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4.19 ɞɥɹ ɩɪɹɦɨɥɢɧɟɣɧɨɝɨ Ʉɗ.Ɋɢɫ. 4.194.5. ɂɫɩɨɥɶɡɭɟɦɵɟ ɫɩɨɫɨɛɵ ɤɨɧɬɪɨɥɹ ɩɨɫɬɪɨɟɧɧɵɯ ɷɩɸɪ M, Q, Nɉɨɫɥɟ ɩɨɫɬɪɨɟɧɢɹ ɷɩɸɪ M, Q, N ɜɪɭɱɧɭɸ ɢɥɢ ɧɚ ɉɄ, ɫ ɩɨɦɨɳɶɸ,78ɧɚɩɪɢɦɟɪ, ɩɪɨɝɪɚɦɦɵ SCAD, ɨɧɢ ɞɨɥɠɧɵ ɛɵɬɶ ɨɛɹɡɚɬɟɥɶɧɨ ɩɪɨɜɟɪɟɧɵɪɚɫɱɟɬɱɢɤɨɦ.ɗɬɨɬ ɤɨɧɬɪɨɥɶ ɜɵɩɨɥɧɹɟɬɫɹ ɤɚɤ ɩɨ ɜɧɟɲɧɟɦɭ ɜɢɞɭ ɷɩɸɪ (ɩɨɩɟɪɟɱɢɫɥɟɧɧɵɦ ɜɵɲɟ ɫɜɨɣɫɬɜɚɦ (ɩɪɢɡɧɚɤɚɦ) ɩɪɚɜɢɥɶɧɵɯ ɷɩɸɪ), ɬɚɤ ɢ ɩɭɬɟɦɩɪɨɜɟɪɤɢ ɪɚɜɧɨɜɟɫɢɹ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɢ ɥɸɛɵɯ ɨɬɫɟɱɟɧɧɵɯ ɢɡ ɧɟɟ ɱɚɫɬɟɣ.ȼ ɩɪɚɤɬɢɤɟ ɪɚɫɱɟɬɨɜ ɞɥɹ ɤɨɧɬɪɨɥɹ ɩɨɫɬɪɨɟɧɧɵɯ ɷɩɸɪ ɢɫɩɨɥɶɡɭɸɬɫɹɫɥɟɞɭɸɳɢɟ ɜɚɪɢɚɧɬɵ ɩɪɢɦɟɧɟɧɢɹ ɬɪɟɯ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɩɥɨɫɤɨɣɡɚɞɚɱɢ:1. ɂɫɩɨɥɶɡɭɟɬɫɹ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ Q=dM/dx ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɨɝɨɷɥɟɦɟɧɬɚ dx ɫɬɟɪɠɧɹ. ɋ ɟɝɨ ɩɨɦɨɳɶɸ ɩɪɨɜɟɪɹɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɢɟ ɷɩɸɪ M ɢ Qɩɨ ɢɯ ɜɢɞɭ ɢ ɡɧɚɤɭ.2.
Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɪɚɜɧɨɜɟɫɢɟ ɜɫɟɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɬ.ɟ.ɢɫɩɨɥɶɡɭɸɬɫɹ ɬɪɢ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɩɥɨɫɤɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɜɢɞɚɫɢɫɬɟɦɵ¦ Ɇiiɫɢɫɬɟɦɵ0,ɫɢɫɬɟɦɵ¦ Pi , X¦ Pi , Z0;i(ɤɨɧɫɬɪɭɤɰɢɹ ɨɬɧɨɫɢɬɫɹ ɤ ɨɛɳɟɣ0iɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ XOZ).3. Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɪɚɜɧɨɜɟɫɢɟ ɭɡɥɨɜ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɬ.ɟ.ɢɫɩɨɥɶɡɭɸɬɫɹ ɬɟ ɠɟ ɬɪɢ ɜɢɞɚ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ, ɧɨ ɞɥɹ ɥɸɛɨɝɨɭɡɥɚɜɵɪɟɡɚɧɧɨɝɨ ɭɡɥɚ:ɭɡɥɚ¦ Ɇiɭɡɥɚ0 , ¦ Pi , Xi0;i¦ Pi, Z0 , ɝɞɟ i – ɧɨɦɟɪ ɫɬɟɪɠɧɹ,iɩɨɞɯɨɞɹɳɟɝɨ ɤ ɭɡɥɭ.ɭɡɥɚ3.1. Ɉɛɵɱɧɨ ɪɚɜɧɨɜɟɫɢɟ ɭɡɥɨɜ ɩɨ ɦɨɦɟɧɬɚɦ ( ¦ Ɇ i0 ) ɢɥɥɸɫɬɪɢɪɭɟɬɫɹiɩɨɤɚɡɨɦ ɜɵɪɟɡɚɧɧɵɯ ɭɡɥɨɜ (ɫɦ.
ɧɚɩɪɢɦɟɪ, ɪɢɫ. 4.17 ɢ ɪɢɫ. 4.18).ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɫɱɟɬɧɵɯ ɪɚɛɨɬ ɭɱɚɳɟɦɭɫɹ, ɞɥɹ ɧɚɝɥɹɞɧɨɫɬɢɪɚɜɧɨɜɟɫɢɹ ɭɡɥɨɜ ɩɨ ɦɨɦɟɧɬɚɦ, ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɨɤɚɡɵɜɚɬɶ ɜɵɪɟɡɚɧɧɵɟ ɭɡɥɵɪɹɞɨɦ ɫ ɱɟɪɬɟɠɨɦ ɷɩɸɪɵ M (ɫɦ. ɞɚɥɟɟ ɩɪɢɦɟɪɵ ɪɚɫɱɟɬɨɜ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ).3.2. Ɋɚɫɫɦɨɬɪɟɧɢɟ ɨɫɬɚɜɲɢɯɫɹ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɭɡɥɨɜ ɩɥɨɫɤɨɣɭɡɥɚɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ( ¦ Pi , Xiɭɡɥɚ0;¦ Pi, Z0 ) ɨɬɪɚɠɚɟɬ ɪɚɜɧɨɜɟɫɢɟ ɭɡɥɨɜ ɩɨiɩɨɩɟɪɟɱɧɵɦ ɢ ɩɪɨɞɨɥɶɧɵɦ ɫɢɥɚɦ.ɗɬɨ ɪɚɜɧɨɜɟɫɢɟ ɬɚɤɠɟ ɢɥɥɸɫɬɪɢɪɭɸɬ ɞɟɦɨɧɫɬɪɚɰɢɟɣ ɜɵɪɟɡɚɧɧɵɯ ɭɡɥɨɜ.ɍɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɭɡɥɨɜ ɩɪɨɜɟɪɹɸɬɫɹ ɥɢɛɨ ɚɧɚɥɢɬɢɱɟɫɤɢ (ɡɚɩɢɫɵɜɚɸɬɫɹɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɧɚ ɧɚɢɛɨɥɟɟ ɩɨɞɯɨɞɹɳɢɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɨɫɢ) ɢɥɢɩɨɤɚɡɵɜɚɟɬɫɹ ɡɚɦɤɧɭɬɵɣ ɩɪɢ ɪɚɜɧɨɜɟɫɢɢ ɦɧɨɝɨɭɝɨɥɶɧɢɤ ɜɫɟɯ ɫɢɥ,ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɭɡɟɥ (ɫɦ., ɧɚɩɪɢɦɟɪ, ɪɢɫ.
4.18).794. Ɉɱɟɧɶ ɛɵɫɬɪɨɣ ɩɪɨɜɟɪɤɨɣ ɩɪɚɜɢɥɶɧɨɫɬɢ ɷɩɸɪ ɜ ɪɚɦɚɯ ɹɜɥɹɟɬɫɹɩɪɨɜɟɪɤɚɪɚɜɧɨɜɟɫɢɹɜɵɪɟɡɚɧɧɵɯɪɢɝɟɥɟɣɪɚɦ.ɗɬɚɩɪɨɜɟɪɤɚɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɚ ɞɚɥɟɟ ɜɨ ɦɧɨɝɢɯ ɩɪɢɦɟɪɚɯ ɪɚɫɱɟɬɚ ɪɚɦ.ɉɟɪɟɣɞɟɦ ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ ɪɚɰɢɨɧɚɥɶɧɵɯ ɫɩɨɫɨɛɨɜ ɢɫɩɨɥɶɡɨɜɚɧɢɹɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɜɪɭɱɧɭɸ (ɛɟɡ ɩɪɢɦɟɧɟɧɢɹ ɉɄ) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜɪɚɡɥɢɱɧɵɯ ɬɢɩɚɯ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ.5. ɂɋɉɈɅɖɁɈȼȺɇɂȿ ɄɈɇɋɌɊɍɄɌɂȼɇɕɏ ɈɋɈȻȿɇɇɈɋɌȿɃɉɅɈɋɄɂɏ ɋɌȺɌɂɑȿɋɄɂ ɈɉɊȿȾȿɅɂɆɕɏ ɋɌȿɊɀɇȿȼɕɏ ɋɂɋɌȿɆȾɅə ȼɕȻɈɊȺ ɊȺɐɂɈɇȺɅɖɇɈȽɈ ɋɉɈɋɈȻȺ ɈɉɊȿȾȿɅȿɇɂəɍɋɂɅɂɃ ɋ ɉɈɆɈɓɖɘ ɍɊȺȼɇȿɇɂɃ ɊȺȼɇɈȼȿɋɂə5.1. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜɪɭɱɧɭɸɍɫɢɥɢɹ ɩɪɢ ɪɚɫɱɟɬɟ ɩɥɨɫɤɢɯ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɢɫɬɟɦɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɪɚɡɥɢɱɧɵɯ ɫɜɹɡɹɯ: ɜ ɨɩɨɪɧɵɯ (ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ), ɜ ɲɚɪɧɢɪɧɵɯ(ɞɚɜɥɟɧɢɹ ɜ ɲɚɪɧɢɪɚɯ), ɜ ɬɪɟɯ ɭɫɥɨɜɧɵɯ ɜɧɭɬɪɟɧɧɢɯ ɫɜɹɡɹɯ ɜ ɤɚɠɞɨɦ ɫɟɱɟɧɢɢɫɬɟɪɠɧɟɣ (ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹ M , Q, N ).ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɷɬɢɯ ɭɫɢɥɢɣ ɩɪɢ ɪɭɱɧɨɦ ɪɚɫɱɟɬɟɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ (ɛɟɡ ɩɪɢɦɟɧɟɧɢɹ ɉɄ) ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɥɢɱɧɨɣ ɢ ɡɚɜɢɫɢɬ ɤɚɤɨɬ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɪɭɱɧɨɝɨ ɪɚɫɱɟɬɚ, ɬɚɤ ɢ ɨɬ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯɨɫɨɛɟɧɧɨɫɬɟɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ.ȼ ɷɬɨɦ ɩɨɞɪɚɡɞɟɥɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɫɬɚɬɢɱɟɫɤɢɨɩɪɟɞɟɥɢɦɭɸ ɫɬɟɪɠɧɟɜɭɸ ɫɢɫɬɟɦɭ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɜɧɟɣ ɜɪɭɱɧɭɸ ɷɩɸɪ ɜɧɭɬɪɟɧɧɢɯ ɭɫɢɥɢɣ M , Q, N .
ɋ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɛɭɞɟɦɫɬɪɨɢɬɶ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɢɦɟɹ ɬɚɤɠɟ ɜ ɜɢɞɭ ɩɨɫɬɪɨɟɧɢɟɧɚɢɛɨɥɟɟ ɪɚɰɢɨɧɚɥɶɧɨɝɨ ɢ ɧɚɝɥɹɞɧɨɝɨ ɩɭɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ.ȼ ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɟ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɜɪɭɱɧɭɸ(ɛɟɡ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɉɄ) ɷɩɸɪ M , Q, N ɜ ɬɚɤɢɯ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɤɚɤ ɪɚɦɵ ɢ ɛɚɥɤɢ ɩɪɢɧɹɬɨ ɫɬɪɨɢɬɶ ɜɧɚɱɚɥɟ ɷɩɸɪɭ M ,ɬɚɤ ɤɚɤ ɡɚɬɟɦ ɩɨ ɧɟɣ ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɷɩɸɪɚ Q . Ⱦɥɹ ɪɚɦ ɩɨ ɷɩɸɪɟ Qɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɷɩɸɪɚ N (ɫɦ.
ɩɨɞɪɚɡɞɟɥ 4.4).ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɩɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ M ɦɨɠɟɬ ɛɵɬɶ ɡɚɬɪɭɞɧɟɧɨ ɢɥɢɧɟɜɨɡɦɨɠɧɨ ɛɟɡ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɢ ɞɚɜɥɟɧɢɣ ɜɲɚɪɧɢɪɚɯ. ɉɨɷɬɨɦɭ ɪɚɫɱɟɬ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɜɪɭɱɧɭɸ ɨɛɵɱɧɨ ɧɚɱɢɧɚɸɬ ɫ ɨɩɪɟɞɟɥɟɧɢɹ ɢɦɟɧɧɨ ɷɬɢɯ ɭɫɢɥɢɣ.ɇɟɤɨɬɨɪɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɧɚ ɬɟɦɭ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜ ɨɩɨɪɧɵɯ ɫɜɹɡɹɯ ɢ80ɞɚɜɥɟɧɢɣ ɜ ɲɚɪɧɢɪɚɯ ɛɵɥɢ ɩɪɢɜɟɞɟɧɵ ɜ ɩɨɞɪɚɡɞɟɥɟ 2.4. Ɍɚɦ ɪɚɫɫɦɨɬɪɟɧɵ ɞɜɟɡɚɞɚɱɢ.ɉɪɢ ɪɟɲɟɧɢɢ ɩɟɪɜɨɣ ɡɚɞɚɱɢ ɜ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɟ ɭɞɚɥɹɸɬɫɹ ɜɫɟɨɩɨɪɧɵɟ ɫɜɹɡɢ ɢ ɫɜɹɡɢ ɜ ɲɚɪɧɢɪɚɯ ɢ ɡɚɦɟɧɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɭɫɢɥɢɹɦɢ.ɋɬɟɪɠɧɟɜɚɹ ɫɢɫɬɟɦɚ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɫɢɫɬɟɦɭ ɨɬɞɟɥɶɧɵɯ ɞɢɫɤɨɜ, ɞɥɹ ɤɚɠɞɨɝɨ ɢɡɤɨɬɨɪɵɯ ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɬɪɢ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ.
ɉɪɢ ɷɬɨɦ ɜ ɫɬɚɬɢɱɟɫɤɢɨɩɪɟɞɟɥɢɦɨɣ ɫɢɫɬɟɦɟ ɛɭɞɟɬ ɫɨɛɥɸɞɚɬɶɫɹ ɪɚɜɟɧɫɬɜɨ (2.17). ɂɡ 3nɞ ɭɪɚɜɧɟɧɢɣɪɚɜɧɨɜɟɫɢɹ ɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɫɟ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ ɢ ɜɫɟ ɞɚɜɥɟɧɢɹ ɜ ɲɚɪɧɢɪɚɯ.Ɂɚɬɟɦ ɧɚ ɤɚɠɞɨɦ ɞɢɫɤɟ ɨɬɞɟɥɶɧɨ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɵ ɷɩɸɪɵ ɭɫɢɥɢɣ.ɉɪɢ ɜɬɨɪɨɦ ɜɚɪɢɚɧɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɟ ɜɧɚɱɚɥɟɭɞɚɥɹɸɬɫɹ ɬɨɥɶɤɨ ɨɩɨɪɧɵɟ ɫɜɹɡɢ. ɉɨ ɲɚɪɧɢɪɚɦ, ɫɨɟɞɢɧɹɸɳɢɦ ɞɢɫɤɢ ɦɟɠɞɭɫɨɛɨɣ, ɫɢɫɬɟɦɚ ɧɟ ɪɚɡɪɟɡɚɟɬɫɹ.ɉɪɢɦɟɱɚɧɢɟ.
ȼ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɪɚɦɚɯ ɫ ɞɢɫɤɚɦɢ ɜ ɜɢɞɟ ɡɚɦɤɧɭɬɵɯ ɤɨɧɬɭɪɨɜɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɷɩɸɪ ɭɫɢɥɢɣ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɢɬɶ «ɪɚɫɤɪɵɬɢɟ» ɤɨɧɬɭɪɨɜ ɩɭɬɟɦɪɚɡɪɟɡɚɧɢɹ ɨɞɧɨɝɨ ɢɡ ɬɪɟɯ ɲɚɪɧɢɪɨɜ, ɢɦɟɸɳɢɯɫɹ ɜ ɤɨɧɬɭɪɟ (ɭɞɚɥɟɧɢɟ ɞɜɭɯ ɫɜɹɡɟɣ) ɢɨɩɪɟɞɟɥɟɧɢɟ ɡɚɦɟɧɹɸɳɢɯ ɲɚɪɧɢɪ ɞɜɭɯ ɞɚɜɥɟɧɢɣ. ɗɬɨ ɛɭɞɟɬ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɨ ɜ ɩɪɢɦɟɪɟɩɨɞɪɚɡɞɟɥɚ (5.3).ɉɨɫɥɟ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɢ ɩɨ ɞɜɚ ɭɫɢɥɢɹ ɜ ɪɚɡɪɟɡɚɧɧɨɦɲɚɪɧɢɪɟ ɤɚɠɞɨɝɨ ɤɨɧɬɭɪɚ ɬɚɤɠɟ ɜɨɡɦɨɠɧɨ ɩɨɫɬɪɨɟɧɢɟ ɜɫɟɯ ɷɩɸɪ ɭɫɢɥɢɣ.ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɪɢɦɟɪɵ ɩɪɢɜɟɞɟɧɵ ɜ ɩɨɞɪɚɡɞɟɥɚɯ (5.3) ɢ (5.4).ɂɧɨɝɞɚ ɩɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ M ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɦɨɩɪɟɞɟɥɟɧɢɟɦ ɬɨɥɶɤɨ ɱɚɫɬɢ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɢɥɢ ɞɚɠɟɛɟɡ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ.
ɗɬɨ ɛɭɞɟɬ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɨ ɧɚ ɩɪɢɦɟɪɟɪɚɫɱɟɬɚ ɪɚɦɵ ɜ ɩɨɞɪɚɡɞɟɥɟ (5.3).ȼ ɞɚɧɧɨɦ ɪɚɡɞɟɥɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɵ ɩɪɢɦɟɪɵɪɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɫɬɟɪɠɧɟɜɵɯɫɢɫɬɟɦ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ: ɭɫɢɥɢɣ ɜ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɟɣ, ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɢɞɚɜɥɟɧɢɣ ɜ ɲɚɪɧɢɪɚɯ.5.2. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɷɬɚɠɧɨɣ ɫɯɟɦɵ ɲɚɪɧɢɪɧɨɣ ɛɚɥɤɢɂɡɭɱɢɦ ɷɬɨɬ ɫɩɨɫɨɛ ɧɚ ɩɪɢɦɟɪɟ ɲɚɪɧɢɪɧɨɣ ɛɚɥɤɢ, ɪɚɫɱɟɬɧɚɹ ɫɯɟɦɚɤɨɬɨɪɨɣ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 1.2, ɜ.ɉɪɢɞɚɞɢɦ ɛɚɥɤɟ ɤɨɧɤɪɟɬɧɵɟ ɪɚɡɦɟɪɵ ɢ ɡɚɝɪɭɡɢɦ ɟɟ ɤɨɧɤɪɟɬɧɨɣɧɚɝɪɭɡɤɨɣ (ɪɢɫ. 5.1, ɚ).
ɉɭɫɬɶ l1 l2 l ; l3 1.4l ; a b 0.2l ; c 0.15l ;d0.2l ; q12 q ; q2q ; P1P20.6ql ; M o0.2ql 2 .ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɫɬɪɭɤɬɭɪɧɨɝɨ ɚɧɚɥɢɡɚ ɷɬɨɣ ɲɚɪɧɢɪɧɨɣ ɛɚɥɤɢ ɫ ɰɟɥɶɸɢɫɫɥɟɞɨɜɚɧɢɹ ɟɟ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɧɟɢɡɦɟɧɹɟɦɨɫɬɢ (ɫɦ. ɩɨɞɪɚɡɞɟɥ 2.5) ɛɵɥɚ81ɚ)Moq10.5l3ABEP1P2q2DCFɛ)dl2cl1aEACBbl3FD0.5lɜ)0.6ql0.6qlqFDVD = 1.55qlVF = 0.85ql1.2l0.12ql20.03ql20.3PlqEC0.85lVE = 0.22qlBA0.2ql2q1l1282ql8ɝ)VE = 0.22qlEq1 (l1 / 2) 2820.25ql 2MA = 0.2VF = 0.85qlFVB = 0.55ql0.15l0.033ql2VA = 1.23qll0.2l0.06ql2VC = 1.27ql0.15l0.19qlq1 = 2q20.2lɆ ·ql22q(l / 2) 28MC = 0.19ql 2160.0625ql 2MD = 0.120.4550.25ɞ)MB = 0.031.23Q·qlVC = 1.270.22VA = 1.230.77VB = 0.55Ɋɢɫ.
5.1821.05VD = 1.550.350.250.6ɢɫɩɨɥɶɡɨɜɚɧɚ ɷɬɚɠɧɚɹ ɫɯɟɦɚ (ɪɢɫ. 5.1,ɛ), Ɉɧɚ ɩɨɤɚɡɚɥɚ, ɱɬɨ ɛɚɥɤɚ ɹɜɥɹɟɬɫɹɝɟɨɦɟɬɪɢɱɟɫɤɢ ɧɟɢɡɦɟɧɹɟɦɨɣ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ ɫɢɫɬɟɦɨɣ.ɗɬɚɠɧɚɹ ɫɯɟɦɚ ɨɤɚɡɵɜɚɟɬɫɹ ɭɞɨɛɧɨɣ ɞɥɹ ɪɚɰɢɨɧɚɥɶɧɨɝɨ ɩɪɢɦɟɧɟɧɢɹɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɛɚɥɤɢ ɢ ɭɫɢɥɢɣ ɜ ɟɟɫɟɱɟɧɢɹɯ.Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɢɡ ɷɬɚɠɧɨɣ ɫɯɟɦɵ ɯɨɪɨɲɨ ɜɢɞɧɨ, ɱɬɨ ɡɜɟɧɨ FD ɹɜɥɹɟɬɫɹɫɚɦɨɣ ɜɟɪɯɧɟɣ ɩɪɢɤɪɟɩɥɟɧɧɨɣ ɱɚɫɬɶɸ ɤɨɧɫɬɪɭɤɰɢɢ ɢ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧɨɧɟɡɚɜɢɫɢɦɨ ɨɬ ɞɪɭɝɢɯ.
ɉɪɢɦɟɧɢɜ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɪɚɫɱɟɬɚ ɷɬɨɣɩɪɢɤɪɟɩɥɟɧɧɨɣ ɱɚɫɬɢ ɢ ɨɩɪɟɞɟɥɢɜ ɜ ɱɢɫɥɟ ɞɪɭɝɢɯ ɧɟɢɡɜɟɫɬɧɵɯ ɢ ɨɩɨɪɧɭɸɪɟɚɤɰɢɸ VF , ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɪɚɫɱɟɬɭ ɨɫɬɚɜɲɟɣɫɹ ɧɢɠɟɥɟɠɚɳɟɣ ɱɚɫɬɢ ɛɚɥɤɢAF , ɤɨɬɨɪɚɹ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɩɪɢɤɪɟɩɥɟɧɧɨɦɭ ɡɜɟɧɭ FD ɹɜɥɹɥɚɫɶ ɨɫɧɨɜɧɨɣɱɚɫɬɶɸ ɤɨɧɫɬɪɭɤɰɢɢ.Ⱥɧɚɥɢɡɢɪɭɹ ɧɢɠɟɥɟɠɚɳɭɸ ɱɚɫɬɶ AF ɜɢɞɢɦ, ɱɬɨ ɜ ɧɟɣ ɡɜɟɧɨ EF ɹɜɥɹɟɬɫɹɩɪɢɤɪɟɩɥɟɧɧɨɣ ɱɚɫɬɶɸ, ɚ ɡɜɟɧɨ AB – ɨɫɧɨɜɧɨɣ ɱɚɫɬɶɸ ɤɨɧɫɬɪɭɤɰɢɢ. ɉɪɢ ɷɬɨɦɪɟɚɤɰɢɸ VF ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɥɨɠɢɬɶ ɤɚɤ ɧɚɝɪɭɡɤɭ ɧɚ ɧɢɠɧɸɸ ɱɚɫɬɶ,ɧɚɩɪɚɜɥɟɧɧɭɸ, ɤɨɧɟɱɧɨ, ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ ɩɨ ɨɬɧɨɲɟɧɢɸ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦɪɟɚɤɰɢɢ VF ɧɚ ɜɵɲɟɥɟɠɚɳɭɸ ɱɚɫɬɶ ɤɨɧɫɬɪɭɤɰɢɢ – ɡɜɟɧɨ FD.Ɉɫɧɨɜɧɨɟ ɡɜɟɧɨ AB ɪɚɫɫɱɢɬɚɬɶ ɨɬɞɟɥɶɧɨ ɧɟɥɶɡɹ, ɬɚɤ ɤɚɤ ɧɟ ɢɡɜɟɫɬɧɚɜɟɥɢɱɢɧɚ VE ɞɚɜɥɟɧɢɹ ɧɚ ɧɟɝɨ ɜɵɲɟɥɟɠɚɳɟɣ ɩɪɢɤɪɟɩɥɟɧɧɨɣ ɱɚɫɬɢ.
ɉɨɷɬɨɦɭɩɪɨɞɨɥɠɟɧɢɟɦ ɪɚɫɱɟɬɚ ɛɭɞɟɬ ɪɚɫɫɦɨɬɪɟɧɢɟ ɫɧɚɱɚɥɚ ɩɪɢɤɪɟɩɥɟɧɧɨɣ ɱɚɫɬɢ, ɚɡɚɬɟɦ ɨɫɧɨɜɧɨɣ.ɍɤɚɡɚɧɧɚɹ ɩɪɨɰɟɞɭɪɚ ɪɚɫɱɟɬɚ ɲɚɪɧɢɪɧɨɣ ɛɚɥɤɢ, ɧɚɡɵɜɚɟɦɚɹɚɧɚɥɢɬɢɱɟɫɤɢɦ ɫɩɨɫɨɛɨɦ, ɨɛɵɱɧɨ ɩɪɢɦɟɧɹɥɚɫɶ ɩɪɢ ɪɭɱɧɨɦ ɪɚɫɱɟɬɟ ɫɩɪɢɦɟɧɟɧɢɟɦ ɦɚɥɵɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɫɪɟɞɫɬɜ (ɧɚɩɪɢɦɟɪ, ɤɚɥɶɤɭɥɹɬɨɪɚ).Ɋɟɡɭɥɶɬɚɬɵ ɬɚɤɨɝɨ ɪɚɫɱɟɬɚ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɛɚɥɤɢ, ɜɡɹɬɵɟ ɢɡɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ [7], ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 5.1, ɜ-ɞ.5.3. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɫɬɚɬɢɱɟɫɤɢɨɩɪɟɞɟɥɢɦɵɯ ɪɚɦ ɛɟɡ ɡɚɦɤɧɭɬɵɯ ɤɨɧɬɭɪɨɜɊɚɫɫɦɨɬɪɢɦ ɜɧɚɱɚɥɟ ɪɚɦɭ, ɢɡɨɛɪɚɠɟɧɧɭɸ ɧɚ ɪɢɫ. 5.2,ɚ.Ɋɚɦɚ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɚ, ɬ.ɤ.:1) ɩɨ ɮɨɪɦɭɥɟ (2.21) ɩɨɥɭɱɚɟɦ n (4 3 0) (3 1) 0 ;2) ɩɪɨɫɬɨɣ ɫɬɪɭɤɬɭɪɧɵɣ ɚɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɪɚɦɚ ɝɟɨɦɟɬɪɢɱɟɫɤɢɧɟɢɡɦɟɧɹɟɦɚ.Ɉɬɦɟɬɢɦ, ɱɬɨ ɪɚɦɚ ɫɨɫɬɨɢɬ ɢɡ ɨɫɧɨɜɧɨɣ ɱɚɫɬɢ ɜ ɜɢɞɟ ɞɢɫɤɚ AC,ɩɪɢɤɪɟɩɥɟɧɧɨɝɨ ɤ ɨɫɧɨɜɚɧɢɸ ɬɪɟɦɹ ɫɜɹɡɹɦɢ ɜ ɡɚɳɟɦɥɹɸɳɟɣ ɨɩɨɪɟ A, ɢɩɪɢɤɪɟɩɥɟɧɧɨɣ ɱɚɫɬɢ ɜ ɜɢɞɟ ɞɢɫɤɚ CB.
ɉɨɫɥɟɞɧɢɣ ɞɢɫɤ ɩɪɢɤɪɟɩɥɟɧ ɞɜɭɦɹ83ɫɜɹɡɹɦɢ ɜ ɲɚɪɧɢɪɟ C ɤ ɨɫɧɨɜɧɨɦɭ ɞɢɫɤɭ ɢ ɨɞɧɨɣ ɫɜɹɡɶɸ (ɜɟɪɬɢɤɚɥɶɧɨɣ) – ɤɨɫɧɨɜɚɧɢɸ.Ɋɢɫ. 5.2ɉɨɫɤɨɥɶɤɭ ɪɚɦɚ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɚ, ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɣɪɚɜɧɨɜɟɫɢɹ ɜ ɧɟɣ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɥɸɛɵɟ ɭɫɢɥɢɹ.Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɢɦɟɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɥɧɨɝɨ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɫɪɟɡɭɥɶɬɚɬɚɦɢ ɪɚɫɱɟɬɚ ɪɚɦɵ ɧɚ ɉɄ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɨ ɩɪɨɝɪɚɦɦɵ SCAD,ɪɟɚɥɢɡɭɸɳɟɣ ɆɄɗ, ɪɚɡɨɛɶɟɦ ɪɚɦɭ ɧɚ ɬɟ ɠɟ Ʉɗ (ɪɢɫ. 5.2, ɛ), ɧɚ ɤɨɬɨɪɵɟ ɨɧɚɪɚɡɛɢɜɚɟɬɫɹ ɩɪɢ ɟɟ ɪɚɫɱɟɬɟ ɩɨ ɭɤɚɡɚɧɧɨɣ ɩɪɨɝɪɚɦɦɟ (ɫɦ. ɩɨɞɪɚɡɞɟɥ 3)Ɂɧɚɤɢ ɜɧɭɬɪɟɧɧɢɯ ɭɫɢɥɢɣ ɛɭɞɟɦ ɨɩɪɟɞɟɥɹɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɞɚɧɧɨɣɞɥɹ ɤɚɠɞɨɝɨ Ʉɗ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɨɣ ɨɫɟɣ ɤɨɨɪɞɢɧɚɬ ɩɨ ɩɪɚɜɢɥɚɦ, ɩɪɢɧɹɬɵɦ ɜɩɪɨɝɪɚɦɦɟ SCAD (ɫɦ.
ɪɚɡɞɟɥ 4).ɑɬɨɛɵ ɧɟ ɪɢɫɨɜɚɬɶ ɧɚ ɤɚɠɞɨɦ ɫɬɟɪɠɧɟ ɨɫɢ ɆɋɄ, ɩɪɢ ɪɭɱɧɨɦ ɫɱɟɬɟ ɛɭɞɟɦɨɬɦɟɱɚɬɶ ɟɟ ɧɚ ɫɯɟɦɟ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɫ ɩɨɦɨɳɶɸ «ɩɪɚɜɢɥɚ ɩɭɧɤɬɢɪɚ» (ɫɦ.ɩɨɞɪɚɡɞɟɥ 4.2).ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɞɚɧɧɨɣ ɧɚɝɪɭɡɤɨɣ ɢ ɫɞɟɥɚɧɧɨɣ ɪɚɡɛɢɜɤɨɣ ɪɚɦɵ ɧɚ Ʉɗɟɳɟ ɞɨ ɜɵɩɨɥɧɟɧɢɹ ɪɚɫɱɟɬɨɜ ɨɛɪɚɳɚɟɦ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɧɚ ɤɚɠɞɨɦɷɥɟɦɟɧɬɟ ɷɩɸɪɚ M ɛɭɞɟɬ ɩɪɹɦɨɥɢɧɟɣɧɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɞɥɹ ɟɟ ɩɨɫɬɪɨɟɧɢɹ ɧɚɤɚɠɞɨɦ ɷɥɟɦɟɧɬɟ ɞɨɫɬɚɬɨɱɧɨ ɢɦɟɬɶ ɞɜɟ ɨɪɞɢɧɚɬɵ ɷɩɸɪɵ ɢɡɝɢɛɚɸɳɢɯɦɨɦɟɧɬɨɜ: ɜ ɧɚɱɚɥɶɧɨɦ ɢ ɤɨɧɟɱɧɨɦ ɫɟɱɟɧɢɢ ɷɥɟɦɟɧɬɨɜ. ɉɪɢ ɷɬɨɦ ɨɱɟɜɢɞɧɨɬɚɤɠɟ, ɱɬɨ ɤɨɧɰɟɜɵɟ ɨɪɞɢɧɚɬɵ ɜ ɭɡɥɟ, ɝɞɟ ɫɯɨɞɹɬɫɹ ɬɨɥɶɤɨ ɞɜɚ ɫɨɫɟɞɧɢɯɷɥɟɦɟɧɬɚ, ɛɭɞɭɬ ɱɢɫɥɟɧɧɨ ɪɚɜɧɵ ɞɪɭɝ ɞɪɭɝɭ (ɡɧɚɤ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹɨɫɢ Z1 ɆɋɄ ɧɚ ɷɬɢɯ ɷɥɟɦɟɧɬɚɯ, ɦɨɠɟɬ ɪɚɡɥɢɱɚɬɶɫɹ, ɫɦ.
ɪɚɡɞɟɥ 4).ɉɨɫɬɚɜɢɦ ɡɚɞɚɱɭ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɢ ɩɨɫɬɪɨɟɧɢɹ ɷɩɸɪɭɫɢɥɢɣ M, Q, N ɪɚɦɵ.84ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɪɭɱɧɭɸɋɬɪɭɤɬɭɪɚ ɪɚɦɵ ɬɚɤɨɜɚ, ɱɬɨ ɜɵɩɨɥɧɢɬɶ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ ɦɨɠɧɨ ɜɪɚɡɥɢɱɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ. Ɋɚɡɥɢɱɢɟ ɜɚɪɢɚɧɬɨɜ ɫɨɫɬɨɢɬ, ɩɪɟɠɞɟ ɜɫɟɝɨ, ɜɩɨɞɯɨɞɟ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ, ɚ ɢɦɟɧɧɨ:ȼɚɪɢɚɧɬ 1. ɉɪɟɠɞɟ ɱɟɦ ɩɪɢɫɬɭɩɚɬɶ ɤ ɩɨɫɬɪɨɟɧɢɸ ɷɩɸɪ ɭɫɢɥɢɣɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɜɫɟ ɱɟɬɵɪɟ ɪɟɚɤɰɢɢ ( H A ,V A , M A ,VB ). Ɂɚɬɟɦ ɩɨɫɬɪɨɢɬɶɷɩɸɪɵ M, Q, Nȼɚɪɢɚɧɬ 2.
Ɉɩɪɟɞɟɥɢɬɶ ɬɨɥɶɤɨ ɪɟɚɤɰɢɸ VB. Ɂɚɬɟɦ ɩɨɫɬɪɨɢɬɶ ɷɩɸɪɵM, Q, N, ɜ ɩɪɨɰɟɫɫɟ ɩɨɫɬɪɨɟɧɢɹ ɤɨɬɨɪɵɯ ɨɩɪɟɞɟɥɹɬɫɹ ɢ ɨɫɬɚɥɶɧɵɟ ɨɩɨɪɧɵɟɪɟɚɤɰɢɢ.ȼɚɪɢɚɧɬ 3. ɗɩɸɪɚ M ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɫɪɚɡɭ, ɛɟɡ ɨɩɪɟɞɟɥɟɧɢɹɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ. Ɂɚɬɟɦ ɩɨ ɧɟɣ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɭɪɚɜɧɟɧɢɹ Q dM / dx ɦɨɠɟɬɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɷɩɸɪɚ Q ɢ ɩɨɬɨɦ ɢɡ ɪɚɫɫɦɨɬɪɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɭɡɥɨɜ ɪɚɦɵ ɦɨɝɭɬɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɩɪɨɞɨɥɶɧɵɟ ɫɢɥɵ ɜ ɷɥɟɦɟɧɬɚɯ ɪɚɦɵ ɢ ɩɨɫɬɪɨɟɧɚ ɷɩɸɪɚ N.ɉɟɪɜɵɣ ɜɚɪɢɚɧɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. ɉɪɢ ɩɨɞɫɱɟɬɟɫɬɟɩɟɧɢ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢ n (ɫɦ. ɧɚɱɚɥɨ ɩɨɞɪɚɡɞɟɥɚ 5.3)ɫɨɩɨɫɬɚɜɥɹɥɨɫɶ ɱɢɫɥɨ (4) ɧɟɢɡɜɟɫɬɧɵɯ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɪɚɦɵ ( H A ,V A , M A ,VB )ɫ ɱɢɫɥɨɦ (3+1) ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɞɥɹ ɢɯɨɩɪɟɞɟɥɟɧɢɹ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɢ ɭɪɚɜɧɟɧɢɹ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:1. ¦ X0; 2. ¦ Z0; 3.
¦ M A0; 4. ¦ M Cɫɩɪɚɜɚ0(5.1)ɉɨɷɬɨɦɭ ɢ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɦɨɠɧɨ ɧɚɱɚɬɶ ɫ ɪɟɲɟɧɢɹ ɷɬɨɣ ɫɢɫɬɟɦɵɭɪɚɜɧɟɧɢɣ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɫɪɚɡɭ ɨɩɪɟɞɟɥɢɬɶ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ ɪɚɦɵ.Ɋɟɲɟɧɢɟ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɩɨ-ɪɚɡɧɨɦɭ.1. Ɇɨɠɧɨ ɫɪɚɡɭ ɫɨɫɬɚɜɢɬɶ ɜɫɸ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ, ɧɚɡɧɚɱɢɜ ɧɚɩɪɚɜɥɟɧɢɹɢɫɤɨɦɵɯ ɪɟɚɤɰɢɣ ɩɪɨɢɡɜɨɥɶɧɨ, ɧɚɩɪɢɦɟɪ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦɨɛɳɟɣ ɫɢɫɬɟɦɵ ɨɫɟɣ ɤɨɨɪɞɢɧɚɬ ɞɥɹ ɪɚɦɵ (ɪɢɫ. 5.2, ɚ), ɢ ɪɟɲɢɬɶ ɟɟ (ɞɥɹ ɪɚɦ ɫɦɧɨɝɢɦɢ ɧɟɢɡɜɟɫɬɧɵɦɢ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɦɨɠɟɬ ɛɵɬɶ ɪɟɲɟɧɚ ɫ ɩɨɦɨɳɶɸɫɩɟɰɢɚɥɶɧɨɣ ɩɪɨɝɪɚɦɦɵ ɞɥɹ ɉɄ, ɧɚɩɪɢɦɟɪ, ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ,ɢɦɟɸɳɟɣɫɹ ɜ ɭɱɟɛɧɨɦ ɤɥɚɫɫɟ ɉɄ.2. ɉɪɢ ɪɟɲɟɧɢɢ ɩɪɨɫɬɵɯ ɡɚɞɚɱ ɪɚɰɢɨɧɚɥɢɡɚɰɢɹ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵɭɪɚɜɧɟɧɢɣ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɧɟɨɛɯɨɞɢɦɨ, ɩɪɟɠɞɟ ɜɫɟɝɨ, ɜɵɞɟɥɢɬɶ ɢɡ ɫɢɫɬɟɦɵɭɪɚɜɧɟɧɢɣ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɫ ɨɞɧɨɣ ɧɟɢɡɜɟɫɬɧɨɣ ɪɟɚɤɰɢɟɣ. ɇɚɩɪɢɦɟɪ, ɜɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɟ ɭɪɚɜɧɟɧɢɣ ɬɚɤɢɯ ɭɪɚɜɧɟɧɢɣ ɞɜɚ (ɩɟɪɜɨɟ ɢ ɱɟɬɜɟɪɬɨɟ).Ɋɟɲɢɜ ɷɬɢ ɭɪɚɜɧɟɧɢɹ, ɫ ɭɱɟɬɨɦ ɭɠɟ ɧɚɣɞɟɧɧɵɯ ɧɟɢɡɜɟɫɬɧɵɯ ɩɪɨɞɨɥɠɢɬɶɩɨɢɫɤ ɬɚɤɢɯ ɠɟ ɭɪɚɜɧɟɧɢɣ.
ȿɫɥɢ ɬɚɤɨɜɵɯ ɧɟɬ, ɢɫɤɚɬɶ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɫɞɜɭɦɹ ɧɟɢɡɜɟɫɬɧɵɦɢ ɢ ɬ. ɞ.85ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɜɫɹ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɦɨɠɟɬ ɛɵɬɶ ɪɟɲɟɧɚ ɤɚɤ ɨɬɞɟɥɶɧɨɟɪɟɲɟɧɢɟ ɱɟɬɵɪɟɯ ɭɪɚɜɧɟɧɢɣ ɫ ɨɞɧɢɦ ɧɟɢɡɜɟɫɬɧɵɦ ɤɚɠɞɨɟ:1.ɂɡ ¦ X 0 ɧɚɣɞɟɦ H A P. .2. ɂɡ ¦ M Cɫɩɪɚɜɚ3. ɂɡ ¦ Z0 ɩɨɥɭɱɢɦ VA4. ɂɡ ¦ M AMA0 ɧɚɣɞɟɦ VBP. P . 4.0 ɨɩɪɟɞɟɥɢɦ, ɱɬɨ ɪɟɚɤɬɢɜɧɵɣ ɦɨɦɟɧɬ ɜ ɡɚɞɟɥɤɟ ɪɚɜɟɧ3Pa .Ɂɧɚɤ « » ɭ ɪɟɚɤɰɢɢ V A ɢ ɭ ɦɨɦɟɧɬɚ M A ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɤɚɠɞɚɹ ɢɡ ɷɬɢɯɪɟɚɤɰɢɣ ɧɚɩɪɚɜɥɟɧɚ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɩɟɪɜɨɧɚɱɚɥɶɧɨ ɡɚɞɚɧɧɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ (ɫɦ.
