦɵ ɨɬ ɝɨɪɢɡɨɧɬɚ, ɬ. ɟ. ɮɨɪɦɢɪɭɟɬɫɹ ɦɨɞɟɥɶ "ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ". ɉɪɢɦɟɦ
u D~
(2)
Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɨɰɟɧɤɢ D~ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɟɬɨɞɚɦɢ ɚɞɚɩɬɢɜɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɢɡ [5]. ɋɨɝɥɚɫɧɨ ɩɪɟɞɥɨɠɟɧɧɨɣ ɜ [5] ɫɯɟɦɟ, ɧɟɨɛɯɨɞɢɦɨ ɡɚɞɚɬɶ ɰɟɥɟɜɭɸ ɮɭɧɤɰɢɸ ɭɩɪɚɜɥɟɧɢɹ. ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɡɚɞɚɱɟ ɜ ɤɚɱɟɫɬɜɟ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɟɫɬɟɫɬɜɟɧɧɨ ɩɪɢɧɹɬɶ ɜɟɥɢɱɢɧɭ ɤɜɚɞɪɚɬɚ ɨɬɤɥɨɧɟɧɢɹ ɤɨɪɩɭɫɚ ɨɬ ɜɟɪɬɢɤɚɥɢ.
Q
1 2 T 2
1 (E D ) 2 2
(3)
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ D - ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨ. ɍɤɚɡɚɧɧɨɟ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɞɥɹ ɭɫɥɨɜɢɣ ɷɤɫɩɟɪɢɦɟɧɬɚ [2] ɜɵɩɨɥɧɟɧɨ, ɬ.ɤ. ɜɨɡɦɭɳɟɧɢɟ ɩɨ D ɫɭɳɟɫɬɜɟɧɧɨ ɛɨɥɟɟ ɦɟɞɥɟɧɧɨɟ, ɱɟɦ ɫɨɛɫɬɜɟɧɧɨɟ ɞɜɢɠɟɧɢɟ ɫɢɫɬɟɦɵ (1) ɩɨ E . ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɦɟɬɨɞɢɤɚɦɢ [5], ɨɰɟɧɤɭ ɞɥɹ Į ɢɳɟɦ ɜ ɜɢɞɟ
w d 2Q
D~ A ~ 2 wD dt
(4)
23
ɝɞɟ ɩɪɨɢɡɜɨɞɧɵɟ ɜɵɱɢɫɥɹɸɬɫɹ ɜ ɫɢɥɭ ɭɪɚɜɧɟɧɢɣ (1), (2). ɉɪɨɞɟɥɚɜ ɜɵɱɢɫɥɟɧɢɹ, ɩɨɥɭɱɢɦ ɧɚ ɨɫɧɨɜɚɧɢɢ (1)-(4)
D~
1 ( E D~ ) T
(5)
ɝɞɟ T - ɧɟɤɨɬɨɪɚɹ ɩɨɥɨɠɢɬɟɥɶɧɚɹ ɤɨɧɫɬɚɧɬɚ ɪɚɡɦɟɪɧɨɫɬɢ ɜɪɟɦɟɧɢ. ɋɥɟɞɭɟɬ ɡɚɦɟɬɢɬɶ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɦɨɞɟɥɢ Ɏɟɥɶɞɦɚɧɚ [4], ɜɟɥɢɱɢɧɚ E D~ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɚɤɬɢɜɧɨɫɬɢ ɦɨɬɨɧɟɣɪɨɧɧɨɝɨ ɩɭɥɚ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɰɟɧɬɪɚɥɶɧɵɦɢ ɭɫɬɚɧɨɜɤɚɦɢ D~ ɢ ɢɧɮɨɪɦɚɰɢɟɣ ɨɬ ɩɪɨɩɪɢɨɰɟɩɬɨɪɨɜ E . Ⱥɧɚɥɨɝɢɱɧɵɣ ɚɥɝɨɪɢɬɦ ɫɬɚɛɢɥɢɡɚɰɢɢ ɩɪɟɞɥɨɠɟɧ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɪɨɜɟɪɟɧ ɜ [6] ɞɥɹ ɭɩɪɚɜɥɟɧɢɹ ɪɨɛɨɬɨɦ. Ⱦɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɢɫɬɟɦɵ (1), (2), (5) ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɜɵɩɨɥɧɹɥɨɫɶ ɫɨɨɬɧɨɲɟɧɢɟ (6):
T!
I K R K mgh
(6)
ɉɨɫɤɨɥɶɤɭ ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɢɧɬɟɪɟɫ ɩɪɨɰɟɫɫɵ ɢɦɟɸɬ ɛɨɥɶɲɢɟ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ, ɱɟɦ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɦɚɹɬɧɢɤɚ ɢɡ (1), ɬɨ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɩɪɢɛɥɢɠɟɧɧɭɸ ɦɨɞɟɥɶ, ɨɩɢɫɵɜɚɸɳɭɸ ɦɟɞɥɟɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɷɬɨɝɨ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɟɬɨɞɚɦɢ ɢɡ [7]. ɉɪɢɛɥɢɠɟɧɧɚɹ ɦɨɞɟɥɶ ɨɩɢɫɵɜɚɟɬɫɹ ɨɞɧɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ:
§ K mgh · ¸¸T T T¨¨ © mgh ¹
§ K · ¸¸D T¨¨ © mgh ¹
(7)
Ɋɟɡɭɥɶɬɚɬɵ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɥɹ ɫɥɭɱɚɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɧɚɤɥɨɧɚ ɩɥɚɬɮɨɪɦɵ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫɭɧɤɟ 4. ɂɫɩɨɥɶɡɨɜɚɥɢɫɶ ɫɥɟɞɭɸɳɢɟ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ:
mgh 800 ɇ ɦ I 100ɤɝ ɦ 2 T 15ɫ K 1200 ɇ ɦ R
24
30 ɇ ɦ/ɫ
ɉɪɢ ɜɵɛɨɪɟ ɦɚɫɫ-ɢɧɟɪɰɢɨɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɞɚɧɧɵɟ ɢɡ [8]. ɇɚ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɟɞɢɧɨɝɨ ɦɧɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɧɚɱɟɧɢɣ ɭɩɪɭɝɨ-ɜɹɡɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɦɨɦɟɧɬɚ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ ɩɪɢ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ (ɫɦ. [9-10]). ɉɨɷɬɨɦɭ ɩɚɪɚɦɟɬɪɵ K , R , T ɢɞɟɧɬɢɮɢɰɢɪɨɜɚɥɢɫɶ ɩɨ ɞɚɧɧɵɦ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢɡ [2] ɜ ɪɚɦɤɚɯ ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ (1), (2), (5). ɉɚɪɚɦɟɬɪ K ɜɵɛɪɚɧ ɢɡ ɭɫɥɨɜɢɹ, ɱɬɨ ɫɨɛɫɬɜɟɧɧɚɹ ɱɚɫɬɨɬɚ ɭɪɚɜɧɟɧɢɹ (1) ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɨɣ 0.3Ƚɰ (ɫɦ. ɜɵɲɟ). ɉɚɪɚɦɟɬɪ T ɨɩɪɟɞɟɥɢɥɫɹ ɝɪɚɮɢɤɚɦɢ ɧɚ ɪɢɫɭɧɤɟ 3. Ʉɨɷɮɮɢɰɢɟɧɬ R ɧɟ ɜɯɨɞɢɬ ɜ ɭɪɚɜɧɟɧɢɟ (7), ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɬɪɟɧɢɟ ɧɟɫɭɳɟɫɬɜɟɧɧɨ ɫɤɚɡɵɜɚɟɬɫɹ ɧɚ ɦɟɞɥɟɧɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɞɜɢɠɟɧɢɹ. ɉɪɢ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɟ T , ɤɨɷɮɮɢɰɢɟɧɬ R ɨɩɪɟɞɟɥɹɥɫɹ ɢɡ (6). ȼ ɫɥɭɱɚɟ ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɜɨɡɦɭɳɟɧɢɹ ɱɢɫɥɟɧɧɨɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦɵ (1), (2), (5) ɢ ɭɪɚɜɧɟɧɢɹ (7) ɩɨɤɚɡɚɥ, ɱɬɨ ɩɪɢ ɜɵɛɪɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɩɚɪɚɦɟɬɪɨɜ ɡɚɩɚɡɞɵɜɚɧɢɟ ɩɨ ɮɚɡɟ ɩɟɪɟɦɟɧɧɨɣ T ɨɬɧɨɫɢɬɟɥɶɧɨ D ɫɨɫɬɚɜɥɹɟɬ 285q , ɱɬɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɢɡ [2]. ȼɵɜɨɞɵ ɉɪɟɞɥɨɠɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɨɩɢɫɵɜɚɟɬ ɪɟɡɭɥɶɬɚɬɵ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɢɡ [2]. Ɇɨɞɟɥɶ ɭɱɢɬɵɜɚɟɬ ɝɢɩɨɬɟɡɭ ɨ ɞɜɭɯɭɪɨɜɧɟɜɨɣ ɫɬɪɭɤɬɭɪɟ ɦɟɯɚɧɢɡɦɚ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ [3]. Ⱥɥɝɨɪɢɬɦ ɫɬɚɛɢɥɢɡɚɰɢɢ ɢɫɩɨɥɶɡɭɟɬ ɬɨɥɶɤɨ ɢɧɮɨɪɦɚɰɢɸ ɨɬ ɩɪɨɩɪɢɨɰɟɩɬɨɪɨɜ, ɱɬɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɩɪɟɞɩɨɥɨɠɟɧɢɹɦɢ ɢɡ [2] ɢ ɞɚɧɧɵɦɢ ɨ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ ɜɟɫɬɢɛɭɥɹɪɧɨɝɨ ɚɩɩɚɪɚɬɚ [11].
25
T
E 1q
D
Ɋɢɫɭɧɨɤ 3. Ɉɬɧɨɫɢɬɟɥɶɧɵɟ ɢɡɦɟɧɟɧɢɹ ɭɝɥɨɜ ɜ ɯɨɞɟ ɦɟɞɥɟɧɧɨɝɨ ɧɚɤɥɨɧɚ ɩɥɚɬɮɨɪɦɵ. Ʉɪɢɜɵɟ ɩɨɥɭɱɟɧɵ ɜ ɪɟɡɭɥɶɬɚɬɟ ɨɫɪɟɞɧɟɧɢɹ ɩɨ ɜɫɟɦ ɢɫɩɵɬɭɟɦɵɦ. ɉɨ ɞɚɧɧɵɦ ɢɡ [2]. 1.5
T (q)
1 0.5 0 0 0.5
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
E (q)
0 -0.5 -1 0 1.5
D (q)
1 0.5 0 0
ȼɪɟɦɹ (ɫ)
Ɋɢɫɭɧɨɤ 4. Ɋɟɡɭɥɶɬɚɬɵ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ɍɨɧɤɨɣ ɥɢɧɢɟɣ ɨɛɨɡɧɚɱɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɫɱɟɬɚ ɞɥɹ ɬɨɱɧɨɣ ɦɨɞɟɥɢ (1), (2), (5), ɠɢɪɧɨɣ - ɞɥɹ ɩɪɢɛɥɢɠɟɧɧɨɣ (7).
26
Ʌɢɬɟɪɚɬɭɪɚ Ƚɭɪɮɢɧɤɟɥɶ ȼ. ɋ., Ʉɨɰ ə. Ɇ., ɒɢɤ Ɇ. Ʌ. Ɋɟɝɭɥɹɰɢɹ ɩɨɡɵ ɱɟɥɨɜɟɤɚ. - Ɇ. ɇɚɭɤɚ, 1965. 2. Gurfinkel V. S., Ivanenko Yu. P., Levik Yu. S., Babakova I. A. Kinesthetic reference for human orthograde posture.// Neuroscience, 68(1), 1995. 3. Lestienne F. G., Gurfinkel V. S. Posture as an organizational structure based on a dual process: a formal basis to interpret changes of posture in weightlessness. // Progress in Brain Research, 76, 1988. 4. Ɏɟɥɶɞɦɚɧ Ⱥ. Ƚ. ɐɟɧɬɪɚɥɶɧɵɟ ɢ ɪɟɮɥɟɤɬɨɪɧɵɟ ɦɟɯɚɧɢɡɦɵ ɭɩɪɚɜɥɟɧɢɹ. - Ɇ. ɇɚɭɤɚ, 1979. 5. Ɏɪɚɞɤɨɜ Ⱥ. Ʌ. Ⱥɞɚɩɬɢɜɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɜ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦɚɯ. - Ɇ. ɇɚɭɤɚ, 1990. 6. Ito S., Nishigaki T., Kawasaki H. Upright posture stabilization by ground reaction force control.// Proceeding of the International Symposium on Measurement, Analysis and Modeling of Human Functions. - Sapporo. 2001. 7. ɇɨɜɨɠɢɥɨɜ ɂ. ȼ. Ɏɪɚɤɰɢɨɧɧɵɣ ɚɧɚɥɢɡ. - Ɇ. ɂɡɞ-ɜɨ ɦɟɯɚɧɢɤɨɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɆȽɍ, 1995. 8. Ȼɟɝɭɧ ɉ.ɂ., ɒɭɤɟɣɥɨ. ɘ.Ⱥ. Ȼɢɨɦɟɯɚɧɢɤɚ. - ɋɉɛ, ɉɨɥɢɬɟɯɧɢɤɚ, 2000. 9. Winter DA, Patla AE, Rietdyk S, Ishac MG. Ankle muscle stiffness in the control of balance during quiet standing.// J Neurophysiol, 85(6), 2001. 10. Morasso PG, Sanguineti V. Ankle muscle stiffness alone cannot stabilize balance during quiet standing.// J Neurophysiol, 88(4), 2002. 11. Fitzpatrick R., McCloskey D. I. Proprioceptive, visual and vestibular thresholds for the perception of sway during standing in humans.// J Physiology, 478(1), 1994. 1.
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Ɉ ɜɨɡɦɨɠɧɨɫɬɹɯ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɚɧɚɥɢɡɚ ɞɜɢɠɟɧɢɣ ɢ ɫɬɚɛɢɥɨɦɟɬɪɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɵ
Ʉɪɭɱɢɧɢɧ ɉ.Ⱥ., Ɇɢɲɚɧɨɜ Ⱥ.ɘ. ɆȽɍ ɢɦ. Ɇ.ȼ.Ʌɨɦɨɧɨɫɨɜɚ
ɋɚɟɧɤɨ Ⱦ.Ƚ. ɂɆȻɉ ɊȺɇ ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɜ ɪɚɡɥɢɱɧɵɯ ɨɛɥɚɫɬɹɯ ɤɥɢɧɢɱɟɫɤɨɣ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɦɟɞɢɰɢɧɵ ɢɫɩɨɥɶɡɭɸɬɫɹ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɟ ɦɟɬɨɞɵ ɚɧɚɥɢɡɚ ɥɨɤɨɦɨɰɢɣ. ɉɪɢ ɷɬɨɦ ɞɥɹ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɢɫɫɥɟɞɨɜɚɧɢɣ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɧɚɛɨɪ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɞɚɬɱɢɤɨɜ, ɢɡɛɵɬɨɱɧɵɣ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ, ɬɪɚɞɢɰɢɨɧɧɵɯ ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɜɢɠɟɧɢɹ. Ɍɨɱɧɨɫɬɶ ɨɬɞɟɥɶɧɵɯ ɢɡɦɟɪɟɧɢɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟɜɟɥɢɤɚ, ɧɚɩɪɢɦɟɪ, ɢɡ-ɡɚ ɩɨɝɪɟɲɧɨɫɬɟɣ ɤɪɟɩɥɟɧɢɹ ɞɚɬɱɢɤɨɜ ɧɚ ɬɟɥɟ ɱɟɥɨɜɟɤɚ. ȼ ɬɚɤɨɣ ɫɢɬɭɚɰɢɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɚɧɚɥɢɡ ɜɨɡɦɨɠɧɨɫɬɢ ɤɨɦɩɥɟɤɫɢɪɨɜɚɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɨɬ ɪɚɡɥɢɱɧɵɯ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɞɚɬɱɢɤɨɜ ɫ ɰɟɥɶɸ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɢ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɩɨɥɭɱɚɟɦɵɯ ɞɚɧɧɵɯ, ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɬɪɚɱɟɧɧɵɯ ɞɚɧɧɵɯ ɢ ɬ.ɞ. ȼ ɧɚɫɬɨɹɳɟɣ ɫɬɚɬɶɟ ɪɚɫɫɦɨɬɪɟɧɚ ɡɚɞɚɱɚ ɤɨɦɩɥɟɤɫɢɪɨɜɚɧɢɹ ɢɧɮɨɪɦɚɰɢɢ, ɩɨɥɭɱɟɧɧɨɣ ɩɪɢ ɨɞɧɨɜɪɟɦɟɧɧɵɯ ɢɡɦɟɪɟɧɢɹɯ ɩɨɫɪɟɞɫɬɜɨɦ ɤɨɦɩɥɟɤɫɚ ɜɢɞɟɨɚɧɚɥɢɡɚ ɞɜɢɠɟɧɢɣ ɫ ɨɞɧɨɣ ɜɢɞɟɨɤɚɦɟɪɨɣ ɢ ɫɬɚɛɢɥɨɦɟɬɪɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɵ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɜɢɠɟɧɢɣ ɬɢɩɚ ɩɪɢɫɟɞɚɧɢɹ ɢ ɜɫɬɚɜɚɧɢɹ. Ɉɩɢɲɟɦ ɨɞɧɭ ɢɡ ɬɪɚɞɢɰɢɨɧɧɵɯ ɫɯɟɦ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɭɫɢɥɢɣ ɜ ɦɵɲɰɚɯ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɜɢɞɟɨɤɚɦɟɪɵ. ɇɚ ɯɚɪɚɤɬɟɪɧɵɟ ɬɨɱɤɢ ɧɚ ɬɟɥɟ ɱɟɥɨɜɟɤɚ ɧɚɤɥɟɢɜɚɸɬɫɹ ɫɜɟɬɨɨɬɪɚɠɚɸɳɢɟ ɷɥɟɦɟɧɬɵ (ɤɚɬɚɮɨɬɵ) (ɋɦ. ɪɢɫ II ɧɚ ɜɤɥɚɞɤɟ). ɑɟɥɨɜɟɤ ɫɨɜɟɪɲɚɟɬ ɞɜɢɠɟɧɢɹ ɡɚɩɢɫɵɜɚɟɦɵɟ ɨɞɧɨɣ ɢɥɢ ɧɟɫɤɨɥɶɤɢɦɢ ɜɢɞɟɨɤɚɦɟɪɚɦɢ. ɉɪɢ ɤɨɦɩɶɸɬɟɪɧɨɣ ɨɛɪɚɛɨɬɤɟ ɜɢɞɟɨɡɚɩɢɫɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨɥɨɠɟɧɢɹ ɯɚɪɚɤɬɟɪɧɵɯ ɬɨɱɟɤ (ɜɪɭɱɧɭɸ ɨɩɟɪɚɬɨɪɨɦ, ɥɢɛɨ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɛɨɬɵ ɤɨɦɩɶɸɬɟɪɧɨɣ ɩɪɨɝɪɚɦɦɵ). ɉɨ ɤɨɨɪɞɢɧɚɬɚɦ ɷɬɢɯ ɬɨɱɟɤ ɜɵɱɢɫɥɹɸɬ ɭɝɥɵ ɜ ɫɭɫɬɚɜɚɯ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ. ɋɢɥɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɦɟɯɚɧɢɤɢ. ɗɬɚ ɡɚɞɚɱɚ ɧɟɤɨɪɪɟɤɬɧɚ, ɩɨɫɤɨɥɶɤɭ ɩɪɢ ɟɟ ɪɟɲɟɧɢɢ ɩɪɢɯɨɞɢɬɶɫɹ ɞɜɚɠɞɵ ɱɢɫɥɟɧɧɨ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɬɶ ɨɰɟɧɤɢ ɫɭɫɬɚɜɧɵɯ ɭɝɥɨɜ, ɫɨɞɟɪɠɚɳɢɟ ɢɡɦɟɪɢɬɟɥɶɧɵɟ ɢ ɜɵɱɢɫɥɢɬɟɥɶɧɵɟ ɩɨɝɪɟɲɧɨɫɬɢ. Ⱦɥɹ ɛɨɪɶɛɵ ɫ ɬɚɤɢɦɢ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɩɪɢɯɨɞɢɬɫɹ ɨɫɪɟɞɧɹɬɶ ɢɡɦɟɪɟɧɢɹ ɩɨ ɧɟɫɤɨɥɶɤɢɦ ɪɟɚɥɢɡɚɰɢɹɦ [1]. ɉɪɢ ɷɬɨɦ ɬɟɪɹɸɬɫɹ ɢɧɞɢɜɢɞɭ28
ɚɥɶɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɟɞɢɧɢɱɧɨɝɨ ɞɜɢɠɟɧɢɹ. ɉɪɨɛɥɟɦɭ ɨɛɪɚɛɨɬɤɢ ɟɞɢɧɢɱɧɨɣ ɪɟɚɥɢɡɚɰɢɢ ɱɚɫɬɢɱɧɨ ɦɨɠɧɨ ɪɚɡɪɟɲɢɬɶ ɢɫɩɨɥɶɡɨɜɚɜ ɩɪɨɰɟɞɭɪɵ ɫɝɥɚɠɢɜɚɧɢɹ, ɤɚɤ ɧɚɩɪɢɦɟɪ ɜ [2]. Ɍɚɤɨɣ ɩɪɢɟɦ ɢɫɤɚɠɚɟɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɞɜɢɠɟɧɢɹ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɢɡɭɱɟɧɢɟ ɜɨɡɦɨɠɧɨɫɬɟɣ ɭɬɨɱɧɟɧɢɹ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦ ɜɢɞɟɨɚɧɚɥɢɡɚ. ȼɬɨɪɵɦ ɧɟɞɨɫɬɚɬɤɨɦ ɬɚɤɢɯ ɫɢɫɬɟɦ ɹɜɥɹɟɬɫɹ ɧɚɥɢɱɢɟ ɫɛɨɟɜ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɢɡɨɛɪɚɠɟɧɢɣ. ɗɬɢ ɫɛɨɢ ɜɨɡɧɢɤɚɸɬ, ɧɚɩɪɢɦɟɪ, ɟɫɥɢ ɨɞɢɧ ɢɡ ɫɜɟɬɨɨɬɪɚɠɚɸɳɢɯ ɷɥɟɦɟɧɬɨɜ ɡɚɤɪɵɬ ɩɪɢ ɫɴɟɦɤɚɯ ɨɞɧɨɣ ɜɢɞɟɨɤɚɦɟɪɵ ɪɭɤɨɣ ɢɥɢ ɞɪɭɝɨɣ ɱɚɫɬɶɸ ɬɟɥɚ ɱɟɥɨɜɟɤɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚ ɧɟɤɨɬɨɪɨɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ ɢɧɮɨɪɦɚɰɢɹ ɨɛ ɨɞɧɨɦ ɢɥɢ ɞɜɭɯ ɢɡ ɭɝɥɨɜ ɦɧɨɝɨɡɜɟɧɧɢɤɚ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɭɬɟɪɹɧɧɨɣ. Ⱥɧɚɥɨɝɢɱɧɚɹ ɫɢɬɭɚɰɢɹ ɜɨɡɦɨɠɧɚ ɢ ɩɪɢ ɚɜɬɨɦɚɬɢɱɟɫɤɨɣ ɨɛɪɚɛɨɬɤɟ ɢɡɨɛɪɚɠɟɧɢɹ, ɤɨɝɞɚ ɞɜɚ ɫɜɟɬɨɨɬɪɚɠɚɸɳɢɯ ɷɥɟɦɟɧɬɚ ɨɤɚɡɚɥɢɫɶ ɜ ɤɚɞɪɟ ɪɹɞɨɦ. ɉɪɨɛɥɟɦɵ ɪɚɡɥɢɱɟɧɢɹ ɷɬɢɯ ɞɚɬɱɢɤɨɜ ɬɚɤɠɟ ɦɨɠɟɬ ɪɚɡɪɟɲɚɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ. ɂɫɬɨɱɧɢɤɨɦ ɷɬɨɣ ɢɧɮɨɪɦɚɰɢɢ ɦɨɠɟɬ ɹɜɥɹɬɶɫɹ ɫɬɚɛɢɥɨɦɟɬɪɢɱɟɫɤɚɹ ɩɥɚɬɮɨɪɦɚ (ɫɬɚɛɢɥɨɝɪɚɮ) – ɩɪɢɛɨɪ, ɢɡɦɟɪɹɸɳɢɣ ɧɨɪɦɚɥɶɧɭɸ ɪɟɚɤɰɢɸ ɨɩɨɪɵ ɢ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɤɢ ɩɪɢɥɨɠɟɧɢɹ ɟɟ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɟɣ (ɰɟɧɬɪ ɞɚɜɥɟɧɢɹ). Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ, ɪɚɫɫɦɨɬɪɢɦ ɡɚɞɚɱɭ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɪɢ ɜɫɬɚɜɚɧɢɢ ɢ ɩɪɢɫɟɞɚɧɢɢ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɷɤɫɩɟɪɢɦɟɧɬ ɩɪɨɜɨɞɢɥɫɹ ɩɪɢ ɭɱɚɫɬɢɢ ɚɜɬɨɪɨɜ ɫɬɚɬɶɢ ɜ ɂɆȻɉ ɊȺɇ. ɑɟɥɨɜɟɤ ɜɵɩɨɥɧɹɥ ɤɨɦɩɥɟɤɫ ɞɜɢɠɟɧɢɣ. ɉɪɢ ɞɜɢɠɟɧɢɢ ɱɟɥɨɜɟɤ ɧɟ ɨɬɪɵɜɚɥ ɩɹɬɨɤ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ. Ɍɭɥɨɜɢɳɟ ɢ ɝɨɥɨɜɭ ɞɟɪɠɚɥ ɩɪɹɦɨ. Ɋɭɤɢ ɞɟɪɠɚɥ ɫɤɪɟɳɟɧɧɵɦɢ, ɩɪɢɠɢɦɚɹ ɢɯ ɤ ɬɭɥɨɜɢɳɭ. Ⱦɜɢɠɟɧɢɹ ɡɚɩɢɫɵɜɚɥɢɫɶ ɜɢɞɟɨɤɚɦɟɪɨɣ ɫ ɱɚɫɬɨɬɨɣ 25 ɤɚɞɪɨɜ ɜ ɫɟɤɭɧɞɭ. ɉɪɢ ɫɨɜɟɪɲɟɧɢɢ ɞɜɢɠɟɧɢɣ ɢɫɩɵɬɭɟɦɵɣ ɛɵɥ ɩɨɜɟɪɧɭɬ ɥɟɜɵɦ ɛɨɤɨɦ ɤ ɜɢɞɟɨɤɚɦɟɪɟ, ɫɬɨɹ ɧɚ ɫɬɚɛɢɥɨɝɪɚɮɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɟ ɆȻɇ. ɉɪɢ ɤɨɦɩɶɸɬɟɪɧɨɣ ɨɛɪɚɛɨɬɤɟ ɜɢɞɟɨɡɚɩɢɫɢ ɩɨɥɨɠɟɧɢɟ ɯɚɪɚɤɬɟɪɧɵɯ ɬɨɱɟɤ ɭɤɚɡɵɜɚɥɨɫɶ ɜɪɭɱɧɭɸ. ɉɨɫɥɟ ɷɬɨɝɨ ɨɩɪɟɞɟɥɹɥɢɫɶ ɤɨɨɪɞɢɧɚɬɵ ɨɩɨɪɧɵɯ ɬɨɱɟɤ ɧɚ ɷɤɪɚɧɟ. ɋɢɥɵ ɨɩɪɟɞɟɥɹɥɢɫɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɩɥɨɫɤɨɣ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɞɢɧɚɦɢɤɢ ɩɨ ɩɨɥɭɱɟɧɧɵɦ ɡɧɚɱɟɧɢɹɦ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ. ɂɫɩɨɥɶɡɨɜɚɥɚɫɶ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɥɨɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ, ɨɛɪɚɡɨɜɚɧɧɨɝɨ ɝɨɥɟɧɶɸ, ɛɟɞɪɨɦ ɢ ɤɨɪɩɭɫɨɦ ɱɟɥɨɜɟɤɚ [3,4]. ȼ ɪɚɦɤɚɯ ɷɬɨɣ ɦɨɞɟɥɢ ɫɱɢɬɚɥɨɫɶ, ɱɬɨ ɫɬɨɩɚ ɧɟɩɨɞɜɢɠɧɚ ɢ ɧɟ ɨɬɪɵɜɚɟɬɫɹ ɨɬ ɩɨɥɚ, ɝɨɥɨɜɚ ɢ ɪɭɤɢ ɧɟɩɨɞɜɢɠɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɪɩɭɫɚ, ɤɨɪɩɭɫ ɧɟ ɢɡɦɟɧɹɟɬ ɫɜɨɟɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɡɵ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ [5] ɡɚɩɢɫɚɧɵ ɞɢɧɚɦɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ, ɜ ɩɚɤɟɬɟ MATLAB ɫɨɫɬɚɜɥɟɧɚ ɩɪɨɝɪɚɦɦɚ ɜɵɱɢɫɥɟɧɢɹ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɬɨɱɟɤ ɭɝɥɨɜ ɦɟɠɞɭ ɡɜɟɧɶɹɦɢ. Ɂɧɚɱɟɧɢɹ ɭɝɥɨɜɵɯ ɫɤɨɪɨɫɬɟɣ ɢ ɭɫɤɨɪɟ29
ɧɢɣ ɩɨɥɭɱɟɧɵ ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɧɟɱɧɨɪɚɡɧɨɫɬɧɨɝɨ ɱɢɫɥɟɧɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ. ɉɪɟɞɩɨɥɚɝɚɥɨɫɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢ ɪɟɲɟɧɢɢ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɞɢɧɚɦɢɤɢ – ɡɚɞɚɱɢ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɨɜ ɜ ɫɭɫɬɚɜɚɯ ɩɨ ɢɡɦɟɪɟɧɧɵɦ ɡɧɚɱɟɧɢɹɦ ɭɝɥɨɜ. Ⱦɥɹ ɭɞɚɥɟɧɢɹ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɨɲɢɛɤɢ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɩɪɨɰɟɞɭɪɚ ɨɤɨɧɧɨɝɨ ɫɝɥɚɠɢɜɚɧɢɹ ɨɤɧɨɦ ɏɚɧɧɚ ɞɥɢɧɨɣ 0.4 ɫɟɤɭɧɞɵ. Ɂɧɚɱɢɬɟɥɶɧɚɹ ɞɥɢɧɚ ɨɤɧɚ (ɩɪɢɦɟɪɧɨ 1/3 ɯɚɪɚɤɬɟɪɧɨɝɨ ɦɚɫɲɬɚɛɚ ɞɜɢɠɟɧɢɣ) ɩɪɢɜɨɞɢɬ ɤ ɩɨɝɪɟɲɧɨɫɬɹɦ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɭɝɥɨɜ. ɂɫɩɨɥɶɡɭɟɦ ɪɟɡɭɥɶɬɚɬ ɷɬɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ ɞɥɹ ɚɧɚɥɢɡɚ ɜɨɡɦɨɠɧɨɫɬɢ ɤɨɪɪɟɤɰɢɢ ɩɨɥɭɱɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɭɝɥɨɜ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɦɟɬɪɢɱɟɫɤɨɣ ɩɥɚɬɮɨɪɦɵ ɢ ɞɥɹ ɚɧɚɥɢɡɚ ɜɨɡɦɨɠɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɤɚɡɚɧɢɣ ɫɬɚɛɢɥɨɝɪɚɮɚ ɞɥɹ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ “ɩɨɬɟɪɹɧɧɵɯ” ɡɧɚɱɟɧɢɣ ɭɝɥɨɜ ɜ ɫɭɫɬɚɜɚɯ ɦɧɨɝɨɡɜɟɧɧɢɤɚ. 1. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɷɤɫɩɟɪɢɦɟɧɬɚ 1.1. ȼɵɜɨɞ ɞɢɧɚɦɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɚɥɝɨɪɢɬɦɚ ɨɛɪɚɛɨɬɤɢ ɜɢɞɟɨɢɡɨɛɪɚɠɟɧɢɹ ɡɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɚɧɬɪɨɩɨɦɨɪɮɧɨɝɨ ɬɪɟɯɡɜɟɧɧɢɤɚ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ. ȼɜɟɞɟɦ ɧɟɩɨɞɜɢɠɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ O1 XY . Ɂɚ ɧɚɱɚɥɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɩɪɢɦɟɦ ɰɟɧɬɪ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ. ɋɯɟɦɚ ɫɤɟɥɟɬɧɨɝɨ ɬɪɟɯɡɜɟɧɧɢɤɚ, ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫɭɧɤɟ 1. ȿɝɨ ɩɨɥɨɠɟɧɢɟ ɨɩɢɲɟɦ ɭɝɥɚɦɢ \ 1 ,\ 2 ,\ 3 . ɑɟɪɟɡ O1 , O2 , O3 ɨɛɨɡɧɚɱɟɧɵ ɰɟɧɬɪɵ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ, ɤɨɥɟɧɧɨɝɨ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɝɨ ɫɭɫɬɚɜɨɜ, ɱɟɪɟɡ C1 , C 2 , C 3 - ɰɟɧɬɪɵ ɦɚɫɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɡɜɟɧɶɟɜ, ɱɟɪɟɡ Li Oi Oi 1 - ɨɛɨɡɧɚɱɟɧɵ Ɋɢɫɭɧɨɤ 1. Ɉɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɞɥɹ ɚɧɬɪɨɩɨɦɨɪɮɧɨɝɨ ɬɪɟɯɡɜɟɧɧɢɤɚ
ɞɥɢɧɵ ai Oi C i
ɡɜɟɧɶɟɜ, ɚ - ɪɚɫɫɬɨɹɧɢɹ ɨɬ
ɧɢɠɧɟɣ ɨɤɨɧɟɱɧɨɫɬɢ ɡɜɟɧɚ
30
ɞɨ ɟɝɨ ɰɟɧɬɪɚ ɦɚɫɫ. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ mi - ɦɚɫɫɭ i-ɝɨ ɡɜɟɧɚ, I i - ɟɝɨ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ. ɋɨɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɜ ɮɨɪɦɟ ɭɪɚɜɧɟɧɢɣ Ʌɚɝɪɚɧɠɚ. ɐɟɧɬɪɵ ɦɚɫɫ ɡɜɟɧɶɟɜ ɜ ɫɢɫɬɟɦɟ O1 XY ɢɦɟɸɬ ɤɨɨɪɞɢɧɚɬɵ C1 (a1 cos\ 1 , a1 sin \ 1 ) (1.1) ( L1 cos\ 1 a 2 cos(\ 1 \ 2 ), L1 sin \ 1 a 2 sin(\ 1 \ 2 ))
C2
(1.2)
( L1 cos\ 1 L2 cos(\ 1 \ 2 ) a3 cos(\ 1 \ 2 \ 3 ), (1.3) L1 sin \ 1 L2 sin(\ 1 \ 2 ) a3 sin(\ 1 \ 2 \ 3 )) ȼɵɱɢɫɥɢɦ ɤɜɚɞɪɚɬɵ ɫɤɨɪɨɫɬɟɣ ɰɟɧɬɪɨɜ ɦɚɫɫ ɡɜɟɧɶɟɜ. ɂɡ (1.1) ɩɨɥɭɱɢɦ ɩɪɨɟɤɰɢɢ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ C1 ɧɚ ɤɨɨɪɞɢɧɚɬɧɵɟ ɨɫɢ O1 XY C3
( a1\ 1 sin \ 1 , a1\ 1 cos\ 1 )
VC1
Ɍɨɝɞɚ VC2 a12 \ 12
(1.4)
1
ɂɡ (1.2) VC ( L1\ 1 sin \ 1 a 2 (\ 1 \ 2 ) sin(\ 1 \ 2 ), 2
L1 \ 1 cos\ 1 a 2 (\ 1 \ 2 ) cos(\ 1 \ 2 ))
Ɍɨɝɞɚ VC2 L12 \ 12 sin 2 \ 1 a 22 (\ 1 \ 2 ) 2 sin 2 (\ 1 \ 2 ) 2
2 L1\ 1 a 2 (\ 1 \ 2 ) sin \ 1 sin(\ 1 \ 2 ) L12\ 12 cos 2 \ 1 a 22 (\ 1 \ 2 ) 2 cos 2 (\ 1 \ 2 ) 2 L 1\ 1 a 2 (\ 1 \ 2 ) cos \ 1 cos( \ 1 \ 2 ) L12\ 12 a 22 (\ 1 \ 2 ) 2 2 L1 a 2\ 1 (\ 1 \ 2 ) cos\ 2
(1.5)
ɂɡ (1.3) ɫɥɟɞɭɟɬ VC ( L1\ 1 sin \ 1 L2 (\ 1 \ 2 ) sin(\ 1 \ 2 ) 3
a3 (\ 1 \ 2 \ 3 ) sin(\ 1 \ 2 \ 3 ), L1\ 1 cos\ 1 L 2 (\ 1 \ 2 ) cos(\ 1 \ 2 ) a 3 (\ 1 \ 2 \ 3 ) cos(\ 1 \ 2 \ 3 ))
Ɍɨɝɞɚ VC2
3
2
L1 \ 12 sin 2 \ 1 L22 (\ 1 \ 2 ) 2 sin 2 (\ 1 \ 2 ) a 32 (\ 1 \ 2 \ 3 ) 2 sin 2 (\ 1 \ 2 \ 3 )
31
2 L1 L2 \ 1 (\ 1 \ 2 ) sin \ 1 sin(\ 1 \ 2 ) 2L2 a3 (\1 \ 2 )(\1 \ 2 \ 3 ) sin(\1 \ 2 ) sin(\1 \ 2 \ 3 ) 2 L1 a 3\ 1 (\ 1 \ 2 \ 3 ) sin \ 1 sin(\ 1 \ 2 \ 3 )
L12\ 12 cos 2 \ 1 L22 (\ 1 \ 2 ) 2 cos 2 (\ 1 \ 2 ) a32 (\ 1 \ 2 \ 3 ) 2 cos2 (\ 1 \ 2 \ 3 ) 2 L1 L2\ 1 (\ 1 \ 2 ) cos\ 1 cos(\ 1 \ 2 ) L2 a3 (\ 1 \ 2 )(\ 1 \ 2 \ 3 ) u
(1.6)
u cos(\ 1 \ 2 ) cos(\ 1 \ 2 ) cos(\ 1 \ 2 \ 3 ) 2 L1 a3\ 1 (\ \ 2 \ 3 ) cos\ 1 cos(\ 1 \ 2 \ 3 ) L12\ 12 L22 (\ 1 \ 2 ) 2 a32 (\ 1 \ 2 \ 3 ) 2 2 L1 L2\ 1 (\ 1 \ 2 ) cos\ 2 2 L2 a3 (\ 1 \ 2 )(\ 1 \ 2 \ 3 ) cos\ 3 2 L1 a 3\ 1 (\ 1 \ 2 \ 3 ) cos(\ 2 \ 3 )
ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (1.4) - (1.6), ɡɚɩɢɲɟɦ ɩɨ ɬɟɨɪɟɦɟ Ʉɟɧɢɝɚ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ m1VC2 m2VC2 m3VC2 \ 2 T I1 1 2 2 2 2 (\ 12 \ 22 \ 32 ) (\ 12 \ 22 ) I2 I3 2 2 m1 2 2 m2 2 2 2 ( L1\ 1 a 2 (\ 1 \ 2 ) 2 a1 \ 1 2 2 2 L 1 a 2\ 1 (\ 1 \ 2 ) cos \ 2 (1.7) 1
2
3
m3 2 2 ( L1\ 1 L22 (\ 1 \ 2 ) 2 a32 (\ 1 \ 2 \ 3 ) 2 2 2 L1 L2\ 1 (\ 1 \ 2 ) cos\ 2 2 L2 a3 (\ 1 \ 2 )(\ 1 \ 2 \ 3 ) cos\ 3 2 L1 a 3\ 1 (\ 1 \ 2 \ 3 ) cos(\ 2 \ 3 ))
I I1 2 I 2 \ 1 (\ 12 \ 22 ) 3 (\ 12 \ 22 \ 32 ) 2 2 2
ɉɟɪɟɝɪɭɩɩɢɪɨɜɚɜ ɫɥɚɝɚɟɦɵɟ ɜ (1.7) ɢ ɨɛɨɡɧɚɱɢɜ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɢ ɤɜɚɞɪɚɬɧɵɯ ɱɥɟɧɚɯ ɱɟɪɟɡ A, B, C , D, E , F , ɡɚɩɢɲɟɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɜɢɞɟ
32
T
A\ 12 B\ 22 C\ 32 D\ 1\ 2 E\ 1\ 3 E\ 2\ 3 F\ 1 (\ 1 \ 2 ) cos\ 2 m3 L1 a3\ 1 (\ 1 \ 2 \ 3 ) cos(\ 2 \ 3 ) m3 L2 a 3 (\ 1 \ 2 )(\ 1 \ 2 \ 3 ) cos\ 3
(1.8)
ɝɞɟ
D
m1 2 m2 2 m2 2 m3 2 m 3 2 m 3 2 I 1 I 2 I 3 a1 L1 a2 L1 L2 a3 2 2 2 2 2 2 2 2 2 m 2 2 m3 2 m3 2 I 2 I 3 a2 L2 a3 2 2 2 2 2 m3 2 I 3 a3 2 2 m2 a 22 m3 L22 m3 a32
E F
m3 a 32 m2 L1 a 2 m3 L1 L2
A B C
ɉɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɟ (1.8) ɜ ɭɪɚɜɧɟɧɢɹ Ʌɚɝɪɚɧɠɚ d wT wT (i=1,2,3) Qi dt w\ i w\ i ɢ ɩɪɨɞɟɥɚɜ ɧɟɨɛɯɨɞɢɦɵɟ ɜɵɱɢɫɥɟɧɢɹ, ɩɨɥɭɱɢɦ ɬɪɢ ɭɪɚɜɧɟɧɢɹ ɜɢɞɚ 2A\1 D\ 2 E\3 2 F (\1 cos\ 2 \ 1\ 2 sin \ 2 ) F (\ 2 cos \ 2 \ 22 sin \ 2 ) 2m 2 L 2 a 3 (\1 cos \ 3 \ 1\ 3 sin \ 3 ) 2m 3 L 2 a 3 (\ 2 cos\ 3 \ 2\ 3 sin \ 3 ) m 3 L 2 a 3 (\3 cos\ 3 \ 32 sin \ 3 ) 2m 3 L1 a 3 (\1 cos(\ 2 \ 3 ) \ 1 (\ 2 \ 3 ) sin(\ 2 \ 3 )) m 3 L1 a 3 (\ 2 cos(\ 2 \ 3 ) \ 2 (\ 2 \ 3 ) sin(\ 2 \ 3 )) m 3 L1 a 3 (\3 cos(\ 2 \ 3 ) \ 3 (\ 2 \ 3 ) sin(\ 2 \ 3 ))
(1.9)
Q1
33
2 B\ 2 D\1 E\3 F (\1 cos \ 2 \ 1\ 2 sin \ 2 ) 2m 3 L 2 a 3 (\1 cos \ 3 \ 1\ 3 sin \ 3 ) 2m 3 L 2 a 3 (\ 2 cos \ 3 \ 2\ 3 sin \ 3 ) m 3 L 2 a 3 (\3 cos\ 3 \ 32 sin \ 3 ) m 3 L1 a 3 (\1 cos(\ 2 \ 3 ) \ 1 (\ 2 \ 3 ) sin(\ 2 \ 3 )) F\ 1 (\ 1 \ 2 ) sin \ 2 m 3 L1 a 3\ 1 (\ 1 \ 2 \ 3 ) sin(\ 2 \ 3 )
(1.10)
Q2
2C\3 E (\1 \ 2 ) m 3 L 2 a 3 ((\1 \ 2 ) cos \ 3 (\ 1 \ 2 )\ 3 sin \ 3 ) m 3 L1 a 3 (\1 cos(\ 2 \ 3 ) \ 1 (\ 2 \ 3 ) sin(\ 2 \ 3 ))
(1.11)
m 3 L 2 a 3 (\ 1 \ 2 )(\ 1 \ 2 \ 3 ) sin \ 3 m 3 L1 a 3\ 1 (\ 1 \ 2 \ 3 ) sin(\ 2 \ 3 ) Q3
Ɂɞɟɫɶ Q1 , Q2 , Q3 - ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ, ɩɨ [3,4] ɪɚɜɧɵ Q1
mgxC M1
Q2
m3 g L2 cos(\ 1 \ 2 ) a3 cos(\1 \ 2 \ 3 )
(1.12)
m2 ga2 cos \ 1 \ 2 M 2
Q3 mga3 cos(\1 \ 2 \ 3 ) M 3 ɝɞɟ Ɇ1, Ɇ2, Ɇ3 - ɦɨɦɟɧɬɵ ɜ ɫɭɫɬɚɜɚɯ ɦɧɨɝɨɡɜɟɧɧɢɤɚ, ɫɨɡɞɚɜɚɟɦɵɟ ɦɵɲɟɱɧɵɦɢ ɭɫɢɥɢɹɦɢ. ɉɪɨɟɤɰɢɢ x C ɢ y C ɰɟɧɬɪɚ ɦɚɫɫ ɬɪɟɯɡɜɟɧɧɢɤɚ ɧɚ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɨɫɶ O1 X ɜɵɱɢɫɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ xC
K1 cos\ 1 K2 cos(\1 \ 2 ) K3 cos(\1 \ 2 \ 3 )
yC K1 sin\1 K2 sin(\1 \ 2 ) K3 sin(\ 1 \ 2 \ 3 ) ɝɞɟ m1a1 m2 L1 m3 L1 m2a2 m3 L2 K1 K2 K3 , , m m
(1.13)
m3a3 . m
1.2. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɨɤɚɡɚɧɢɣ ɫɬɚɛɢɥɨɝɪɚɮɚ ɋɬɚɛɢɥɨɝɪɚɮɢɱɟɫɤɚɹ ɩɥɚɬɮɨɪɦɚ, ɢɥɢ ɫɬɚɛɢɥɨɝɪɚɮ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɜɟ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɩɥɢɬɵ, ɫ ɭɫɬɚɧɨɜɥɟɧɧɵɦɢ ɦɟɠɞɭ ɧɢɦɢ ɬɪɟɦɹ ɞɚɬɱɢɤɚɦɢ ɫɢɥɵ [6]. ɉɨ ɩɨɤɚɡɚɧɢɹɦ ɞɚɬɱɢɤɨɜ ɩɪɨɝɪɚɦɦɧɨɟ ɨɛɟɫɩɟɱɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬ ɜɟɪɬɢɤɚɥɶɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɢ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɤɢ ɩɪɢɥɨɠɟɧɢɹ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɟɣ
34
ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ. ɍɫɬɚɧɨɜɤɚ ɩɚɰɢɟɧɬɚ ɧɚ ɩɥɚɬɮɨɪɦɭ ɩɪɨɢɫɯɨɞɢɬ ɩɹɬɤɚɦɢ ɤ ɪɟɛɪɭ ɫ ɞɜɭɦɹ ɞɚɬɱɢɤɚɦɢ, ɚ ɧɨɫɤɚɦɢ – ɤ ɪɟɛɪɭ ɫ ɨɞɧɢɦ ɞɚɬɱɢɤɨɦ. Ɍɨɱɧɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɬɨɱɤɢ ɩɪɢɥɨɠɟɧɢɹ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɫɨɫɬɚɜɥɹɟɬ (+/-1 ɦɦ). Ɍɚɤɚɹ ɬɨɱɧɨɫɬɶ ɹɜɥɹɟɬɫɹ ɞɨɩɭɫɬɢɦɨɣ ɞɥɹ ɤɥɢɧɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɟɝɤɨ ɪɟɚɥɢɡɭɟɬɫɹ ɬɟɯɧɢɱɟɫɤɢ. ɇɨɦɢɧɚɥɶɧɚɹ ɪɚɛɨɱɚɹ ɧɚɝɪɭɡɤɚ ɩɥɚɬɮɨɪɦɵ 20-120 ɤɝ. Ɋɚɛɨɱɚɹ ɱɚɫɬɨɬɚ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ 50Ƚɰ. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ N , x N ɡɧɚɱɟɧɢɹ ɜɟɤɬɨɪɚ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɢ ɤɨɨɪɞɢɧɚɬɭ X ɟɝɨ ɬɨɱɤɢ ɩɪɢɥɨɠɟɧɢɹ ɜ ɨɫɹɯ O1 X . ɗɬɢ ɜɟɥɢɱɢɧɵ ɜɵɞɚɟɬ ɜ ɤɚɱɟɫɬɜɟ ɢɡɦɟɪɟɧɢɣ ɩɪɨɝɪɚɦɦɧɨɟ ɨɛɟɫɩɟɱɟɧɢɟ ɫɬɚɛɢɥɨɝɪɚɮɚ. ɍɪɚɜɧɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɦɨɦɟɧɬɚ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɫɬɨɩɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ ɩɪɢɦɟɬ ɜɢɞ M 1 N x N RW ' 0 ɝɞɟ M 1 - ɦɨɦɟɧɬ, ɫɨɡɞɚɜɚɟɦɵɣ ɭɫɢɥɢɹɦɢ ɦɵɲɰ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ, RW - ɩɪɨɞɨɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɢɥɵ ɪɟɚɤɰɢɢ, ' - ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɨɫɢ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ ɞɨ ɩɨɜɟɪɯɧɨɫɬɢ ɨɩɨɪɵ. ɉɪɨɜɟɞɟɦ ɨɰɟɧɤɭ ɜɟɥɢɱɢɧɵ ɩɪɨɞɨɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɢɥɵ ɪɟɚɤɰɢɢ ɢ ɟɟ ɦɨɦɟɧɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ. Ɂɚɩɢɲɟɦ ɬɟɨɪɟɦɭ ɨ ɞɜɢɠɟɧɢɢ ɰɟɧɬɪɚ ɦɚɫɫ ɬɪɟɯɡɜɟɧɧɢɤɚ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɨɫɶ. (1.14) mxC RW Ɋɢɫɭɧɨɤ 2. ɋɢɥɵ ɢ ɦɨɦɟɧɬɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɫɬɨɩɭ.
35
Ɋɢɫɭɧɨɤ 3. Ɍɪɚɟɤɬɨɪɢɢ ɰɟɧɬɪɚ ɦɚɫɫ ɱɟɥɨɜɟɤɚ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɫɚɝɢɬɬɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ (ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɩɪɨɜɟɞɟɧɧɵɯ ɜ ɂɆȻɉ ɊȺɇ)
ɇɚ ɪɢɫ.3 ɩɪɢɜɟɞɟɧɵ ɯɚɪɚɤɬɟɪɧɵɟ ɬɪɚɟɤɬɨɪɢɢ ɰɟɧɬɪɚ ɦɚɫɫ ɱɟɥɨɜɟɤɚ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɫɚɝɢɬɬɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ, ɜɵɱɢɫɥɟɧɧɵɟ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɨɛɪɚɛɨɬɤɢ ɜɢɞɟɨɢɡɨɛɪɚɠɟɧɢɹ ɩɨ (1.13). Ⱥɧɚɥɢɡ ɩɪɢɜɟɞɟɧɧɵɯ ɬɪɚɟɤɬɨɪɢɣ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜɨ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ xC ɧɟ ɩɪɟɜɵɲɚɟɬ 0.5 ɦ / c 2 , ɩɪɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɭɫɤɨɪɟɧɢɹ ɰɟɧɬɪɚ ɦɚɫɫ yC ~ 2 ɦ / c 2 . ȼ ɩɪɨɜɟɞɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ x N ~ 0.02 ɦ . ɋɱɢɬɚɟɦ ɦɚɫɫɭ m | 100ɤɝ , ɢ ɜɟɥɢɱɢɧɭ ' | 0.08 ɦ . ɋɥɟɞɨɜɚɬɟɥɶɧɨ, RW ɜɟɥɢɱɢɧɚ ɩɨɪɹɞɤɚ 90 ɧ , N ɜɟɥɢɱɢɧɚ ɩɨɪɹɞɤɚ 1000 ɧ. Ɍɨɝɞɚ ɜɟɥɢɱɢɧɚ N x N ɢɦɟɟɬ ɩɨɪɹɞɨɤ 40 ɧ ɦ , ɚ ɜɟɥɢɱɢɧɚ RW ' - 7.5 ɧ ɦ . ɗɬɢ ɪɚɫɱɟɬɵ ɩɨɡɜɨɥɹɸɬ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɜɥɢɹɧɢɟ ɩɪɨɞɨɥɶɧɨɣ ɫɢɥɵ ɜ ɫɬɨɩɟ ɱɟɥɨɜɟɤɚ, ɦɚɥɨ ɢ ɩɪɢ ɞɚɥɶɧɟɣɲɢɯ ɪɚɫɱɟɬɚɯ ɟɟ ɜɥɢɹɧɢɟɦ ɛɭɞɟɦ ɩɪɟɧɟɛɪɟɝɚɬɶ. Ɍɨɝɞɚ ɦɨɦɟɧɬ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ ɨɬɧɨɫɢɬɟɥɶɧɨ O1 ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ ɩɨ ɮɨɪɦɭɥɟ M 1 N xN (1.15) ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (1.12) M1 Q1 mgxC , (1.16) 36
ɝɞɟ Q1 - ɧɚɯɨɞɢɬɫɹ ɢɡ (1.9) 2. Ʉɨɪɪɟɤɰɢɹ ɭɝɥɨɜɵɯ ɢɡɦɟɪɟɧɢɣ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ Ɋɚɫɫɦɨɬɪɢɦ ɡɚɞɚɱɭ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ ɫɢɫɬɟɦɵ ɜɢɞɟɨɧɚɛɥɸɞɟɧɢɣ ɢ ɫɬɚɛɢɥɨɝɪɚɮɚ. Ⱦɥɹ ɩɨɫɬɚɧɨɜɤɢ ɷɬɨɣ ɡɚɞɚɱɢ ɥɢɧɟɚɪɢɡɭɟɦ ɩɨɥɭɱɟɧɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɢ ɩɪɟɞɫɬɚɜɢɦ ɢɯ ɞɢɫɤɪɟɬɧɵɣ ɚɧɚɥɨɝ. ɉɪɟɞɫɬɚɜɢɦ ɭɝɥɵ ɜ ɜɢɞɟ ɫɭɦɦɵ j 1,2,3 (2.1) \ j \ S \ ' j
j
ɝɞɟ \ S - “ ɨɩɨɪɧɵɟ ɡɧɚɱɟɧɢɹ” ɭɝɥɨɜ (ɩɪɢɛɥɢɠɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɨj
ɥɭɱɟɧɧɵɟ ɧɚ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɦ ɷɬɚɩɟ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɤɨɬɨɪɵɟ ɜɵɛɢɪɚɸɬɫɹ ɨɬɞɟɥɶɧɨ ɞɥɹ ɤɚɠɞɨɣ ɤɨɧɤɪɟɬɧɨɣ ɡɚɞɚɱɢ), \ ' - ɩɨɩɪɚɜɤɚ, j
ɪɚɡɧɢɰɚ ɦɟɠɞɭ \ j ɢ \ S , ɩɪɟɞɩɨɥɚɟɦɚɹ ɦɚɥɨɣ. ɉɨɫɬɪɨɢɦ ɚɥɝɨɪɢɬɦ j
ɨɩɪɟɞɟɥɟɧɢɹ \
'
j
.
2.1. Ʌɢɧɟɚɪɢɡɨɜɚɧɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɉɨɞɫɬɚɜɢɦ (1.15) ɢ (1.9) ɜ (1.16). ɍɱɢɬɵɜɚɹ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɭɝɥɨɜ ɜ ɜɢɞɟ (2.1), ɥɢɧɟɚɪɢɡɭɟɦ ɩɨɥɭɱɢɜɲɟɟɫɹ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɩɨɪɧɵɯ ɭɝɥɨɜ \ S ,\ S ,\ S 1
2
3
37
N xN
2 A(\S1 \'1 ) D(\S 2 \' 2 ) E (\S3 \' 3 )
2F ((\S1 \'1 )(cos\ S 2 \ ' 2 sin\ S 2 ) (\ S1 \ '1 )(\ S 2 \ ' 2 )(sin\ S 2 \ ' 2 cos\ S 2 )) F ((\S 2 \' 2 )(cos\ S 2 \ ' 2 sin\ S 2 ) (\ S22 2\ S 2 \ ' 2 \ '22 )(sin\ S 2 \ ' 2 cos\ S 2 )) 2m3 L2 a 3 ((\S1 \'1 )(cos\ S3 \ ' 3 sin\ S3 ) (\ S1 \ '1 )(\ S3 \ ' 3 )(sin\ S3 \ ' 3 cos\ S3 )) 2m3 L2 a 3 ((\S 2 \' 2 )(cos\ S3 \ ' 3 sin\ S3 ) (\ S 2 \ ' 2 )(\ S3 \ ' 3 )(sin\ S3 \ ' 3 cos\ S3 )) m3 L2 a 3 ((\S3 \' 3 )(cos\ S3 \ ' 3 sin\ S3 ) (\ S23 2\ S3\ ' 3 \ '23 )(sin\ S3 \ ' 3 cos\ S3 ))
2m3 L1 a 3 ((\S1 \'1 )(cos \ S 2 \ S3
(\ ' 2 \ ' 3 ) sin \ S 2 \ S3 )
(\ S1 \ '1 )(\ S 2 \ S3 \ ' 2 \ ' 3 )(sin \ S 2 \ S3
(\ ' 2 \ ' 3 ) cos \ S 2 \ S3 ))
m3 L1 a 3 ((\S 2 \' 2 )(cos \ S 2 \ S3
(2.2)
(\ ' 2 \ ' 3 ) sin \ S 2 \ S3 )
(\ S 2 \ ' 2 )(\ S 2 \ S3 \ ' 2 \ ' 3 )(sin \ S 2 \ S3
(\ ' 2 \ ' 3 ) cos \ S 2 \ S3 ))
m3 L1 a 3 ((\S3 \' 3 )(cos \ S 2 \ S3
(\ ' 2 \ ' 3 ) sin \ S 2 \ S3 )
(\ S3 \ ' 3 )(\ S 2 \ S3 \ ' 2 \ ' 3 )(sin \ S 2 \ S3
(\ ' 2 \ ' 3 ) cos \ S 2 \ S3 ))
mg( K 1 (cos\ S1 \ '1 sin\ S1 ) K 2 (cos \ S1 \ S 2
(\ '1 \ ' 2 ) sin \ S1 \ S 2 )
K 3 (cos \ S1 \ S 2 \ S3
(\ '1 \ ' 2 \ ' 3 ) sin \ S1 \ S 2 \ S3 ))
Ɋɚɫɤɪɵɜ ɫɤɨɛɤɢ ɢ ɩɟɪɟɝɪɭɩɩɢɪɨɜɚɜ ɫɥɚɝɚɟɦɵɟ ɜ (2.2), ɩɨɥɭɱɢɦ
38
Al1\ '1 Al 2 \ ' 2 Al3 \ ' 3 B l1\ '1 B l2 \ ' 2 Bl3 \ ' 3 C l1\ '1 C l2 \ ' 2 C l3 \ ' 3
(2.3)
N x N Dl0
Ɂɞɟɫɶ Al1
mgK 3 sin \ S1 \ S 2 \ S 3
Al
2
mgK 1 sin \ S1 mgK 2 sin \ S1 \ S 2
2 F\ S sin \ S 2 F\ S \ S cos \ S F\ S sin \ S F\ S2 cos \ S 1
2
1
2
2
2
2
2
2
2m 3 L1 a 3\ S sin \ S \ S 2m 3 L1 a 3\ S (\ S \ S ) cos \ S \ S 1
sin \
2
3
1
\ m L a \ (\ mgK sin \ \
2
3
) cos \
2
3
m 3 L1 a 3\ S sin \ S \ S m 3 L1 a 3\ S (\ S \ S ) cos \ S \ S 2
m 3 L1 a 3\ S
3
2
S2
mgK 2 sin \ S \ S Al
3
3
1
S3
2
3
1
3
2
2
S3
S2
S1
2
\ S \ S
S2
3
3
2
3
S2
3
\ S
3
2m 3 L 2 a 3\ S sin \ S 2m 3 L 2 a 3\ S \ S cos\ S 2m 3 L 2 a 3\ S sin \ S 1
3
1
3
3
2
3
2m 3 L 2 a 3\ S \ S cos\ S m 3 L 2 a 3\ S sin \ S m 3 L 2 a 3\ S2 cos \ S 2
3
3
3
3
3
3
2m 3 L1 a 3\ S sin \ S \ S 2m 3 L1 a 3\ S (\ S \ S ) cos \ S \ S 1
sin \
2
3
m L a \
1
2
3
2
3
m 3 L1 a 3\ S sin \ S \ S m 3 L1 a 3 (\ S \ S ) cos \ S \ S 2
m 3 L1 a 3\ S
3
2
3
\ S
S2
3
mgK 3 sin \ S \ S \ S Bl
1
Bl
3
1
2
3
1
3
2
S3
3
3
2
(\ S \ S ) cos \ S \ S 2
3
2
3
3
2 F\ S sin \ S 2m 3 L 2 a 3\ S sin \ S 2m 3 L1 a 3 (\ S \ S ) sin \ S \ S 2
2
3
3
2
3
2
2 F\ S sin \ S F\ S sin \ S 2m 3 L 2 a 3\ S sin \ S 1
2
2
2
3
3
2m 3 L1 a 3\ S sin \ S \ S m 3 L1 a 3 (\ S \ S ) sin \ S \ S 1
2
3
2
3
m 3 L1 a 3\ S sin \ S \ S m 3 L1 a 3\ S sin \ S \ S 2
Bl
3
2
3
3
2
3
2
3
2m 3 L 2 a 3\ S sin \ S 2m 3 L 2 a 3\ S sin \ S 2m 3 L 2 a 3\ S sin \ S 1
3
2
3
3
3
2m 3 L1 a 3\ S sin \ S \ S m 3 L1 a 3\ S sin \ S \ S 1
2
3
2
2
3
m 3 L1 a 3 (\ S \ S ) sin \ S \ S m 3 L1 a 3\ S sin \ S \ S 2
Cl
1
3
2
3
3
2 A 2 m 3 L 2 a 3 cos \ S 2 m 3 L1 a 3 cos \ S \ S 3
2
3
2
3
39
3
Cl
2
D E F cos \ S 2 m 3 L 2 a 3 cos \ S m 3 L1 a 3 cos \ S \ S
3
m3 L2 a 3 cos\ S m3 L1 a 3 cos \ S \ S
Cl
Dl
2
3
3
2
3
2
3
2 A\ S D\ S E\ S 2 F\ S cos \ S 2 F\ S \ S sin \ S
0
1
2
2
F\ S cos\ S F\ 2
2
1
2
1
2
2
sin \ S 2m 3 L 2 a 3\ S cos\ S
2 S2
2
1
3
2m 3 L 2 a 3\ S \ S sin \ S 2m 3 L 2 a 3\ S cos \ S 1
3
3
2
3
2m 3 L 2 a 3\ S \ S sin \ S m 3 L 2 a 3\ S cos\ S m 3 L 2 a 3\ S2 sin \ S 2
3
3
3
3
3
3
2m 3 L1 a 3\ S cos \ S \ S 2m 3 L1 a 3\ S (\ S \ S ) sin \ S \ S 1
cos \
2
3
1
2
3
\ m L a \ (\ \ ) sin \ mgK cos \ \ mgK cos \ \
2
3
m 3 L1 a 3\ S cos \ S \ S m 3 L1 a 3\ S (\ S \ S ) sin \ S \ S 2
m 3 L1 a 3\ S
3
mgK 1 cos \ S
1
2
3
S2
S3
3
1
S1
2
3
2
2
3
2
S3
S2
S3
S2
S2
3
S1
S2
3
\ S
3
\ S
3
Ɍɚɤ ɤɚɤ ɜɨ ɜɪɟɦɹ ɩɪɨɜɟɞɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨɥɨɠɟɧɢɟ ɫɬɨɩɵ ɱɟɥɨɜɟɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɬɚɛɢɥɨɝɪɚɮɚ ɧɟ ɨɩɪɟɞɟɥɹɥɨɫɶ, ɩɪɢɦɟɦ x N xO ~ xN (2.4) ɝɞɟ xO - ɧɟɢɡɜɟɫɬɧɨɟ ɩɨɥɨɠɟɧɢɟ ɧɚɱɚɥɚ ɨɬɫɱɟɬɚ ɫɬɚɛɢɥɨɝɪɚɮɚ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ O1 XY , ɚ ~ x N - ɟɝɨ ɩɨɤɚɡɚɧɢɹ. 2.2. ɍɪɚɜɧɟɧɢɹ ɜ ɤɨɧɟɱɧɵɯ ɪɚɡɧɨɫɬɹɯ Ⱦɥɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɱɢɫɥɟɧɧɵɯ ɚɥɝɨɪɢɬɦɨɜ ɩɪɟɞɫɬɚɜɢɦ ɩɪɨɢɡɜɨɞɧɵɟ ɜ ɜɢɞɟ ɤɨɧɟɱɧɵɯ ɪɚɡɧɨɫɬɟɣ. d\ ' (t i )
1
dt
W
j
d 2\ ' (t i ) j
dt
2
\ 1
W2
'j
(t i 1 ) \ ' (t i )
\
'j
j
(2.5)
(t i 1 ) \ ' (t i 1 ) 2\ ' (t i ) j
j
(2.6)
j 1,2,3 ɉɨɞɫɬɚɜɢɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɪɚɡɧɨɫɬɧɵɯ ɫɯɟɦ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɩɪɨɢɡɜɨɞɧɨɣ (2.5), (2.6) ɢ ɜɵɪɚɠɟɧɢɟ (2.4) ɜ (2.3) ɢ ɫɝɪɭɩɩɢɪɭɟɦ ɫɥɚɝɚɟɦɵɟ
40
U 1 t i \ ' (t i 1 ) V1 t i \ ' (t i 1 ) W1 t i \ ' (t i 1 ) U 2 t i \ ' (t i ) 1
2
3
1
V 2 t i \ ' (t i ) W 2 t i \ ' (t i ) U 3 t i \ ' (t i 1 ) 2
3
1
V3 t i \ ' (t i 1 ) W3 t i \ ' (t i 1 ) 2
(2.7)
3
N t i x O N x N t i Dl t i 0
ɝɞɟ
Cl t i
U 1i { U 1 t i
1
W2
Bl t i
U 2i { U 2 t i
V2i { V2 t i V3i { V3 t i
W
Bl t i
U 3i { U 3 t i
V1i { V1 t i
1
1
W
2
Cl t i 1
W2
Cl t i 1
W2
Cl t i 2
W2 Al t i 2
Bl t i 2
W
Bl t i 2
W
2
Cl t i
Cl t i 2
W2
(2.8)
2
W2
Cl t i
W1i { W1 t i
3
W2
Bl t i
W2i { W2 ti
Al ti
W3i { W3 ti
Bl ti Cl t i 2
3
3
W
3
W
2
Cl ti 3
W2
3
W
ȼ ɢɬɨɝɟ ɩɨɥɭɱɢɥɢ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ ɜɢɞɚ (2.7) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧ \ ' (t i ) ɩɨ ɢɡɜɟɫɬɧɵɦ ɢɡɦɟɪɟɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ - N t i , ~ x t . j
N
i
2.3. ɋɨɜɦɟɫɬɧɚɹ ɨɛɪɚɛɨɬɤɚ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɧɚɛɥɸɞɟɧɢɣ ɢ ɫɬɚɛɢɥɨɝɪɚɮɚ ɉɨɥɨɠɟɧɢɟ ɫɤɟɥɟɬɧɨɝɨ ɬɪɟɯɡɜɟɧɧɢɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɝɥɚɦɢ
\ 1 ,\ 2 ,\ 3 . ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɛɪɚɛɨɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ [5] ɜɵɱɢɫɥɟɧɵ ɜɟɥɢɱɢɧɵ ɷɬɢɯ ɭɝɥɨɜ. ɉɪɟɞɫɬɚɜɢɦ ɧɚɣɞɟɧɧɵɟ ɜɟɥɢɱɢɧɵ
41
ɭɝɥɨɜ \ P (t i ) ɜ ɜɢɞɟ ɫɭɦɦɵ ɭɝɥɨɜ \ j (t i ) , ɪɟɚɥɢɡɭɟɦɵɯ ɜ ɞɜɢɠɟɧɢɢ j
ɬɪɟɯɡɜɟɧɧɢɤɚ, ɢ ɚɞɞɢɬɢɜɧɨɣ ɩɨɝɪɟɲɧɨɫɬɢ [ ij , ɜɨɡɧɢɤɲɟɣ ɜ ɪɟɡɭɥɶɬɚɬɟ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ ɜɢɞɟɨɤɚɦɟɪɵ. j 1,2,3 \ P (t i ) \ j (t i ) [ ij
(2.8)
j
Ɍɨɝɞɚ ɢɡ (2.1) ɫ ɭɱɟɬɨɦ (2.8) ɫɥɟɞɭɟɬ j \ ' (t i ) \ P (t i ) \ S (t i ) [ ij j
j
j
(2.9)
1,2,3
ɉɪɢ ɨɛɪɚɛɨɬɤɟ ɜɢɞɟɨɢɡɨɛɪɚɠɟɧɢɹ ɜɵɞɟɥɟɧ ɭɱɚɫɬɨɤ ɞɥɢɧɨɣ n ɤɚɞɪɨɜ ɫ ɱɚɫɬɨɬɨɣ k ɤɚɞɪɨɜ ɜ ɫɟɤɭɧɞɭ, ɫɢɧɯɪɨɧɢɡɢɪɨɜɚɧɧɵɣ ɫ ɞɚɧɧɵɦɢ ɫɬɚɛɢɥɨɝɪɚɮɚ. Ⱦɥɹ ɷɬɨɝɨ ɭɱɚɫɬɤɚ ɡɚɩɢɲɟɦ 3n ɭɪɚɜɧɟɧɢɣ ɜɢɞɚ (2.9). Ⱦɨɛɚɜɢɦ ɤ ɫɢɫɬɟɦɟ ɭɪɚɜɧɟɧɢɹ (2.7). Ɂɚɦɟɬɢɦ, ɱɬɨ ɭɪɚɜɧɟɧɢɹ ɜɢɞɚ (2.7) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɬɨɥɶɤɨ ɞɥɹ n 2 ɦɨɦɟɧɬɨɜ ɜɪɟɦɟɧɢ, ɬɚɤ ɤɚɤ ɩɟɪɜɨɟ ɢ ɩɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɹ ɦɨɝɭɬ ɫɥɭɠɢɬɶ ɞɥɹ ɨɬɵɫɤɚɧɢɹ ɧɟɢɡɜɟɫɬɧɵɯ ɜɟɥɢɱɢɧ \ ' (t 0 ) ɢ \ ' (t n 1 ) , ɨɬɵɫɤɚɧɢɟ ɤɨɬɨɪɵɯ ɧɟ ɢɦɟɟɬ j
j
ɫɦɵɫɥɚ, ɬɚɤ ɤɚɤ ɞɥɹ ɧɢɯ ɧɟ ɡɚɞɚɧɨ ɨɩɨɪɧɨɟ ɪɟɲɟɧɢɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɩɪɚɜɨɤ \ ' ɢɫɩɨɥɶɡɭɟɦ j
3n ɭɪɚɜɧɟɧɢɣ ɜɢɞɚ (2.9) ɢ n 2 ɭɪɚɜɧɟɧɢɣ ɜɢɞɚ (2.7) ɞɥɹ 3n ɧɟɢɡɜɟɫɬɧɵɯ ɜɟɥɢɱɢɧ \ ' (t i ) . ȿɳɟ ɨɞɧɨɣ ɧɟɢɡɜɟɫɬɧɨɣ ɜɟɥɢɱɢɧɨɣ ɹɜɥɹj
ɟɬɫɹ xO , ɨɩɢɫɵɜɚɸɳɚɹ ɩɪɨɞɨɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɧɚɱɚɥɚ ɨɬɫɱɟɬɚ ɩɥɚɬɮɨɪɦɵ ɫɬɚɛɢɥɨɝɪɚɮɚ ɨɬ ɨɫɢ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ. Ɉɛɴɟɞɢɧɢɦ ɭɪɚɜɧɟɧɢɹ (2.7) ɢ (2.9) ɜ ɟɞɢɧɭɸ ɫɢɫɬɟɦɭ ɢ ɩɪɟɞɫɬɚɜɢɦ ɟɟ ɜ ɦɚɬɪɢɱɧɨɦ ɜɢɞɟ :x 4 [ , (2.10) ɝɞɟ
42
:
§ 1 ¨ ¨ 0 ¨ 0 ¨ ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨ # ¨ ¨ ¨ # ¨ ¨ 0 ¨U 12 ¨ ¨ # ¨ 0 ©
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
"
"
%
0 V12
0 W12
"
0
0 U 22
0 V 22
0 W 22
0 U 32
0 V32
0 W32
% " "
0 0
U 1n 1 V1n 1 W1n 1 U 2n 1 V 2n 1 W 2n 1 U 3n 1 V3n 1
\ P (t1 ) \ S (t1 ) § · ¨ ¸ \ P (t1 ) \ S (t1 ) ¨ ¸ ¨ ¸ \ P (t1 ) \ S (t1 ) ¸ ¨ ¸ ¨ \ P (t2 ) \ S (t2 ) ¸ ¨ \ P (t2 ) \ S (t2 ) ¸ ¨ ¸ ¨ \ P (t2 ) \ S (t2 ) ¸ ¨ # ¸ ¨ ¸ ¨ ¸ ¨ # ¸ ¨ ¸ ¨ \ P (tn ) \ S (tn ) ¸ ¨ ¸ ¨ \ P (tn ) \ S (tn ) ¸ ¨ t t \ \ ( ) ( ) n S n P ¸ ¨ ¨ N (t 2 ) ~ xN (t2 ) Dl (t 2 ) ¸ ¸ ¨ # ¸ ¨ ¨ N (t ) ~ xN (tn 2 ) Dl (t n 2 ) ¸¹ n2 © 1
4
0 0 0 0
1
2
2
3
3
1
1
2
2
3
3
1
· ¸ ¸ ¸ ¸ ¸ ¸ 0 0 ¸ ¸ 0 0 ¸ 0 0 ¸ ¸ 0 0 ¸ # # ¸ ¸ ¸ ¸ # # ¸ 1 0 ¸ 0 N t 2 ¸ ¸ # # ¸ W3n 1 N t n 1 ¸¹ 0 0 0 0
1
2
2
3
3
0
§ \ ' (t1 ) · ¨ ¸ ¨ \ ' (t1 ) ¸ ¨ \ (t ) ¸ ¨ ' 1 ¸ ¨ \ ' (t 2 ) ¸ ¨ ¸ ¨\ ' (t ) ¸ ¨ \ ' (t 2 ) ¸ ¨ ¸ ¨ # ¸ ¨ ¸ ¨ ¸ ¨ # ¸ ¨ \ (t ) ¸ ¨ ' n ¸ ¨ \ ' (t n ) ¸ ¨ ¸ ¨ \ ' (t n ) ¸ ¨ x ¸ O © ¹ 1
2
3
1
2
2
3
x
1
2
3
0
[ - ɜɟɤɬɨɪ ɩɨɝɪɟɲɧɨɫɬɢ ɢɡɦɟɪɟɧɢɣ Ɇɚɬɪɢɰɚ : ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ( 3n 1 u 4n 2 ), ɜɟɤɬɨɪ x - ɪɚɡɦɟɪɧɨɫɬɶ ( 1 u 3n 1 ), ɜɟɤɬɨɪ 4 -ɪɚɡɦɟɪɧɨɫɬɶ ( 1 u 4n 2 ). Ɋɟɲɚɹ ɷɬɨ ɩɟɪɟɨɩɪɟɞɟɥɟɧɧɨɟ ɦɚɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ [7], ɩɨɥɭɱɚɟɦ ɪɟɲɟɧɢɟ ɞɥɹ x ɜ ɜɢɞɟ x ( : 7 : ) 1 : 7 4 (2.11) ɉɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɹɜɥɹɟɬɫɹ ɜɟɤɬɨɪɨɦ ɩɨɩɪɚɜɨɱɧɵɯ ɡɧɚɱɟɧɢɣ, ɭɬɨɱɧɹɸɳɢɯ ɜɵɛɪɚɧɧɵɟ ɜ ɧɚɱɚɥɟ ɩɪɢɛɥɢɠɟɧɧɨ “ɨɩɨɪɧɵɟ
43
ɡɧɚɱɟɧɢɹ” ɭɝɥɨɜ \ S . Ɉɰɟɧɤɭ ɭɝɥɨɜ ɫɥɟɞɭɟɬ ɢɫɤɚɬɶ ɜ ɜɢɞɟ \~ \ \ j
j
'j
Sj
2.4. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɡɚɞɚɱɢ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɧɚɛɥɸɞɟɧɢɣ ɢ ɫɬɚɛɢɥɨɝɪɚɮɚ ɉɪɨɜɟɞɟɦ ɱɢɫɥɟɧɧɭɸ ɩɪɨɜɟɪɤɭ ɜɵɲɟɨɩɢɫɚɧɧɨɝɨ ɚɥɝɨɪɢɬɦɚ ɫ ɩɨɦɨɳɶɸ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ɋɚɫɫɦɨɬɪɢɦ ɦɨɞɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ, ɭ ɤɨɬɨɪɨɝɨ ɜɨ ɜɪɟɦɹ ɩɪɢɫɟɞɚɧɢɣ ɢ ɜɫɬɚɜɚɧɢɣ ɬɚɡɨɛɟɞɪɟɧɧɵɣ ɫɭɫɬɚɜ ɞɜɢɠɟɬɫɹ ɜɟɪɬɢɤɚɥɶɧɨ ɢ ɧɚɯɨɞɢɬɫɹ ɧɚɞ ɝɨɥɟɧɨɫɬɨɩɧɵɦ ɫɭɫɬɚɜɨɦ. ȼɪɟɦɹ ɞɜɢɠɟɧɢɹ ɩɪɢɦɟɦ ɪɚɜɧɵɦ ɨɞɧɨɣ ɫɟɤɭɧɞɟ, T 1ɫɟɤ . Ɍɨɝɞɚ ɭɝɨɥ \ 1 ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ \ 2 ɩɨ ɮɨɪɦɭɥɟ § L L2 cos\ 2 · ¸¸ arctg ¨¨ 1 © L2 sin \ 2 ¹ ɉɨɥɨɠɢɦ, ɱɬɨ \ 2 ɢ \ 3 ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɡɚɤɨɧɭ
\1
\2 \3
(2.12)
sin(Z 2 t )
(2.13)
S
\ 1 \ 2 Z 3t (2.14) 2 Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɛɭɞɟɦ ɩɪɨɢɡɜɨɞɢɬɶ ɞɥɹ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ
Z2 Z3
S 3T
Z 2 / 10
ɉɪɢɦɟɦ ɫɥɟɞɭɸɳɢɟ ɩɚɪɚɦɟɬɪɵ ɫɢɫɬɟɦɵ L1 0.4 ɦ L 2 0.38 ɦ a1 0.22 ɦ m 96 ɤɝ - ɦɚɫɫɚ ɱɟɥɨɜɟɤɚ
a2
0.21ɦ
a3
0.35 ɦ
m1 8.3 ɤɝ - ɦɚɫɫɚ ɞɜɭɯ ɝɨɥɟɧɟɣ m2
27.2 ɤɝ - ɦɚɫɫɚ ɞɜɭɯ ɛɟɞɟɪ
m3 57.9 ɤɝ - ɦɚɫɫɚ ɬɭɥɨɜɢɳɚ (ɜɤɥɸɱɚɹ ɝɨɥɨɜɭ ɢ ɪɭɤɢ) I1 0.1 ɤɝ ɦ 2 - ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɝɨɥɟɧɟɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɯ ɨɛɳɟɝɨ ɰɟɧɬɪɚ ɦɚɫɫ I 2 0.54ɤɝ ɦ 2 - ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɛɟɞɟɪ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɯ ɨɛɳɟɝɨ ɰɟɧɬɪɚ ɦɚɫɫ I 3 1.5ɤɝ ɦ 2 - ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɭɥɨɜɢɳɚ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɟɝɨ ɰɟɧɬɪɚ ɦɚɫɫ
44
O 1 / 25 - ɩɟɪɢɨɞ ɞɢɫɤɪɟɬɢɡɚɰɢɢ (ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɱɚɫɬɨɬɟ 25 ɤɚɞɪɨɜ ɜ ɫɟɤɭɧɞɭ) Ɂɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɜɵɛɪɚɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ [8] ɞɥɹ ɢɫɩɵɬɭɟɦɨɝɨ, ɩɪɢɧɢɦɚɜɲɟɝɨ ɭɱɚɫɬɢɟ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ. ɂɡɦɟɪɟɧɢɹ \ P ,\ P ,\ P ɡɚɞɚɧɵ ɜ ɪɟɡɭɥɶɬɚɬɟ ɞɨɛɚɜɥɟɧɢɹ ɤ 1
2
3
ɡɧɚɱɟɧɢɹɦ \ 1 ,\ 2 ,\ 3 ɢɡ (2.12) - (2.14) ɯɚɪɚɤɬɟɪɧɵɯ ɩɨɝɪɟɲɧɨɫɬɟɣ '\ j
\P
j
\ j '\ j k\
j
(2.15)
1,2,3
ȼ ɤɚɱɟɫɬɜɟ ɝɪɭɛɨɣ ɦɨɞɟɥɢ ɩɨɝɪɟɲɧɨɫɬɟɣ ɢɫɩɨɥɶɡɨɜɚɧɵ ɜɟɥɢɱɢɧɵ '\ j \ Pexp \ Sexp j 1,2,3 j
ɝɞɟ
\
exp Sj
j
\ Pexp - ɢɡɦɟɪɟɧɢɹ ɭɝɥɨɜ, ɜɡɹɬɵɟ ɢɡ ɪɟɚɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ, j
- ɜɟɥɢɱɢɧɵ ɬɟɯ ɠɟ ɭɝɥɨɜ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɝɥɚɠɢɜɚɧɢɹ
ɩɨɤɚɡɚɧɢɣ ɨɤɧɨɦ ɏɚɧɧɚ ɲɢɪɢɧɨɣ 0.4 ɫɟɤɭɧɞɵ [5], k\ - ɡɚɞɚɧɧɵɣ ɞɥɹ ɜɫɟɣ ɪɟɚɥɢɡɚɰɢɢ ɤɨɷɮɮɢɰɢɟɧɬ, ɩɨɡɜɨɥɹɸɳɟɣ ɜɚɪɶɢɪɨɜɚɬɶ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɜɨɡɦɭɳɟɧɢɹ. ɋɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜɟɥɢɱɢɧɵ '\ 1 ɨɬ ɧɭɥɟɜɨɝɨ ɫɪɟɞɧɟɝɨ ɫɨɫɬɚɜɢɥɨ V 1O 0.37 0 ɞɥɹ ɭɝɥɚ ȥ1,
V 2O
0.78 0 ɞɥɹ ɭɝɥɚ ȥ2 ɢ V 3O
0.40 0 ɞɥɹ ɭɝɥɚ ȥ3.
Ⱦɥɹ ɦɨɞɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɦɟɧɬ M 1mod ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ ɜɵɱɢɫɥɢɦ ɩɨ ɮɨɪɦɭɥɟ (1.16). ɂɡɦɟɪɟɧɢɹ ɫɬɚɛɢɥɨɝɪɚɮɚ ɦɨɞɟɥɢɪɭɸɬɫɹ ɜ ɜɢɞɟ M 1mod M 1mod 'M 1 . Ɂɞɟɫɶ 'M 1 - ɫɥɭɱɚɣɧɚɹ ɩɨP ɝɪɟɲɧɨɫɬɶ “ɢɡɦɟɪɟɧɢɹ”. (2.16) 'M 1 max M 1mod k M K ɝɞɟ K - ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɨɬ -1 ɞɨ 1, ɚ k M - ɤɨɧɫɬɚɧɬɚ, ɡɚɞɚɸɳɚɹ ɜɟɥɢɱɢɧɭ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɢɡɦɟɪɟɧɢɣ ɦɨɦɟɧɬɚ. ȼɟɥɢɱɢɧɭ xO ɫɱɢɬɚɟɦ ɪɚɜɧɨɣ ɧɭɥɸ. ɉɪɨɜɟɪɢɦ ɪɚɛɨɬɭ ɩɪɟɞɥɚɝɚɟɦɨɝɨ ɚɥɝɨɪɢɬɦɚ. Ⱦɥɹ ɷɬɨɝɨ ɢɫɩɨɥɶɡɭɟɦ ɜ ɤɚɱɟɫɬɜɟ ɡɧɚɱɟɧɢɣ \ S ɜɟɥɢɱɢɧɵ, ɩɨɥɭɱɟɧɧɵɟ ɢɡ ɫɨɨɬɧɨj
ɲɟɧɢɣ (2.12) – (2.14), ɢ ɜɵɱɢɫɥɢɦ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ (2.10) ɜɟɤɬɨɪ x ɩɨ “ɢɡɦɟɪɟɧɢɹɦ” ɭɝɥɨɜ \ P ɢɡ (2.15) ɢ “ɢɡɦɟɪɟɧj
ɧɵɦ” ɡɧɚɱɟɧɢɹɦ ɦɨɦɟɧɬɚ M 1mod P . Ⱦɥɹ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɡɚɞɚɱɢ ɩɪɢ ɢɞɟɚɥɶɧɨɦ ɪɟɲɟɧɢɢ ɩɨɩɪɚɜɤɢ \ ' ɞɨɥɠɧɵ ɩɪɢɧɢɦɚɬɶ ɧɭɥɟɜɵɟ ɡɧɚɱɟj
ɧɢɹ. ȼɵɱɢɫɥɟɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɜ ɩɚɤɟɬɟ MATLAB. ȼ ɬɚɛɥɢɰɭ 1 ɫɜɟɞɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɭɝɥɨɜ \ P ɢɡ (2.15) ɫ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɪɚɡɧɨɣ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɢ j
45
ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɢɡɦɟɪɟɧɢɹ ɦɨɦɟɧɬɚ k M 1 / 50 . ɉɪɢɜɟɞɟɧɵ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɢɟ ɨɬɤɥɨɧɟɧɢɹ ɨɲɢɛɤɢ ɨɰɟɧɢɜɚɧɢɹ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɜɢɞɟɨɤɚɦɟɪɵ ɢ ɨɲɢɛɤɢ ɨɰɟɧɢɜɚɧɢɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɩɨɤɚɡɚɧɢɣ ɜɢɞɟɨɤɚɦɟɪɵ ɢ ɫɬɚɛɢɥɨɝɪɚɮɚ. ȼɢɞɧɨ, ɱɬɨ ɞɥɹ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɩɨɝɪɟɲɧɨɫɬɟɣ '\ j ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɭɝɥɨɜ ɩɪɟɞɥɨɠɟɧɧɚɹ ɩɪɨɰɟɞɭɪɚ ɤɨɪɪɟɤɰɢɢ ɩɨɧɢɠɚɟɬ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɹ ɩɨɝɪɟɲɧɨɫɬɟɣ ɨɰɟɧɨɤ ɭɝɥɨɜ. Ɉɞɧɚɤɨ ɞɥɹ ɪɟɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɩɨɝɪɟɲɧɨɫɬɢ, ɧɚɛɥɸɞɚɸɳɟɣɫɹ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ, ɭɬɨɱɧɟɧɢɟ ɧɟ ɩɪɨɢɫɯɨɞɢɬ. ɉɪɢ ɷɬɨɦ ɧɚɛɥɸɞɚɟɬɫɹ ɫɢɫɬɟɦɚɬɢɱɟɫɤɚɹ ɨɲɢɛɤɚ ɦɟɬɨɞɚ ~ 1ɨ. ɗɬɨɬ ɦɨɞɟɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ ɤɨɫɜɟɧɧɨ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɩɪɢ ɩɨɩɵɬɤɟ ɨɛɪɚɛɨɬɤɢ ɪɟɡɭɥɶɬɚɬɨɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɚɩɢɫɟɣ, ɩɪɨɜɟɞɟɧɧɵɯ ɜ ɂɆȻɉ ɊȺɇ.
ɋɪ. ɤɜ. ɨɬɤɥɨɧɟɧɢɟ ɨɰɟɧɤɢ \ '
ɋɪ. ɤɜ. ɨɬɤɥɨɧɟɧɢɟ ɨɰɟɧɤɢ \ '
ɋɪ. ɤɜ. ɨɬɤɥɨɧɟɧɢɟ ɨɰɟɧɤɢ \ '
V 1 (ɝɪɚɞɭɫɵ)
V 2 (ɝɪɚɞɭɫɵ)
V 3 (ɝɪɚɞɭɫɵ)
ȼɢɞɟɨɤɚɦɟɪɚ
0.37
0.78
0.40
ɋɨɜɦɟɫɬɧɚɹ ɨɛɪɚɛɨɬɤɚ
0.62
0.77
0.42
ȼɢɞɟɨɤɚɦɟɪɚ
0.75
1.56
0.80
ɋɨɜɦɟɫɬɧɚɹ ɨɛɪɚɛɨɬɤɚ
0.63
0.80
0.41
ȼɢɞɟɨɤɚɦɟɪɚ
1.13
2.34
1.20
'\ j
1
k\
k\
k\
1
2
2
3
3
ɋɨɜɦɟɫɬɧɚɹ 0.67 0.84 0.41 ɨɛɪɚɛɨɬɤɚ Ɍɚɛɥɢɰɚ 1. Ɋɟɡɭɥɶɬɚɬɵ ɱɢɫɥɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɡɚɞɚɱɢ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɩɨɤɚɡɚɧɢɣ ɫɢɫɬɟɦɵ ɜɢɞɟɨɧɚɛɥɸɞɟɧɢɣ ɢ ɫɬɚɛɢɥɨɝɪɚɮɚ. ɉɨ-ɜɢɞɢɦɨɦɭ, ɨɫɧɨɜɧɭɸ ɞɨɥɸ ɨɲɢɛɤɢ ɜ ɩɪɨɜɟɞɟɧɧɵɯ ɪɚɫɱɟɬɚɯ ɫɨɫɬɚɜɥɹɸɬ ɩɨɝɪɟɲɧɨɫɬɢ ɚɥɝɨɪɢɬɦɚ, ɫɜɹɡɚɧɧɵɟ ɫ ɨɲɢɛɤɚɦɢ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɢɡɜɨɞɧɵɯ ɩɪɢ ɧɚɥɢɱɢɢ ɞɢɫɤɪɟɬɧɵɯ ɢɡɦɟɪɟɧɢɣ. ɋɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɟ ɷɬɨɣ ɱɚɫɬɢ ɚɥɝɨɪɢɬɦɚ, ɦɨɠɧɨ ɧɚɞɟɹɬɶɫɹ, ɩɨɡɜɨɥɢɬ ɩɨɜɵɫɢɬɶ ɟɝɨ ɬɨɱɧɨɫɬɶ.
46
3. ȼɨɫɫɬɚɧɨɜɥɟɧɢɟ ɡɧɚɱɟɧɢɣ ɭɝɥɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɨɤɚɡɚɧɢɣ ɫɬɚɛɢɥɨɝɪɚɮɚ
Ɋɚɫɫɦɨɬɪɢɦ ɡɚɞɚɱɭ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ \ 3 ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ. ɗɬɚ ɡɚɞɚɱɚ ɜɨɡɧɢɤɚɟɬ, ɧɚɩɪɢɦɟɪ, ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɩɪɢ ɞɜɢɠɟɧɢɢ ɱɟɥɨɜɟɤɚ ɧɟ ɭɞɚɟɬɫɹ ɜɨɫɫɬɚɧɨɜɢɬɶ ɤɨɨɪɞɢɧɚɬɵ ɜɟɪɯɧɟɝɨ ɤɚɬɚɮɨɬɚ ɧɚ ɬɭɥɨɜɢɳɟ ɞɥɹ ɧɟɤɨɬɨɪɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ. Ɍɨɝɞɚ ɧɚ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ [t 2 , t n 1 ] ɜɟɥɢɱɢɧɚ ɭɝɥɚ \ 3 ɨɫɬɚɟɬɫɹ ɧɟɢɡɜɟɫɬɧɨɣ. ɂɫɩɨɥɶɡɭɟɦ ɩɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɨɞɧɨɝɨ ɢɡ ɭɝɥɨɜ ɦɧɨɝɨɡɜɟɧɧɢɤɚ ɩɨ ɞɜɭɦ ɞɪɭɝɢɦ ɢ ɦɨɦɟɧɬɭ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ. ɉɭɫɬɶ ɢɡɦɟɪɹɸɬɫɹ ɡɧɚɱɟɧɢɹ ɭɝɥɨɜ \ 1 , \ 2 ɜɨ ɜɫɟ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɢ ɬɪɟɛɭɟɬɫɹ ɨɰɟɧɢɬɶ ɭɝɨɥ \ 3 ɩɨ ɨɩɨɪɧɨɦɭ ɡɧɚɱɟɧɢɸ \ S 3
ɢ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ. ȼ ɤɚɱɟɫɬɜɟ ɨɩɨɪɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ, ɧɚɩɪɢɦɟɪ, ɥɢɧɟɣɧɭɸ ɢɧɬɟɪɩɨɥɹɰɢɸ. ɇɚɱɚɥɶɧɨɟ \ P (t1 ) ɢ ɤɨɧɟɱɧɨɟ \ P (t n ) ɡɧɚɱɟɧɢɹ ɭɝɥɚ \ 3 ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ 3
3
ɫɭɫɬɚɜɟ ɢɡɜɟɫɬɧɵ. ɉɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɟɞɩɨɥɨɠɟɧɢɹɦɢ, ɫɞɟɥɚɧɧɵɦɢ ɜ ɝɥɚɜɟ 1, ɜɵɱɢɫɥɹɥɫɹ ɦɨɦɟɧɬ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ M 1 N x N
3.1.ɋɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɞɥɹ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɨ ɞɜɭɦ ɞɪɭɝɢɦ ɭɝɥɚɦ ɢ ɦɨɦɟɧɬɭ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ ɫɭɫɬɚɜɟ ɉɪɟɨɛɪɚɡɭɟɦ ɫɢɫɬɟɦɭ (2.11). ɋɱɢɬɚɟɦ, ɱɬɨ ɜɟɥɢɱɢɧɵ \ 3 (t1 ) , \ 3 (t n ) ɢɡɜɟɫɬɧɵ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɢɯ ɩɨɩɪɚɜɤɢ \ ' (t1 ) ɢ \ ' (t n ) ɪɚɜ3
3
ɧɵ ɧɭɥɸ. Ɉɩɨɪɧɨɟ ɪɟɲɟɧɢɟ ɞɥɹ \ 3 (t i ) ɜɵɛɟɪɟɦ ɜ ɜɢɞɟ ɥɢɧɟɣɧɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ. \ P 3 (t n ) \ P 3 (t 1 ) \ S 3 \ P 3 (t 1 ) ti t n t1 ɂɫɤɥɸɱɢɦ ɢɡ (2.7) ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ, ɫɱɢɬɚɹ, ɱɬɨ \ ' (t i ) 0, \ ' (t i ) 0, i 2,...n 2 , ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɢɡ n 2 1
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ɭɪɚɜɧɟɧɢɣ ɫ n 2 ɧɟɢɡɜɟɫɬɧɵɦɢ \ ' (t i ), i 3
2,..., n 1 . ɋɱɢɬɚɟɦ ɜɟ-
ɥɢɱɢɧɭ xO ɬɚɤɠɟ ɢɡɜɟɫɬɧɨɣ. ɋɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ \ ' ɩɪɢɦɟɬ ɜɢɞ 3
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- ɜɟɤɬɨɪ ɩɨɝɪɟɲɧɨɫɬɢ.
ȼ ɦɚɬɪɢɱɧɨɦ ɜɢɞɟ ɫɢɫɬɟɦɚ ɢɦɟɟɬ ɜɢɞ :1 x1 41 [ ɲɚɹ ɷɬɨ ɦɚɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɩɨɥɭɱɚɟɦ ɪɟɲɟɧɢɟ \ ' (t i ), i 2,..., n 2 .
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Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɞɟɣɫɬɜɢɣ ɩɪɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɢ ɭɝɥɚ ɢɦɟɟɬ ɜɢɞ: 1. ȼɵɛɢɪɚɟɦ ɨɩɨɪɧɨɟ ɪɟɲɟɧɢɟ \ S . 3
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ȼɵɱɢɫɥɹɟɦ ɦɚɬɪɢɰɵ :1 , 41 . Ɋɟɲɚɟɦ ɡɚɞɚɱɭ (3.1) ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ. ȼɵɱɢɫɥɹɟɦ \ P \ S \ ' . 3
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3.2.Ʉɨɦɩɶɸɬɟɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɡɚɞɚɱɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ.
Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɜɵɲɟɨɩɢɫɚɧɧɨɝɨ ɚɥɝɨɪɢɬɦɚ ɪɚɫɫɦɨɬɪɢɦ ɬɭ ɠɟ ɦɨɞɟɥɶɧɭɸ ɡɚɞɚɱɭ, ɱɬɨ ɢ ɜ 2.4. ɇɚ ɪɢɫ.6 ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɨɰɟɧɢɜɚɧɢɹ ɭɝɥɚ \ 3 ɞɥɹ ɦɨɞɟɥɶɧɨɣ ɡɚɞɚɱɢ ɩɪɢ O 1 / 25 , ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɱɚɫɬɨɬɟ ɞɢɫɤɪɟɬɧɵɯ ɢɡɦɟɪɟɧɢɣ 25 ɤɚɞɪɨɜ ɜ ɫɟɤɭɧɞɭ.
48
Ɋɢɫɭɧɨɤ 4. Ɋɟɡɭɥɶɬɚɬ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɪɢ ɱɚɫɬɨɬɟ ɜɢɞɟɨɫɴɟɦɤɢ 25 ɝɰ.
ɉɭɧɤɬɢɪɧɨɣ ɥɢɧɢɟɣ ɢɡɨɛɪɚɠɟɧɨ ɨɩɨɪɧɨɟ ɡɧɚɱɟɧɢɟ \ S 3 - ɥɢɧɟɣɧɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɡɧɚɱɟɧɢɹ ɞɥɹ ɭɝɥɚ \ 3 , ɲɬɪɢɯ-ɩɭɧɤɬɢɪɧɨɣ ɥɢɧɢɟɣ ɢɡɨɛɪɚɠɟɧɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ \ 3 , ɫɩɥɨɲɧɨɣ ɥɢɧɢɟɣ ɢɡɨɛɪɚɠɟɧɨ ɜɨɫɫɬɚɧɨɜɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ \ S 3 \ ' 3 . ɉɪɢɜɟɞɟɧɧɵɣ ɝɪɚɮɢɤ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɞɥɹ ɨɩɢɫɚɧɧɨɣ ɱɚɫɬɨɬɵ ɢɡɦɟɪɟɧɢɣ ɜ 25 ɝɟɪɰ ɜɨɫɫɬɚɧɨɜɢɬɶ ɡɧɚɱɟɧɢɹ ɭɝɥɚ \ 3 ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ ɧɟ ɭɞɚɟɬɫɹ: ɩɨɝɪɟɲɧɨɫɬɶ ɦɟɬɨɞɚ ɜɵɱɢɫɥɟɧɢɣ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɨɲɢɛɤɭ ɚɩɪɢɨɪɧɨɝɨ ɥɢɧɟɣɧɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ.
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Ɋɢɫɭɧɨɤ 5. Ɋɟɡɭɥɶɬɚɬ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɪɢ ɱɚɫɬɨɬɟ ɜɢɞɟɨɫɴɟɦɤɢ 100 ɝɰ.
ɇɚ ɪɢɫɭɧɤɟ 5 ɢɡɨɛɪɚɠɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɱɢɫɥɟɧɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɭɝɥɚ \ 3 ɞɥɹ ɱɚɫɬɨɬɵ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ 100 ɝɟɪɰ. ɉɪɢɜɟɞɟɧɧɵɣ ɝɪɚɮɢɤ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɞɥɹ ɫɤɨɪɨɫɬɧɨɣ ɜɢɞɟɨɫɴɟɦɤɢ ɢɫɩɨɥɶɡɭɟɦɨɣ ɧɚɢɛɨɥɟɟ ɛɨɥɟɟ ɦɨɳɧɵɦɢ ɫɢɫɬɟɦɚɦɢ ɚɧɚɥɢɡɚ ɞɜɢɠɟɧɢɣ [9] ɩɨɞɨɛɧɚɹ ɤɨɪɪɟɤɰɢɹ ɨɫɭɳɟɫɬɜɢɦɚ.
3.3.Ɋɟɡɭɥɶɬɚɬɵ ɨɛɪɚɛɨɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɜ ɡɚɞɚɱɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɂɫɩɨɥɶɡɭɟɦ ɢɦɟɸɳɢɟɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɨɰɟɧɤɢ ɜɨɡɦɨɠɧɨɫɬɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ \ 3 ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɫɬɚɛɢɥɨɝɪɚɮɚ. Ɂɚɩɢɫɢ ɷɤɫɩɟɪɢɦɟɧɬɚ, ɩɪɨɜɟɞɟɧɧɨɝɨ ɜ ɂɆȻɉ ɊȺɇ, ɩɨɡɜɨɥɹɸɬ ɫɦɨɞɟɥɢɪɨɜɚɬɶ ɫɢɬɭɚɰɢɸ ɫ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟɦ ɡɧɚɱɟɧɢɣ ɨɞɧɨɝɨ ɢɡ ɭɝɥɨɜ ɚɧɬɪɨɩɨɦɨɪɮɧɨɝɨ ɬɪɟɯɡɜɟɧɧɢɤɚ. Ɂɚɩɢɫɶ ɫɢɫɬɟɦɵ ɜɢɞɟɨɚɧɚɥɢɡɚ ɩɪɨɜɨɞɢɥɚɫɶ ɫ ɱɚɫɬɨɬɨɣ 25 ɝɰ. ɉɪɢ ɨɛɪɚɛɨɬɤɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ, ɱɬɨ ɡɧɚɱɟɧɢɟ ɭɝɥɚ \ 3 ɭɬɟɪɹɧɨ ɧɚ ɧɟɤɨɬɨɪɨɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ. ɂɫɩɨɥɶɡɨɜɚɥɚɫɶ ɩɪɨɰɟɞɭɪɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɨɩɢɫɚɧɧɚɹ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ
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ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ. ɂɫɩɨɥɶɡɨɜɚɧɚ ɜɟɥɢɱɢɧɚ xO ɨɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɜɵɱɢɫɥɟɧɢɣ ɪɚɡɞɟɥɚ 2. Ɋɟɡɭɥɶɬɚɬ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɫɪɚɜɧɢɜɚɥɫɹ ɫ ɜɟɥɢɱɢɧɚɦɢ ɭɝɥɚ \ 3 , ɨɩɪɟɞɟɥɹɟɦɵɦɢ ɩɪɹɦɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ.
Ɋɢɫɭɧɨɤ 6. Ɋɟɡɭɥɶɬɚɬ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɪɢ ɱɚɫɬɨɬɟ ɜɢɞɟɨɫɴɟɦɤɢ 25 ɝɰ.
Ɋɟɡɭɥɶɬɚɬɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɬɨɣ ɩɪɨɰɟɞɭɪɵ ɩɨɞɬɜɟɪɠɞɚɸɬ ɢɬɨɝɢ ɱɢɫɥɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɏɚɪɚɤɬɟɪɧɵɣ ɩɪɢɦɟɪ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɭɝɥɚ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫɭɧɤɟ 6. Ʉɚɤ ɢ ɞɥɹ ɦɨɞɟɥɶɧɨɣ ɡɚɞɚɱɢ ɪɟɡɭɥɶɬɚɬ ɨɰɟɧɢɜɚɧɢɹ ɭɝɥɚ ɩɪɢ ɱɚɫɬɨɬɟ ɜɢɞɟɨɫɶɟɦɤɢ 25 Ƚɰ. ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɧɟɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɵɦ. Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɩɨɝɪɟɲɧɨɫɬɢ ɨɰɟɧɢɜɚɧɢɹ ɞɥɹ ɦɨɞɟɥɶɧɨɝɨ ɩɪɢɦɟɪɚ ɢ ɞɥɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɵɣ ɩɨɪɹɞɨɤ. ɗɬɨɬ ɪɟɡɭɥɶɬɚɬ ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɨ ɬɨɦ, ɱɬɨ ɨɲɢɛɤɢ, ɜɵɡɜɚɧɧɵɟ ɞɨɩɭɳɟɧɢɹɦɢ, ɫɞɟɥɚɧɧɵɦɢ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ, ɧɟ ɩɪɟɜɵɲɚɸɬ ɨɲɢɛɨɤ, ɜɵɡɜɚɧɧɵɯ ɞɢɫɤɪɟɬɢɡɚɰɢɟɣ ɦɨɞɟɥɢ ɢ ɩɨɝɪɟɲɧɨɫɬɟɣ ɦɟɬɨɞɚ ɨɰɟɧɢɜɚɧɢɹ.
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Ɂɚɤɥɸɱɟɧɢɟ
ȼ ɡɚɤɥɸɱɟɧɢɟ ɩɨɞɜɟɞɟɦ ɢɬɨɝ ɩɪɨɜɟɞɟɧɧɵɦ ɢɫɫɥɟɞɨɜɚɧɢɹɦ. ȼ ɪɚɛɨɬɟ ɪɚɫɫɦɨɬɪɟɧɵ ɞɜɚ ɜɚɪɢɚɧɬɚ ɤɨɦɩɥɟɤɫɢɪɨɜɚɧɢɹ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ. ɉɟɪɜɵɣ ɢɡ ɧɢɯ ɫɜɹɡɚɧ ɫ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɜɨɡɦɨɠɧɨɫɬɶɸ ɭɬɨɱɧɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɢɡɦɟɪɟɧɢɣ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɪɟɡɭɥɶɬɚɬɨɜ ɢɡɦɟɪɟɧɢɹ ɪɚɡɧɨɪɨɞɧɵɯ ɞɚɬɱɢɤɨɜ. ȼɬɨɪɨɣ – ɩɨɡɜɨɥɹɟɬ ɜɨɫɫɬɚɧɚɜɥɢɜɚɬɶ ɭɬɟɪɹɧɧɵɟ ɢɡɦɟɪɟɧɢɹ. ȼɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɪɟɞɥɚɝɚɟɦɵɯ ɩɨɞɯɨɞɨɜ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧɚ ɧɚ ɩɪɢɦɟɪɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɱɟɥɨɜɟɤɚ ɜ ɫɚɝɢɬɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɪɢ ɜɫɬɚɜɚɧɢɢ ɢ ɩɪɢɫɟɞɚɧɢɢ. ɂɫɩɨɥɶɡɨɜɚɧ ɨɞɢɧ ɢɡ ɩɪɨɫɬɟɣɲɢɯ ɬɢɩɨɜ ɚɥɝɨɪɢɬɦɨɜ ɬɟɨɪɢɢ ɨɰɟɧɢɜɚɧɢɹ. ɉɨɩɵɬɤɢ ɪɟɲɟɧɢɹ ɤɨɧɤɪɟɬɧɵɯ ɡɚɞɚɱ, ɩɨɡɜɨɥɹɸɬ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ: ɑɚɫɬɨɬɚ ɫɴɟɦɚ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨɤɚɡɵɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɩɪɟɞɥɚɝɚɟɦɵɯ ɚɥɝɨɪɢɬɦɨɜ. Ɉɲɢɛɤɢ, ɜɵɡɜɚɧɧɵɟ ɞɨɩɭɳɟɧɢɹɦɢ, ɫɞɟɥɚɧɧɵɦɢ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ, ɫɤɨɪɟɟ ɜɫɟɝɨ ɧɟ ɩɪɟɜɵɲɚɸɬ ɨɲɢɛɨɤ, ɜɵɡɜɚɧɧɵɯ ɞɢɫɤɪɟɬɢɡɚɰɢɟɣ ɦɨɞɟɥɢ ɢ ɩɨɝɪɟɲɧɨɫɬɟɣ ɦɟɬɨɞɚ ɨɰɟɧɢɜɚɧɢɹ. ɋɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɟ ɬɟɯɧɨɥɨɝɢɢ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ ɦɨɠɟɬ ɩɨɡɜɨɥɢɬɶ ɫɧɢɡɢɬɶ ɭɪɨɜɟɧɶ ɩɨɝɪɟɲɧɨɫɬɟɣ ɞɥɹ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɤɨɦɩɥɟɤɫɨɜ ɫ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɨɣ ɫɴɟɦɚ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ. Ɋɚɡɪɚɛɨɬɤɚ ɚɥɝɨɪɢɬɦɨɜ ɭɬɨɱɧɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɢɡɦɟɪɟɧɢɣ ɩɪɢ ɫɨɜɦɟɫɬɧɨɣ ɨɛɪɚɛɨɬɤɟ ɩɨɤɚɡɚɧɢɣ ɧɟɫɤɨɥɶɤɢɯ ɞɚɬɱɢɤɨɜ ɰɟɥɟɫɨɨɛɪɚɡɧɚ ɬɨɥɶɤɨ ɞɥɹ ɫɥɭɱɚɹ ɝɪɭɛɨɣ ɢɧɮɨɪɦɚɰɢɢ. ɉɪɟɞɥɚɝɚɟɦɵɣ ɩɨɞɯɨɞ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɦ ɜ ɡɚɞɚɱɚɯ ɞɢɚɝɧɨɫɬɢɤɢ ɩɨɝɪɟɲɧɨɫɬɟɣ ɢ ɫɛɨɟɜ ɜ ɛɢɨɦɟɯɚɧɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɹɯ, ɚ ɬɚɤɠɟ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ ɚɥɝɨɪɢɬɦɨɜ ɭɫɬɪɚɧɟɧɢɹ ɷɬɢɯ ɫɛɨɟɜ.
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6. 7. 8. 9.
ȼɢɬɟɧɡɨɧ Ⱥ.ɋ. Ɂɚɤɨɧɨɦɟɪɧɨɫɬɢ ɧɨɪɦɚɥɶɧɨɣ ɢ ɩɚɬɨɥɨɝɢɱɟɫɤɨɣ ɯɨɞɶɛɵ ɱɟɥɨɜɟɤɚ.- Ɇ. ɐɇɂɂɉɉ. 1998. ȼɨɪɨɧɨɜ Ⱥ.ȼ. Ɋɨɥɶ ɨɞɧɨ- ɢ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɧɢɠɧɟɣ ɤɨɧɟɱɧɨɫɬɢ ɜ ɧɚɡɟɦɧɵɯ ɥɨɤɨɦɨɰɢɹɯ// Ɏɢɡɢɨɥɨɝɢɹ ɱɟɥɨɜɟɤɚ. 2004. Ɍ.30. N 4. ɋ. 114-122. ɇɨɜɨɠɢɥɨɜ ɂ.ȼ. ɢ ɞɪ. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫɝɢɛɚɬɟɥɶɧɨ-ɪɚɡɝɢɛɚɬɟɥɶɧɵɯ ɞɜɢɠɟɧɢɣ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɚ. – Ɇ. ɂɡɞ-ɜɨ ɦɟɯ-ɦɚɬ ɮ-ɬɚ ɆȽɍ. 2001 ɝ. Ʉɨɩɵɥɨɜ ɂ.Ⱥ., Ʉɪɭɱɢɧɢɧ ɉ.Ⱥ., ɇɨɜɨɠɢɥɨɜ ɂ.ȼ. Ɉ ɪɟɚɥɢɡɭɟɦɨɫɬɢ ɞɜɢɠɟɧɢɣ ɩɨ ɇ.Ⱥ.Ȼɟɪɧɲɬɟɣɧɭ.// ɂɡɜɟɫɬɢɹ ɊȺɇ. MTT. 2003. N 5. C. 39-49. Ɇɢɲɚɧɨɜ Ɇ.ɘ., ɋɚɪɤɢɫɹɧ Ɇ.ȼ. Ɉɩɪɟɞɟɥɟɧɢɟ ɦɵɲɟɱɧɵɯ ɭɫɢɥɢɣ ɩɪɢ ɫɝɢɛɚɬɟɥɶɧɨ-ɪɚɡɝɢɛɚɬɟɥɶɧɵɯ ɞɜɢɠɟɧɢɹɯ ɱɟɥɨɜɟɤɚ // ɋɨɜɪɟɦɟɧɧɵɟ ɬɟɯɧɨɥɨɝɢɢ ɜ ɡɚɞɚɱɚɯ ɭɩɪɚɜɥɟɧɢɹ ɚɜɬɨɦɚɬɢɤɢ ɢ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ. Ɍɪɭɞɵ XII Ɇɟɠɞɭɧɚɪɨɞɧɨɝɨ ɧɚɭɱɧɨ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɟɦɢɧɚɪɚ. - Ɇ. ɂɡɞ-ɜɨ Ɇɗɂ. 2003. ɋ. 134-135. ɋɤɜɨɪɰɨɜ Ⱦ.ȼ. Ʉɥɢɧɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɞɜɢɠɟɧɢɣ. ɋɬɚɛɢɥɨɦɟɬɪɢɹ.- Ɇ. ɇɚɭɱɧɨ-ɦɟɞɢɰɢɧɫɤɚɹ ɮɢɪɦɚ ɆȻɇ. Ⱥɧɬɢɞɨɪ. 2000. Ⱥɥɟɤɫɚɧɞɪɨɜ ȼ.ȼ. ɢ ɞɪ. Ɉɩɬɢɦɢɡɚɰɢɹ ɞɢɧɚɦɢɤɢ ɭɩɪɚɜɥɹɟɦɵɯ ɫɢɫɬɟɦ.- Ɇ. ɂɡɞ-ɜɨ ɆȽɍ, 2000. Ȼɟɝɭɧ ɉ.ɂ., ɒɭɤɟɣɥɨ ɘ.Ⱥ. Ȼɢɨɦɟɯɚɧɢɤɚ. - ɋɉɛ. ɂɡɞ-ɜɨ ɉɨɥɢɬɟɯɧɢɤɚ. 2000 ɝ. ȼɨɪɨɧɨɜ ȼ.Ⱥ. Ⱦɨɰɟɧɤɨ ȼ.ɂ., Ɍɢɬɚɪɟɧɤɨ ɇ.ɘ. Ɍɢɬɚɪɟɧɤɨ Ʉ.ȿ. Ʉɨɦɩɶɸɬɟɪɧɵɣ ɜɢɞɟɨɚɧɚɥɢɡ ɞɜɢɠɟɧɢɣ ɜ ɧɚɭɱɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɢ ɤɥɢɧɢɱɟɫɤɨɣ ɩɪɚɤɬɢɤɟ. // Ȼɢɨɦɟɯɚɧɢɤɚ 2004. VII ȼɫɟɪɨɫɫɢɣɫɤɚɹ ɤɨɧɮɟɪɟɧɰɢɹ ɩɨ ɛɢɨɦɟɯɚɧɢɤɟ. Ɍɟɡɢɫɵ ɞɨɤɥɚɞɨɜ. - ɇɢɠɧɢɣ ɇɨɜɝɨɪɨɞ 2004. ɫ. 36-38.
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Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɧɚɪɭɲɟɧɢɣ ɩɨɡɵ ɛɨɥɶɧɵɯ ɩɪɢ rectus-ɫɢɧɞɪɨɦɟ ɢ hamstring-ɫɢɧɞɪɨɦɟ
ɀɭɪɚɜɥɟɜ Ⱥ.Ɇ., ɁȺɈ «Ⱥɤɨɧɢɬ-Ɇɟɞɢɚ»
Ʉɪɭɱɢɧɢɧ ɉ.Ⱥ., ɏɚɤɢɦɨɜ Ⱥ.ɂ. ɆȽɍ ɢɦ. Ɇ.ȼ.Ʌɨɦɨɧɨɫɨɜɚ ȼɚɠɧɨɣ ɢ ɱɪɟɡɜɵɱɚɣɧɨ ɫɥɨɠɧɨɣ ɡɚɞɚɱɟɣ ɛɢɨɦɟɯɚɧɢɤɢ ɹɜɥɹɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɡɵ ɢ ɞɜɢɠɟɧɢɣ ɱɟɥɨɜɟɤɚ ɫ ɧɚɪɭɲɟɧɢɹɦɢ ɫɢɫɬɟɦɵ ɪɟɝɭɥɹɰɢɢ ɞɜɢɠɟɧɢɣ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɧɟɨɛɯɨɞɢɦɨ ɦɨɞɟɥɢɪɨɜɚɬɶ ɨɫɨɛɟɧɧɨɫɬɢ ɭɩɪɚɜɥɹɸɳɢɯ ɫɢɝɧɚɥɨɜ ɩɨɫɬɭɩɚɸɳɢɯ ɫɨ ɫɬɨɪɨɧɵ ɧɟɪɜɧɨɣ ɫɢɫɬɟɦɵ. ɉɨɩɵɬɤɢ ɦɚɤɫɢɦɚɥɶɧɨ ɬɨɱɧɨ ɨɬɨɛɪɚɡɢɬɶ ɨɫɨɛɟɧɧɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ (ɧɚɩɪɢɦɟɪ, ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɟɯɧɨɥɨɝɢɢ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ [1]) ɞɨ ɧɚɫɬɨɹɳɟɝɨ ɜɪɟɦɟɧɢ ɧɟ ɞɚɸɬ ɭɞɨɛɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ, ɩɨɡɜɨɥɹɸɳɟɝɨ ɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɩɨɡɵ ɢɥɢ ɩɨɯɨɞɤɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɨɩɟɪɚɬɢɜɧɨɝɨ ɜɦɟɲɚɬɟɥɶɫɬɜɚ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ, ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɫɧɨɜɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɩɨɡɵ ɢ ɞɜɢɠɟɧɢɹ ɛɨɥɶɧɵɯ ɫ ɩɨɦɨɳɶɸ ɭɩɪɨɳɟɧɧɵɯ ɫɬɪɭɤɬɭɪɧɵɯ ɦɨɞɟɥɟɣ ɢ «ɝɪɭɛɵɯ» ɩɪɟɞɩɨɥɨɠɟɧɢɣ ɨ ɰɟɥɹɯ ɢ ɫɜɨɣɫɬɜɚɯ ɭɩɪɚɜɥɟɧɢɹ ɦɵɲɟɱɧɵɦɢ ɭɫɢɥɢɹɦɢ. ɉɨɞɨɛɧɵɣ ɩɨɞɯɨɞ ɪɚɡɪɚɛɚɬɵɜɚɥɫɹ ɪɚɧɟɟ ɜ [2,3]. Ɋɚɫɫɦɨɬɪɢɦ ɩɨɞɪɨɛɧɨ ɡɚɞɚɱɭ ɬɚɤɨɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨɡɵ ɧɚ ɩɪɢɦɟɪɟ ɛɨɥɶɧɵɯ ɫ ɫɢɦɩɬɨɦɨɤɨɦɩɥɟɤɫɚɦɢ ɬɢɩɚ rectus-ɫɢɧɞɪɨɦ ɢ hamstring-ɫɢɧɞɪɨɦ. Ȼɨɥɶɧɵɟ ɫ ɷɬɢɦɢ ɫɢɧɞɪɨɦɚɦɢ ɨɬɧɨɫɹɬɫɹ ɤ ɝɪɭɩɩɟ ɛɨɥɶɧɵɯ ɫ ɡɚɛɨɥɟɜɚɧɢɹɦɢ ɞɟɬɫɤɨɝɨ ɰɟɪɟɛɪɚɥɶɧɨɝɨ ɩɚɪɚɥɢɱɚ ɢ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɩɨɜɵɲɟɧɧɵɦ ɬɨɧɭɫɨɦ ɪɚɡɥɢɱɧɵɯ ɝɪɭɩɩ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ [4,5]. ɉɪɢ rectus-ɫɢɧɞɪɨɦɟ ɩɨɜɵɲɟɧ ɬɨɧɭɫ ɩɪɹɦɨɣ ɦɵɲɰɵ ɛɟɞɪɚ (m. rectus femoris), ɚ ɩɪɢ hamstring-ɫɢɧɞɪɨɦɟ ɩɨɜɵɲɟɧ ɬɨɧɭɫ ɡɚɞɧɟɣ ɝɪɭɩɩɵ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɩɨɥɭɫɭɯɨɠɢɥɶɧɨɣ (m. semitendinosus), ɩɨɥɭɩɟɪɟɩɨɧɱɚɬɨɣ (m. semimembranosus) ɢ ɧɟɠɧɨɣ (m. gracilis) ɦɵɲɰ. ȼɨɡɦɨɠɧɵɦɢ ɤɥɢɧɢɱɟɫɤɢɦɢ ɩɪɨɹɜɥɟɧɢɹɦɢ ɝɢɩɟɪɬɨɧɭɫɚ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɧɚɤɥɨɧ ɬɚɡɚ, ɤɨɦɩɟɧɫɚɬɨɪɧɵɣ ɝɢɩɟɪɥɨɪɞɨɡ ɢ ɜɬɨɪɢɱɧɚɹ ɮɥɟɤɫɢɹ ɥɢɛɨ ɷɤɫɬɟɧɡɢɹ ɤɨɥɟɧɧɵɯ ɫɭɫɬɚɜɨɜ, ɚ ɜɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ - ɮɢɤɫɢɪɨɜɚɧɧɚɹ ɮɥɟɤɫɢɹ ɤɨɥɟɧɧɵɯ ɫɭɫɬɚɜɨɜ. ɂɫɯɨɞɧɚɹ ɩɨɡɚ ɷɬɢɯ ɛɨɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɬɪɨɣɧɵɦ ɫɝɢɛɚɧɢɟɦ ɜ ɫɭɫɬɚɜɚɯ ɧɢɠɧɢɯ ɤɨɧɟɱɧɨɫɬɟɣ (Z-ɨɛɪɚɡɧɨɣ ɩɨɡɨɣ ɩɪɢ ɫɬɨɹɧɢɢ). Ɋɚɫɫɦɨɬɪɢɦ ɦɨɞɟɥɶ, ɩɪɢɡɜɚɧɧɭɸ ɨɩɢɫɚɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɣ ɜɚɪɢɚɧɬ ɫɨɯɪɚɧɟɧɢɹ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɭ ɬɚɤɢɯ ɛɨɥɶɧɵɯ: ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɪɬɢɤɚɥɶɧɚɹ ɩɨɡɚ ɧɚ ɩɨɥɭɫɨɝɧɭɬɵɯ ɤɨɧɟɱɧɨɫɬɹɯ ɫɨ ɫɥɚɛɨ ɜɵɪɚɠɟɧɧɵɦɢ ɥɨɪɞɨɡɨɦ ɢ ɧɚɤɥɨɧɨɦ ɬɚɡɚ, ɤɚɤ ɦɨɠɧɨ ɜɢɞɟɬɶ ɧɚ ɮɨɬɨɝɪɚɮɢɹɯ, ɩɨɦɟɳɟɧɧɵɯ ɧɚ ɫɬɪɚɧɢɰɚɯ 3 ɢ 4 ɜɤɥɚɞɵɲɚ. 54
Ɉɩɢɲɟɦ ɩɨɥɨɠɟɧɢɟ ɤɨɪɩɭɫɚ ɱɟɥɨɜɟɤɚ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɫɚɝɝɢɬɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ. Ɋɚɫɫɦɨɬɪɢɦ ɬɪɚɞɢɰɢɨɧɧɭɸ ɩɥɨɫɤɭɸ ɬɪɟɯɡɜɟɧɧɭɸ ɚɧɬɪɨɩɨɦɨɪɮɧɭɸ ɫɯɟɦɭ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ: ɧɟɜɟɫɨɦɵɟ ɫɬɨɩɚ, ɝɨɥɟɧɶ, ɛɟɞɪɨ, ɢ ɬɹɠɟɥɵɣ ɤɨɪɩɭɫ (ɪɢɫ. 1). Ƚɨɥɨɜɚ ɢ ɪɭɤɢ ɫɱɢɬɚɸɬɫɹ ɧɟɩɨɞɜɢɠɧɵɦɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɪɩɭɫɚ, ɦɨɞɟɥɢɪɭɟɦɨɝɨ ɬɜɟɪɞɵɦ ɬɟɥɨɦ ɦɚɫɫɨɣ m, ɫɬɨɩɚ ɧɟɩɨɞɜɢɠɧɚ ɢ ɧɟ ɨɬɪɵɜɚɟɬɫɹ ɨɬ ɩɨɥɚ. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ Ɉ1, Ɉ2, Ɉ3 ɰɟɧɬɪɵ ɜɪɚɳɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ, ɤɨɥɟɧɧɨɝɨ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɝɨ ɫɭɫɬɚɜɨɜ, ɱɟɪɟɡ |Ɉ1Ɉ2|=L1, |Ɉ2Ɉ3|=L2 ɞɥɢɧɵ ɝɨɥɟɧɢ ɢ ɛɟɞɪɚ, M1, M2, M3 -ɭɝɥɵ ɩɨɜɨɪɨɬɨɜ Ɋɢɫɭɧɨɤ 1. Ɉɛɨɛɳɟɧɧɵɟ ɡɜɟɧɶɟɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɩɨɞɜɢɠɧɨɣ ɤɨɨɪɞɢɧɚɬɵ ɞɥɹ ɨɩɢɫɚɧɢɹ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ Ɉ1XYZ, ɫɜɹɡɚɧɧɨɣ ɩɨɡɵ. ɫɨ ɫɬɨɩɨɣ. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ \1 = M1, \2 =M2 - M1, \3 =M3 - M2 - ɭɝɥɵ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɩɨɜɨɪɨɬɨɜ. ɇɚ ɪɢɫɭɧɤɟ 2 ɩɪɟɞɫɬɚɜɥɟɧɚ ɪɚɫɱɟɬɧɚɹ ɦɨɞɟɥɶ ɨɫɧɨɜɧɵɯ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰɚɧɬɨɝɨɧɢɫɬɨɜ. ɇɚ ɪɢɫɭɧɤɟ ɫɩɥɨɲɧɵɦɢ ɥɢɧɢɹɦɢ ɢɡɨɛɪɚɠɟɧɵ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɢɟ ɷɥɟɦɟɧɬɵ ɫɤɟɥɟɬɚ ɢ ɫɭɯɨɠɢɥɶɧɵɟ ɨɤɨɧɱɚɧɢɹ ɦɵɲɰ, ɦɨɞɟɥɢɪɭɟɦɵɟ ɧɟɪɚɫɬɹɠɢɦɵɦɢ ɧɢɬɹɦɢ. Ⱦɟɮɨɪɦɢɪɭɟɦɵɟ, ɫɢɥɨɜɵɟ ɷɥɟɦɟɧɬɵ ɦɵɲɰ ɢɡɨɛɪɚɠɟɧɵ ɩɭɧɤɬɢɪɨɦ. ɇɚ ɪɢɫɭɧɤɟ ɨɛɨɡɧɚɱɟɧɵ ɬɚɤɠɟ ɭɝɥɵ ɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ, ɢɫɩɨɥɶɡɨɜɚɧɧɵɟ ɞɥɹ ɨɩɢɫɚɧɢɹ ɨɫɨɛɟɧɧɨɫɬɟɣ ɤɪɟɩɥɟɧɢɹ ɦɵɲɰ. Ȼɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɞɜɭɫɭɫɬɚɜɧɵɟ ɦɵɲɰɵ ɢɝɪɚɸɬ ɜɟɞɭɳɭɸ ɪɨɥɶ ɜ ɮɨɪɦɢɪɨɜɚɧɢɢ ɩɨɡɵ. ɍɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɜɵɜɟɞɟɧɵ ɜ [6,7] ɢ ɢɦɟɸɬ ɜɢɞ mgx c M \ 1 M 1 0 mga c cos(\ 1 \ 2 \ 3 D c ) M \ 3 M 3
0
(1)
mg[ L2 cos(\ 1 \ 2 ) a c cos(\ 1 \ 2 \ 3 D c )]
M \ 2 M 2
0
Ɂɞɟɫɶ x c L1 cos\ 1 L2 cos(\ 1 \ 2 ) a c cos(\ 1 \ 2 \ 3 D c )
(2)
55
Ɋɢɫɭɧɨɤ 2. ɉɪɢɛɥɢɠɟɧɧɚɹ ɫɯɟɦɚ ɤɪɟɩɥɟɧɢɹ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ.
- ɤɨɨɪɞɢɧɚɬɚ ɰɟɧɬɪɚ ɦɚɫɫ ɋ. M1, M2, M3- ɦɨɦɟɧɬɵ, ɫɨɡɞɚɜɚɟɦɵɟ ɨɞɧɨɫɭɫɬɚɜɧɵɦɢ ɦɵɲɰɚɦɢ ɜ ɝɨɥɟɧɨɫɬɨɩɧɨɦ, ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ; M\1, M\2, M\3 – ɦɨɦɟɧɬɵ, ɫɨɡɞɚɜɚɟɦɵɟ ɜ ɷɬɢɯ ɠɟ ɫɭɫɬɚɜɚɯ ɞɜɭɫɭɫɬɚɜɧɵɦɢ ɦɵɲɰɚɦɢ. ɗɬɢ ɦɨɦɟɧɬɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɫɯɟɦɚɦɢ ɧɚ ɪɢɫ. 2 ɱɟɪɟɡ ɭɫɢɥɢɹ ɜ ɦɵɲɰɚɯ ɩɨ ɮɨɪɦɭɥɚɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ [6,7] ad M \ 1 F1a 0 0 sin(\ 1 D 0 G 0 ) F1b s0 sin(\ 1 V 0 V 1 ) , A0 D0 M\ 2
F2a R2 F2b r2 F1b
s2 [' 1 sin(\ 2 V 2 ) L1
(3)
L1 sin V 1 cos(\ 2 V 2 )] ,
M\ 3
F a3 cos(\ 3 D 3 ) F2b b3 cos(\ 2 E 3 ) ,
ɝɞɟ A0 D0
a 2
a 02 d 02 2a 0 d 0 cos(\ 1 D 0 G 0 ) .
ȼ ɷɬɢ ɜɵɪɚɠɟɧɢɹ ɜɯɨɞɹɬ ɱɟɬɵɪɟ ɫɢɥɵ F1a, F1b, F2a, F2b ɪɚɡɜɢɜɚɟɦɵɟ ɝɪɭɩɩɚɦɢ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ ɢ ɝɨɥɟɧɢ. Ɂɞɟɫɶ ɢ ɞɚɥɟɟ ɜɟɪɯɧɢɟ ɢɧɞɟɤɫɵ a ɢ b ɩɪɢɧɚɞɥɟɠɚɬ ɜɟɥɢɱɢɧɚɦ, ɨɩɢɫɵɜɚɸɳɢɦ ɫɨɫɬɨɹɧɢɟ ɩɟɪɟɞɧɢɯ ɢ ɡɚɞɧɢɯ ɝɪɭɩɩ ɦɵɲɰ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɇɢɠɧɢɣ ɢɧɞɟɤɫ 1 ɭɤɚɡɵɜɚɟɬ ɧɚ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɩɚɪɚɦɟɬɪɚ ɤ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɦɵɲɰ ɝɨɥɟɧɢ, ɚ ɢɧɞɟɤɫ 2 – ɧɚ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɩɚɪɚɦɟɬɪɚ ɤ ɝɪɭɩɩɟ ɦɵɲɰ ɛɟɞɪɚ. 56
Ⱦɥɹ ɭɞɟɪɠɚɧɢɹ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɨɡɵ ɱɟɥɨɜɟɤɨɦ ɯɚɪɚɤɬɟɪɧɨ ɩɨɥɨɠɟɧɢɟ ɰɟɧɬɪɚ ɦɚɫɫ ɫɦɟɳɟɧɧɨɟ ɜɩɟɪɟɞ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɫɢ ɝɨɥɟɧɨɫɬɨɩɧɨɝɨ ɫɭɫɬɚɜɚ [8]. ɉɪɢ ɬɚɤɨɦ ɩɨɥɨɠɟɧɢɢ ɛɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɩɟɪɟɞɧɹɹ ɝɪɭɩɩɚ ɦɵɲɰ ɛɟɞɪɚ ɧɟ ɧɚɩɪɹɠɟɧɚ, ɢ ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ F1a 0. Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɫɢɥɢɣ ɨɫɬɚɥɶɧɵɯ ɝɪɭɩɩ ɦɵɲɰ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɨɞɟɥɶɸ ɦɵɲɟɱɧɨɣ ɫɢɥɵ ɢɡ [9]. ɂɞɟɚɥɢɡɢɪɨɜɚɧɧɚɹ ɫɬɚɬɢɱɟk
ɫɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɫɢɥɵ Fik ɨɬ ɞɥɢɧɵ l i ɦɵɲɰɵ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ
Fi k (l ik , Oik )
0, ® k k k ( K l ¯ i i Oi ),
ɩɪɢ l ik < O ik (4) ɩɪɢ l ik t Oik
Ɂɞɟɫɶ Kik=const – ɤɪɭɬɢɡɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ȼɟɥɢɱɢɧɚ ɷɬɨɣ ɤɪɭɬɢɡɧɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɵɦ ɫɬɪɟɬɱ-ɷɮɮɟɤɬɨɦ - ɢɧɧɟɪɜɚɰɢɟɣ ɦɵɲɟɱɧɵɯ ɜɨɥɨɤɨɧ ɡɚ ɫɱɟɬ ɜɧɭɬɪɢɦɵɲɟɱɧɵɯ ɨɛɪɚɬɧɵɯ ɫɜɹɡɟɣ. ȼɟɥɢɱɢɧɚ Oik - ɫɞɜɢɝ ɧɭɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ - ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɫɲɢɦɢ ɨɬɞɟɥɚɦɢ ɧɟɪɜɧɨɣ ɫɢɫɬɟɦɵ ɢ ɹɜɥɹɟɬɫɹ ɭɩɪɚɜɥɹɸɳɢɦ ɩɚɪɚɦɟɬɪɨɦ ɫɢɥɵ ɦɵɲɰɵ. ȼɵɜɟɞɟɦ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɞɥɢɧ ɭɤɚɡɚɧɧɵɯ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ. a
1) Ⱦɥɢɧɚ l 2 ɩɪɹɦɨɣ ɦɵɲɰɵ ɛɟɞɪɚ. ɉɪɟɞɫɬɚɜɢɦ ɞɥɢɧɭ ɩɪɹɦɨɣ ɦɵɲɰɵ ɛɟɞɪɚ ɜ ɜɢɞɟ ɫɭɦɦɵ l 2a A1 A11 * A11 A2 A2 A3 . (ɫɦ. ɪɢɫ.3) Ⱦɥɢɧɚ A1 A11 ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɨɜ ɜ ɫɭɫɬɚɜɚɯ ɢ ɹɜɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɩɨɫɬɨɹɧɧɨɣ. Ⱦɥɢɧɭ A2 A3 ɧɚɣɞɟɦ ɢɫɩɨɥɶɡɭɹ ɬɟɨɪɟɦɭ ɤɨɫɢɧɭɫɨɜ ɜ 'O2O3A3 ɢ ɬɟɨɪɟɦɭ ɉɢɮɚɝɨɪɚ ɜ ɩɪɹɦɨɭɝɨɥɶɧɨɦ 'O2A2A3 Ɋɢɫɭɧɨɤ 3. ɇɢɬɹɧɚɹ ɦɨɞɟɥɶ ɩɪɹɦɨɣ ɦɵɲɰɵ ɛɟɞɪɚ.
A2 A3
L22 a 32 2 L 2 a 3 sin(\ 3 D 3 ) R 22
.ɇɚɤɨɧɟɰ, ɞɥɢɧɭ ɞɭɝɢ * A11 A2 ɧɚɣɞɟɦ ɜ ɜɢɞɟ
57
* A11 A2
R2 G a
R2 (S J 23a D 23a \ 2 ) .
ȼ ɷɬɨɦ ɜɵɪɚɠɟɧɢɢ «ɚɧɚɬɨɦɢɱɟɫɤɢɣ» ɭɝɨɥ ɡɚɜɢɫɢɬ ɨɬ ɡɧɚɱɟɧɢɣ \2 ɢ \3 , ɚ ɡɧɚɱɟɧɢɟ ɭɝɥɚ
J 23a
D 23a
ɧɟ
ɨɩɪɟɞɟɥɢɦ
ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɬɪɟɭɝɨɥɶɧɢɤɨɜ 'O2O3A3 ɢ 'O2A2A3 º ª R2 » J 23a arccos « « L22 a 32 2 L 2 a 3 sin(\ 3 D 3 ) » ¬ ¼ ª a 3 cos \ 3 D 3 º (5) arctg « » ¬ L 2 a 3 sin \ 3 D 3 ¼ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, l 2a
L22 a 32 2 L 2 a 3 sin(\ 3 D 3 ) R 22 R 2 (\ 2 J 23a S D 23a ) A1 A11
(6)
b
2) Ⱦɥɢɧɚ l 2 ɡɚɞɧɟɣ ɝɪɭɩɩɵ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ (ɝɪɭɩɩɵ hamstring). b
Ⱥɧɚɥɨɝɢɱɧɨ ɩɪɟɞɵɞɭɳɟɦɭ, ɞɥɢɧɚ l 2 ɡɚɞɧɟɣ ɝɪɭɩɩɵ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ ɜɵɱɢɫɥɹɟɬɫɹ ɜ ɜɢɞɟ l 2b
L22 b32 2 L2 b3 sin(\ 3 E 3 ) r22
r2 (S \ 2 J 23b D 23b ) B1 B11
(7)
ɝɞɟ
J 23b
ª º r2 » . arccos« «¬ L22 b32 2 L2 b3 sin(\ 3 E 3 ) »¼ ª b cos \ 3 E 3 º arctg « 3 » ¬ L2 b3 sin \ 3 E 3 ¼
(8)
ɚ ɜɟɥɢɱɢɧɵ B1 B11 ɢ D 23b ɤɚɤ ɢ ɚɧɚɥɨɝɢɱɧɵɟ ɢɦ ɜɟɥɢɱɢɧɵ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɭɝɥɨɜ ɜ ɤɨɥɟɧɧɨɦ ɢ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɚɯ. b
3) Ⱦɥɢɧɚ l1 ɢɤɪɨɧɨɠɧɨɣ ɦɵɲɰɵ. b
Ⱦɥɢɧɭ l1 ɢɤɪɨɧɨɠɧɨɣ ɦɵɲɰɵ ɫ ɪɢɫ. 4 ɩɨ ɮɨɪɦɭɥɟ
l1b 58
S 0 S 1 S1 S 2 .
ɧɚɣɞɟɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ
Ⱦɥɢɧɭ
S 0 S1
ɧɚɣɞɟɦ ɢɫɩɨɥɶɡɭɹ ɬɟɨɪɟɦɭ ɤɨɫɢɧɭɫɨɜ ɜ
'S0O1S1, ɚ ɞɥɢɧɭ S1 S 2 ɧɚɣɞɟɦ ɢɫɩɨɥɶɡɭɹ ɬɟɨɪɟɦɭ ɤɨɫɢɧɭɫɨɜ ɜ 'S2O2S1 S 0 S1
s12 s 02 2 s 0 s1 cos(S V 0 V 1 \ 1 )
S1 S 2
s 22 O 2 S 1 2 s 2 O 2 S 1 cos(S \ 2 V 2 S 1 O 2 O1 ) ,
ɝɞɟ
O2 S 1
L12 s12 2 L1 s1 cos V 1 ,
ª s º arcsin « 1 sin V 1 » . «¬ O2 S1 »¼ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ɢ S1O2 O1
l1b
(9) (10)
s12 s 02 2s 0 s1 cos(\ 1 V 0 V 1 )
s 22 O2 S12 2s 2 O2 S1 cos(\ 2 V 2 S1O2 O1 )
Ɋɢɫɭɧɨɤ 4. ɇɢɬɹɧɚɹ ɦɨɞɟɥɶ ɢɤɪɨɧɨɠɧɨɣ ɦɵɲɰɵ
(11)
ɋɨɨɬɧɨɲɟɧɢɹ (1)-(11) ɨɛɪɚɡɭɸɬ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ, ɨɩɢɫɵɜɚɸɳɢɯ ɜɡɚɢɦɨɫɜɹɡɶ ɫɢɥ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ F1b, F2a, F2b, ɦɨɦɟɧɬɨɜ ɨɞɧɨɫɭɫɬɚɜɧɵɯ ɦɵɲɰ M1, M2, M3, ɭɝɥɨɜ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ \1, \2, \3, ɢ ɩɚɪɚɦɟɬɪɨɜ ɭɩɪɚɜɥɟɧɢɹ ɦɵɲɟɱɧɵɦɢ ɭɫɢɥɢɹɦɢ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ O1b, O2a, O2b. Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨɡɵ ɛɨɥɶɧɨɝɨ ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɨɞɢɧ ɢɡ ɩɚɪɚɦɟɬɪɨɜ ɭɩɪɚɜɥɟɧɢɹ Oik ɞɥɹ ɩɨɪɚɠɟɧɧɨɣ ɝɪɭɩɩɵ ɦɵɲɰ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɚɬɨɥɨɝɢɱɟɫɤɢɦ ɧɟɪɜɧɵɦ ɢɦɩɭɥɶɫɨɦ. Ʉɥɢɧɢɱɟɫɤɢɣ ɨɩɵɬ [4,5] ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜɟɥɢɱɢɧɚ Oik ɞɥɹ ɛɨɥɶɧɨɝɨ ɦɟɧɶɲɟ ɞɥɢɧɵ
Oiok
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɝɪɭɩɩɵ ɦɵɲɰ ɡɞɨɪɨɜɨɝɨ ɱɟɥɨɜɟɤɚ ɜ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɨɣɤɟ ɫ ɜɵɩɪɹɦɥɟɧɧɵɦɢ ɧɨɝɚɦɢ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɧɚ 4ɫɦ. ɉɪɨɱɢɟ ɩɟɪɟɦɟɧɧɵɟ \1, \2, \3, M1, M2, M3 ɢ ɡɧɚɱɟɧɢɹ Oik ɞɥɹ ɧɟɩɨɪɚɠɟɧɧɵɯ ɦɵɲɰ ɩɪɢ ɨɩɢɫɚɧɢɢ ɩɨɡɵ ɛɨɥɶɧɨɝɨ ɫɱɢɬɚɟɦ ɧɟɢɡɜɟɫɬɧɵɦɢ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɩɨɡɵ ɩɪɢɦɟɦ ɫɥɟɞɭɸɳɢɟ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɢ ɡɚɩɢɲɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɫɨɨɬɧɨɲɟɧɢɹ.
59
ɐɟɧɬɪ ɦɚɫɫ ɛɨɥɶɧɨɝɨ ɧɚɯɨɞɢɬɫɹ ɧɚɞ ɝɨɥɟɧɨɫɬɨɩɧɵɦ ɫɭɫɬɚɜɨɦ (ɪɟɚɥɶɧɨɟ ɟɝɨ ɫɦɟɳɟɧɢɟ ɧɚ ɧɟɫɤɨɥɶɤɨ ɫɚɧɬɢɦɟɬɪɨɜ ɜɩɟɪɟɞ ɫɪɚɜɧɢɦɨ ɫ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɧɟ ɭɱɢɬɵɜɚɥɨɫɶ) x c L1 cos\ 1 L2 cos(\ 1 \ 2 ) a c cos(\ 1 \ 2 \ 3 D c ) 0. (12) 2. Ʉɨɪɩɭɫ ɭɞɟɪɠɢɜɚɟɬɫɹ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɩɨɥɨɠɟɧɢɢ \ 1 \ 2 \ 3 S / 2 . (13) 3. ɋɭɦɦɚ ɤɜɚɞɪɚɬɨɜ ɦɨɦɟɧɬɨɜ ɨɞɧɨɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɦɢɧɢɦɚɥɶɧɚ 2 2 (14) M 1 M 2 M 32 o min ɉɨɫɥɟɞɧɟɟ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɩɪɢɧɹɬɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɤɚɤ ɨɞɧɨ ɢɡ ɢɫɩɨɥɶɡɭɟɦɵɯ (ɫɦ. ɧɚɩɪɢɦɟɪ [10,11]). ɉɪɢɧɰɢɩɢɚɥɶɧɨ ɜɨɡɦɨɠɧɚ ɦɢɧɢɦɢɡɚɰɢɹ ɢ ɞɪɭɝɢɯ ɮɭɧɤɰɢɨɧɚɥɨɜ. ɉɟɪɜɵɟ ɞɜɚ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɩɨɞɬɜɟɪɠɞɚɸɬɫɹ ɚɧɚɥɢɡɨɦ ɤɥɢɧɢɱɟɫɤɢɯ ɞɚɧɧɧɵɯ. ɂɯ ɩɨɞɬɜɟɪɠɞɟɧɢɟɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɬɚɤɠɟ ɮɨɬɨ, ɩɪɢɜɟɞɟɧɧɨɟ ɧɚ ɪɢɫ. III ɢ IV ɜɤɥɚɞɤɢ. Ⱦɥɹ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɜɵɪɚɡɢɦ ɢɡ ɭɪɚɜɧɟɧɢɹ (13) ɭɝɨɥ \3 \ 3 S / 2 \ 1 \ 2 (15) ɉɨɞɫɬɚɜɢɦ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ ɭɪɚɜɧɟɧɢɟ (12) ɢ ɪɚɡɪɟɲɢɦ ɟɝɨ ɨɬɧɨɫɢɬɟɥɶɧɨ \2 · §a L \ 2 \ 1 arccos¨¨ c sin D c 1 cos\ 1 ¸¸ (16) L2 ¹ © L2 1.
ɢ ɫɨɨɬɧɨɲɟɧɢɟ (14) ɩɪɢɦɟɬ ɜɢɞ · §a L S \3 arccos¨¨ c sin D c 1 cos\ 1 ¸¸ . L L 2 2 ¹ © 2
(17) 2
2
Ɍɨɝɞɚ ɚɥɝɨɪɢɬɦ ɜɵɱɢɫɥɟɧɢɹ ɮɭɧɤɰɢɨɧɚɥɚ J(M)= M 1 M 2 M 32 ɩɨ ɡɚɞɚɧɧɵɦ ɡɧɚɱɟɧɢɹɦ \1 ɢ Oik ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ: 1) ɂɡ ɫɨɨɬɧɨɲɟɧɢɣ (16) ɢ (17) ɜɵɱɢɫɥɹɸɬɫɹ ɡɧɚɱɟɧɢɹ \2 ɢ \3 ɩɨ ɜɟɥɢɱɢɧɟ \1 . 2) Ⱦɥɢɧɵ ɦɵɲɰ lik ɜɵɱɢɫɥɹɸɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɜɵɪɚɠɟɧɢɣ (5)-(11). 3) ɉɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ lik ɢ ɡɚɞɚɧɧɵɟ ɜɟɥɢɱɢɧɵ Oik ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰɚɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɦɨɞɟɥɶɸ Ɏɟɥɶɞɦɚɧɚ (4). 4) ȼɵɱɢɫɥɹɸɬɫɹ ɦɨɦɟɧɬɵ M\1, M\2, M\3 ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ (3). 5) ɍɪɚɜɧɟɧɢɹ (1) ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɦɨɦɟɧɬɨɜ M1, M2, M3. 60
6) ȼɵɱɢɫɥɹɟɬɫɹ ɦɢɧɢɦɢɡɢɪɭɟɦɚɹ ɜɟɥɢɱɢɧɚ 2 2 J (\ 1 , O1b , Oa2 , Ob2 ) M 1 M 2 M 32 . Ɂɚɞɚɱɚ ɦɢɧɢɦɢɡɚɰɢɢ ɷɬɨɝɨ ɮɭɧɤɰɢɨɧɚɥɚ ɪɟɲɚɥɚɫɶ ɱɢɫɥɟɧɧɨ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ fminsearch ɩɚɤɟɬɚ MATLAB ɞɥɹ ɫɥɟɞɭɸɳɢɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ: m=50 ɤɝ, ı0=ʌ/4, ˯1=2o, ˯2=2,5o, s0 = 7ɫɦ, s1 = 37ɫɦ, s2 = 3ɫɦ, L1=37ɫɦ, L2=40ɫɦ, R2=5ɫɦ, r2=3ɫɦ, a3 =6.5ɫɦ, b3 =8,5ɫɦ, Į3=28º, ȕ3=28º, ac = 10ɫɦ, Įc =0, K=50 ɤɇ/ɦ. ɗɬɢ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɩɪɢɛɥɢɠɟɧɧɨ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɱɟɥɨɜɟɤɭ ɫ ɪɨɫɬɨɦ 150 ɫɦ.,ɢɬɦ ɫɪɟɞɧɟɝɨ ɬɟɥɨɫɥɨɠɟɧɢɹ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɨɡɵ ɛɨɥɶɧɨɝɨ ɫ ɫɢɦɩɬɨɦɨɤɨɦɩɥɟɤɫɨɦ ɬɢɩɚ rectus-ɫɢɧɞɪɨɦ ɡɧɚɱɟɢɟ Oa2 ɩɪɢɧɢɦɚɥɨɫɶ ɪɚɜɧɵɦ Oa2 l 2a ( 0 ) 'Oa2 , ɝɞɟ l 2a ( 0 ) ɞɥɢɧɚ ɩɪɹɦɨɣ ɦɵɲɰɵ ɛɟɞɪɚ ɜ ɜɵɩɪɹɦɥɟɧɧɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɨɣɤɟ ɞɥɹ ɡɞɨɪɨɜɨɝɨ ɱɟɥɨɜɟɤɚ (\1 = 90ɨ, \2 =\3 =0), ɚ 'O2a – ɢɡɦɟɧɟɧɢɹ ɫɞɜɢɝɚ ɧɭɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɹɦɨɣ ɦɵɲɰɵ ɛɟɞɪɚ, ɜɵɡɜɚɧɧɨɟ ɩɚɬɨɥɨɝɢɱɟɫɤɢɦ ɧɟɪɜɧɵɦ ɢɦɩɭɥɶɫɨɦ. ɍɝɥɵ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ ɢ ɜɟɥɢɱɢɧɵ O1b , Ob2 ɩɪɢɧɢɦɚɥɢɫɶ ɡɚ ɧɟɢɡɜɟɫɬɧɵɟ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɮɨɪɦɚɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɦɢɧɢɦɢɡɚɰɢɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɧɚɱɚɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ ɧɚɣɞɟɧɵ ɬɪɢ ɥɨɤɚɥɶɧɵɯ ɦɢɧɢɦɭɦɚ. ɉɪɢ 'O2a =4ɫɦ ɷɬɢ ɦɢɧɢɦɭɦɵ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɩɨɡɚɦ ɫɨ ɡɧɚɱɟɧɢɹɦɢ ɭɝɥɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 1. ɂɡɨɛɪɚɠɟɧɢɟ ɩɨɡ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 5. ɉɟɪɜɨɟ ɪɟɲɟɧɢɟ ɨɩɢɫɵɜɚɟɬ ɝɥɭɛɨɤɢɣ ɩɪɢɫɟɞ ɛɨɥɶɧɨɝɨ, ɚ ɬɪɟɬɶɟ ɪɟɲɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɡɟ ɫ ɪɟɤɭɪɜɚɰɢɟɣ ɤɨɥɟɧɟɣ. ɉɪɟɞɫɬɚɜɥɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɧɟ ɨɩɢɫɵɜɚɟɬ ɨɫɨɛɟɧɧɨɫɬɟɣ ɛɢɨɦɟɯɚɧɢɤɢ ɦɵɲɟɱɊɢɫɭɧɨɤ 5. Ɋɟɲɟɧɢɹ ɫɢɫɧɨɣ ɫɢɫɬɟɦɵ, ɜɚɠɧɵɯ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɬɟɦɵ ɭɪɚɜɧɟɧɢɣ, ɨɩɢɫɵɧɢɢ ɭɤɚɡɚɧɧɵɯ ɩɨɡ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ, ɜɚɸɳɟɣ ɩɨɡɭ ɩɪɢ rectusɫɪɚɜɧɟɧɢɟ 1-ɣ ɢ 3-ɣ ɩɨɡ ɫ ɤɥɢɧɢɱɟɫɤɢɫɢɧɞɪɨɦɟ ɦɢ ɞɚɧɧɵɦɢ ɛɟɫɫɦɵɫɥɟɧɧɨ.
61
Ɍɚɛɥɢɰɚ 1.
ɇɨɦɟɪ ɪɟɲɟɧɢɹ
1 43ɨ 91ɨ
\1 \2 \3
-44
2 65ɨ ɨ
49 o
3 158ɨ -130ɨ
-24ɨ
62ɨ
ɉɪɟɞɥɨɠɟɧɧɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɪɟɞɧɚɡɧɚɱɚɥɚɫɶ ɞɥɹ ɨɩɢɫɚɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɣ Z-ɨɛɪɚɡɧɨɣ ɩɨɡɵ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɜɬɨɪɨɦɭ ɪɟɲɟɧɢɸ ɬɚɛɥɢɰɵ 1. Ɋɟɲɟɧɢɹ ɷɬɨɝɨ ɬɢɩɚ ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɦɢɧɢɦɢɡɚɰɢɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ 'O2a ɡɧɚɱɟɧɢɹ ɭɝɥɨɜ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 2. ȼ ɷɬɨɣ ɠɟ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɷɬɢɯ ɭɝɥɨɜ ɞɥɹ ɞɜɭɯ ɛɨɥɶɧɵɯ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɢɡɦɟɪɟɧɢɣ ɩɪɨɜɟɞɟɧɧɵɯ ɩɨ ɮɨɬɨɝɪɚɮɢɹɦ ɢɡ ɚɪɯɢɜɚ Ⱥ.Ɇ. ɀɭɪɚɜɥɟɜɚ. Ⱥɧɚɥɢɡ ɷɬɢɯ ɡɧɚɱɟɧɢɣ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢɜɟɞɟɧɧɚɹ ɦɨɞɟɥɶ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɨɩɢɫɵɜɚɟɬ ɤɚɱɟɫɬɜɟɧɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɭɞɟɪɠɚɧɢɹ ɩɨɡɵ ɛɨɥɶɧɵɦ ɩɪɢ rectus-ɫɢɧɞɪɨɦɟ. Ɍɚɛɥɢɰɚ 2
Ȼɨɥɶɧɨɣ 1
Ɇɨɞɟɥɶ
'O2a
Ȼɨɥɶɧɨɣ 2
ɧɟɢɡɜɟɫɬɧɚ
2
3
4
5
\1
78ɨ
71ɨ
65ɨ
58ɨ
77 º
56 º
\2
24ɨ
36ɨ
49 o
62ɨ
34 º
64 º
\3
-12ɨ
-18ɨ
-24ɨ
-30ɨ
19 º
41 º
(ɫɦ)
Ɂɚɦɟɬɢɦ ɬɚɤɠɟ, ɱɬɨ ɫɧɹɬɢɟ ɬɪɟɛɨɜɚɧɢɹ ɨ ɜɟɪɬɢɤɚɥɶɧɨɦ ɩɨɥɨɠɟɧɢɢ ɤɨɪɩɭɫɚ ɛɨɥɶɧɨɝɨ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɜɟɞɟɬ ɤ ɜɵɩɪɹɦɥɟɧɢɸ ɤɨɥɟɧ ɦɨɞɟɥɢɪɭɸɳɟɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ, ɢ ɫɨɯɪɚɧɹɟɬ ɭɝɨɥ ɜ ɬɚɡɨɛɟɞɪɟɧɧɨɦ ɫɭɫɬɚɜɟ ɜ ɪɚɣɨɧɟ 23ɨ, ɱɬɨ ɤɨɪɪɟɫɩɨɧɞɢɪɭɟɬɫɹ ɫ ɢɡɜɟɫɬɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ ɱɚɫɬɢ ɛɨɥɶɧɵɯ, ɫɤɥɨɧɧɵɯ ɤ ɝɥɭɛɨɤɨɦɭ ɥɨɪɞɨɡɭ ɩɨɡɜɨɧɨɱɧɢɤɚ ɜ «ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɨɣɤɟ». Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɢɫɥɟɧɧɨ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɩɪɟɞɩɨɥɨɠɟɧɢɟ Ⱥ.Ɇ.ɀɭɪɚɜɥɟɜɚ ɨ ɬɨɦ, ɱɬɨ Z-ɨɛɪɚɡɧɚɹ ɫɬɨɣɤɚ ɛɨɥɶɧɨɝɨ ɜɵɡɜɚɧɚ ɫɬɪɟɦɥɟɧɢɟɦ ɛɨɥɶɧɨɝɨ ɭɞɟɪɠɢɜɚɬɶ ɬɭɥɨɜɢɳɟ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɩɨɥɨɠɟɧɢɢ, ɢɡɛɟɝɚɹ ɝɥɭɛɨɤɨɝɨ ɥɨɪɞɨɡɚ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɨɡɵ ɛɨɥɶɧɨɝɨ ɫ ɫɢɦɩɬɨɦɨɤɨɦɩɥɟɤɫɨɦ ɬɢɩɚ hamstring-cɢɧɞɪɨɦ ɡɧɚɱɟɧɢɟ Ob2 ɩɪɢɧɢɦɚɥɨɫɶ ɪɚɜɧɵɦ
Ob2 62
l 2b ( 0 ) 'Ob2 , ɝɞɟ l2b ( 0) ɞɥɢɧɚ ɨɛɨɛɳɟɧɧɨɣ ɦɵɲɰɵ ɞɥɹ ɡɚɞɧɟɣ ɝɪɭɩ-
ɩɵ ɞɜɭɫɭɫɬɚɜɧɵɯ ɦɵɲɰ ɛɟɞɪɚ ɜ ɜɵɩɪɹɦɥɟɧɧɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɨɣɤɟ ɞɥɹ ɡɞɨɪɨɜɨɝɨ ɱɟɥɨɜɟɤɚ (\1 = 90ɨ, \2 =\3 =0), ɚ 'O2b – ɢɡɦɟɧɟɧɢɹ ɫɞɜɢɝɚ ɧɭɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɵɲɰ ɷɬɨɣ ɝɪɭɩɩɵ, ɜɵɡɜɚɧɧɨɟ ɩɚɬɨɥɨɝɢɱɟɫɤɢɦ ɧɟɪɜɧɵɦ ɢɦɩɭɥɶɫɨɦ. ɍɝɥɵ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ ɢ ɜɟɥɢɱɢɧɵ O1b , Oa2 ɩɪɢɧɢɦɚɥɢɫɶ ɡɚ ɧɟɢɡɜɟɫɬɧɵɟ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɢɪɚɥɢɫɶ ɡɧɚɱɟɧɢɹ ɭɝɥɨɜ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ Z-ɨɛɪɚɡɧɨɣ ɩɨɡɟ ɛɨɥɶɧɨɝɨ. Ɂɧɚɱɟɧɢɹ ɭɝɥɨɜ ɫɤɟɥɟɬɧɨɝɨ ɦɧɨɝɨɡɜɟɧɧɢɤɚ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɦɢɧɢɦɢɡɚɰɢɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ 'O2b, ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 3. ȼ ɷɬɨɣ ɠɟ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɷɬɢɯ ɭɝɥɨɜ ɞɥɹ ɞɜɭɯ ɛɨɥɶɧɵɯ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɢɡɦɟɪɟɧɢɣ ɩɪɨɜɟɞɟɧɧɵɯ ɩɨ ɮɨɬɨɝɪɚɮɢɹɦ ɢɡ ɚɪɯɢɜɚ Ⱥ.Ɇ. ɀɭɪɚɜɥɟɜɚ. Ⱥɧɚɥɢɡ ɷɬɢɯ ɡɧɚɱɟɧɢɣ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢɜɟɞɟɧɧɚɹ ɦɨɞɟɥɶ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɨɩɢɫɵɜɚɟɬ ɤɚɱɟɫɬɜɟɧɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɭɞɟɪɠɚɧɢɹ ɩɨɡɵ ɛɨɥɶɧɵɦ ɩɪɢ hamstring-ɫɢɧɞɪɨɦɟ.
Ɍɚɛɥɢɰɚ 3 Ɇɨɞɟɥɶ a
'O2
Ȼɨɥɶɧɨɣ 1
Ȼɨɥɶɧɨɣ 2
ɧɟɢɡɜɟɫɬɧɚ
2
3
4
5
6
\1
76o
67o
60o
51o
40o
50o
67o
\2
28o
43o
59o
76o
95o
66o
47o
\3
-14o
-21o
-29o
-37o
-46o
-28o
-40º
(ɫɦ)
Ⱥɜɬɨɪɵ ɛɥɚɝɨɞɚɪɹɬ ɞɨɤɬɨɪɚ ɉ.ɉ.Ⱦɟɦɢɧɚ ɡɚ ɩɨɥɟɡɧɵɟ ɤɨɧɫɭɥɶɬɚɰɢɢ ɢ ɫɬɭɞɟɧɬɨɜ Ɇ.ȼ.ɋɚɪɤɢɫɹɧ ɢ Ʉ.ȼ.ɇɢɤɢɲɢɧɚ ɡɚ ɩɨɦɨɳɶ ɜ ɩɪɨɜɟɞɟɧɢɢ ɜɵɱɢɫɥɟɧɢɣ. Ʌɢɬɟɪɚɬɭɪɚ
1.
2.
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