ɎȿȾȿɊȺɅɖɇɈȿ ȺȽȿɇɌɋɌȼɈ ɉɈ ɈȻɊȺɁɈȼȺɇɂɘ ȽɈɋɍȾȺɊɋɌȼȿɇɇɈȿ ɈȻɊȺɁɈȼȺɌȿɅɖɇɈȿ ɍɑɊȿɀȾȿɇɂȿ ȼɕɋɒȿȽɈ ɉɊɈɎȿɋɋɂɈɇȺɅɖɇɈȽɈ ɈȻɊȺɁɈȼȺɇɂə «ȼɈɊɈɇȿɀɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ»
ɄȼȺɇɌɈȼȺə ɌȿɈɊɂə ȾȼɈɃɇɈȽɈ ɂ ɌɊɈɃɇɈȽɈ ȾȿɅȿɇɂə ȺɌɈɆɇɕɏ əȾȿɊ ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ ɋɨɫɬɚɜɢɬɟɥɢ: ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ, Ʌ.ȼ. Ɍɢɬɨɜɚ
ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ 2007
ɍɬɜɟɪɠɞɟɧɨ ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɢɦ 16 ɚɩɪɟɥɹ 2007 ɝ., ɩɪɨɬɨɤɨɥ ʋ 4
ɫɨɜɟɬɨɦ
ɮɢɡɢɱɟɫɤɨɝɨ
ɮɚɤɭɥɶɬɟɬɚ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɨɞɝɨɬɨɜɥɟɧɨ ɧɚ ɤɚɮɟɞɪɟ ɹɞɟɪɧɨɣ ɮɢɡɢɤɢ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɤɚɤ ɞɥɹ ɚɭɞɢɬɨɪɧɨɣ, ɬɚɤ ɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɩɨɞɝɨɬɨɜɤɢ.
Ⱦɥɹ ɫɩɟɰɢɚɥɶɧɨɫɬɢ: 010700 (510400) – Ɏɢɡɢɤɚ 2
ȼȼȿȾȿɇɂȿ ȼ ɧɚɫɬɨɹɳɟɦ ɩɨɫɨɛɢɢ ɪɚɫɫɦɨɬɪɟɧɵ ɫɨɜɪɟɦɟɧɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɩɨɞɯɨɞɵ ɤ ɨɩɢɫɚɧɢɸ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɢɧɞɭɰɢɪɨɜɚɧɧɨɝɨ ɞɜɨɣɧɨɝɨ ɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɨɛɳɢɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɞɟɥɟɧɢɢ ɹɞɟɪ, ɚ ɬɚɤɠɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɪɚɡɜɢɜɚɸɳɟɣɫɹ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ. Ɇɚɬɟɪɢɚɥɵ ɧɚɫɬɨɹɳɟɝɨ ɩɨɫɨɛɢɹ ɩɨɞɝɨɬɨɜɥɟɧɵ ɞɥɹ ɥɟɤɰɢɨɧɧɨɝɨ ɤɭɪɫɚ «əɞɟɪɧɚɹ ɮɢɡɢɤɚ» ɢ ɫɩɟɰɤɭɪɫɚ «Ɍɟɨɪɢɹ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ». ɍɱɟɛɧɵɟ ɦɚɬɟɪɢɚɥɵ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɫɩɟɰɢɚɥɶɧɨɫɬɢ «əɞɟɪɧɚɹ ɮɢɡɢɤɚ», ɨɞɧɚɤɨ ɦɨɝɭɬ ɩɪɟɞɫɬɚɜɥɹɬɶ ɢɧɬɟɪɟɫ ɢ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɨɛɭɱɚɸɳɢɯɫɹ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɹɦ «Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɮɢɡɢɤɚ». 1. Ɉɛɳɢɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɫɩɨɧɬɚɧɧɨɦ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɢɧɞɭɰɢɪɨɜɚɧɧɨɦ ɞɜɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ ɋɭɬɶ ɩɪɨɰɟɫɫɚ ɞɟɥɟɧɢɹ ɚɬɨɦɧɵɯ ɹɞɟɪ ɫɨɫɬɨɢɬ ɜ ɪɚɡɜɚɥɟ ɹɞɪɚ ɧɚ ɞɜɚ ɨɫɤɨɥɤɚ ɫ ɩɪɢɦɟɪɧɨ ɪɚɜɧɵɦɢ ɡɚɪɹɞɚɦɢ ɢ ɦɚɫɫɚɦɢ (ɪɟɠɟ ɧɚ ɬɪɢ ɢɥɢ ɱɟɬɵɪɟ ɨɫɤɨɥɤɚ). Ⱦɟɥɟɧɢɟ ɹɞɪɚ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ – ɫɩɨɧɬɚɧɧɨɟ ɞɟɥɟɧɢɟ, ɢɥɢ ɛɵɬɶ ɜɵɡɜɚɧɨ ɜɨɡɞɟɣɫɬɜɢɟɦ ɪɚɡɥɢɱɧɵɯ ɜɢɞɨɜ ɢɡɥɭɱɟɧɢɣ ɢ ɱɚɫɬɢɰ – ɜɵɧɭɠɞɟɧɧɨɟ ɞɟɥɟɧɢɟ. əɜɥɟɧɢɟ ɜɵɧɭɠɞɟɧɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ɭɪɚɧɚ ɬɟɩɥɨɜɵɦɢ ɧɟɣɬɪɨɧɚɦɢ ɛɵɥɨ ɨɬɤɪɵɬɨ ɜ 1939 ɝ. Ɉ. Ƚɚɧɧɨɦ ɢ Ɏ. ɒɬɪɚɫɫɦɚɧɨɦ, ɤɨɬɨɪɵɟ ɨɛɧɚɪɭɠɢɥɢ, ɱɬɨ ɩɨɫɥɟ ɨɛɥɭɱɟɧɢɹ ɧɟɣɬɪɨɧɚɦɢ ɜ ɹɞɪɟ U ɜɨɡɧɢɤɚɟɬ ɪɚɞɢɨɚɤɬɢɜɧɨɫɬɶ ɧɟ ɫ ɨɞɧɢɦ, ɚ ɫɨ ɦɧɨɝɢɦɢ ɩɟɪɢɨɞɚɦɢ ɩɨɥɭɪɚɫɩɚɞɚ. ȼ 1940 ɝ. Ƚ.ɇ. Ɏɥɟɪɨɜ ɢ Ʉ.Ⱥ. ɉɟɬɪɠɚɤ ɨɬɤɪɵɥɢ ɹɜɥɟɧɢɟ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɚɬɨɦɧɵɯ ɹɞɟɪ. Ɉɤɚɡɚɥɨɫɶ, ɱɬɨ ɧɟɤɨɬɨɪɵɟ ɬɹɠɟɥɵɟ ɹɞɪɚ ɦɨɝɭɬ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ ɞɟɥɢɬɶɫɹ ɧɚ ɞɜɚ ɨɫɤɨɥɤɚ ɫ ɜɵɯɨɞɨɦ ɧɟɣɬɪɨɧɨɜ ɢ ɜɵɞɟɥɟɧɢɟɦ ɷɧɟɪɝɢɢ ɛɟɡ ɜɧɟɲɧɟɝɨ ɜɨɡɞɟɣɫɬɜɢɹ. Ʌ. Ɇɟɣɬɧɟɪ ɢ Ɉ. Ɏɪɢɲ ɤɚɱɟɫɬɜɟɧɧɨ ɨɛɴɹɫɧɢɥɢ ɨɫɧɨɜɧɵɟ ɱɟɪɬɵ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɞɟɥɟɧɢɹ, ɜɡɹɜ ɡɚ ɨɫɧɨɜɭ ɢɞɟɸ H. Ȼɨɪɚ ɨ ɩɨɜɟɞɟɧɢɢ ɹɞɪɚ ɤɚɤ ɠɢɞɤɨɣ ɤɚɩɥɢ. ɉɪɢ ɜɵɧɭɠɞɟɧɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ ɫɬɚɥɤɢɜɚɸɳɚɹɫɹ ɱɚɫɬɢɰɚ ɢ ɹɞɪɨ ɨɛɪɚɡɭɸɬ ɫɢɫɬɟɦɭ, ɤɨɬɨɪɚɹ ɫɭɳɟɫɬɜɭɟɬ, ɧɟ ɪɚɫɩɚɞɚɹɫɶ, ɜ ɬɟɱɟɧɢɟ ɜɪɟɦɟɧɢ, ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɝɨ ɯɚɪɚɤɬɟɪɧɵɟ ɹɞɟɪɧɵɟ ɜɪɟɦɟɧɚ, ɢ ɧɚɡɜɚɧɧɭɸ ɇ. Ȼɨɪɨɦ ɫɨɫɬɚɜɧɵɦ ɹɞɪɨɦ. ɉɨɡɞɧɟɟ ɇ. Ȼɨɪ ɢ Ⱦɠ. ɍɢɥɥɟɪ, ɢ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɧɢɯ ə.ɂ. Ɏɪɟɧɤɟɥɶ, ɩɪɟɞɫɬɚɜɢɥɢ ɛɨɥɟɟ ɞɟɬɚɥɶɧɭɸ ɤɚɪɬɢɧɭ ɞɟɥɟɧɢɹ, ɤɨɬɨɪɚɹ ɯɨɪɨɲɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɥɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ, ɢɡɜɟɫɬɧɵɟ ɜ ɬɟ ɝɨɞɵ. ɂɯ ɨɩɢɫɚɧɢɟ ɫɬɚɥɨ ɨɫɧɨɜɨɣ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɢ ɞɟɥɟɧɢɹ ɢ ɩɨɡɜɨɥɢɥɨ ɪɚɫɫɱɢɬɚɬɶ ɩɨɬɟɧɰɢɚɥɵ ɞɟɮɨɪɦɚɰɢɢ, ɛɚɪɶɟɪɵ ɞɟɥɟɧɢɹ ɢ ɞɟɥɢɬɟɥɶɧɵɟ ɲɢɪɢɧɵ ɹɞɟɪ. Ɍɚɤɠɟ ɜ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɢ ɞɟɥɟɧɢɹ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ ɛɵɥɢ ɢɫɫɥɟɞɨɜɚɧɵ ɦɚɫɫɨɜɵɟ ɢ ɡɚɪɹɞɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɢ ɜɟɪɨɹɬɧɨɫɬɢ ɜɵɯɨɞɚ ɦɝɧɨɜɟɧɧɵɯ ɢ ɡɚɞɟɪɠɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ ɞɟɥɟɧɢɹ. ȼ ɷɬɨɦ ɩɨɞɯɨɞɟ ɞɟɥɟɧɢɟ ɫɜɹɡɚɧɨ ɫ ɩɪɨɰɟɫɫɨɦ ɢɡɦɟɧɟɧɢɹ ɮɨɪɦɵ ɹɞɪɚ: ɢɡ ɫɮɟɪɢɱɟɫɤɨɝɨ ɨɧɨ ɩɟɪɟɯɨɞɢɬ ɫɧɚɱɚɥɚ ɜ ɜɵɬɹɧɭɬɵɣ ɫɮɟɪɨɢɞ, ɭ ɤɨɬɨɪɨɝɨ ɡɚɬɟɦ ɨɛɪɚɡɭɟɬɫɹ 3
ɲɟɣɤɚ ɫ ɜɨɡɧɢɤɧɨɜɟɧɢɟɦ ɝɚɧɬɟɥɟɨɛɪɚɡɧɨɣ ɮɨɪɦɵ ɹɞɪɚ, ɜ ɞɚɥɶɧɟɣɲɟɦ ɲɟɣɤɚ ɪɜɟɬɫɹ, ɢ ɨɛɪɚɡɭɸɬɫɹ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ (ɪɢɫ. 1). Ʉɨɧɤɭɪɟɧɰɢɹ ɫɢɥ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɧɚɬɹɠɟɧɢɹ, ɭɞɟɪɠɢɜɚɸɳɢɯ ɹɞɪɨ ɨɬ ɪɚɡɜɚɥɚ, ɢ ɫɢɥ ɤɭɥɨɧɨɜɫɤɨɝɨ ɨɬɬɚɥɤɢɜɚɧɢɹ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɚɪɚɦɟɬɪɨɦ ɞɟɥɢɦɨɫɬɢ Z 2 A , ɡɚɜɢɫɹɳɢɦ ɨɬ ɡɚɪɹɞɚ Z ɢ ɚɬɨɦɧɨɝɨ ɜɟɫɚ A ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɜɨɡɪɚɫɬɚɟɬ ɧɟɫɬɚɛɢɥɶɧɨɫɬɶ ɹɞɪɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɟɥɟɧɢɹ [1].
Ɋɢɫ. 1. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɫɬɚɞɢɢ ɞɟɥɟɧɢɹ ɚɬɨɦɧɨɝɨ ɹɞɪɚ Ɉɫɧɨɜɧɚɹ ɱɚɫɬɶ ɷɧɟɪɝɢɢ ɩɪɢ ɞɟɥɟɧɢɢ ɚɬɨɦɧɨɝɨ ɹɞɪɚ ɜɵɞɟɥɹɟɬɫɹ ɜ ɮɨɪɦɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɚɡɥɟɬɚɸɳɢɯɫɹ ɨɫɤɨɥɤɨɜ. Ɇɟɧɶɲɚɹ ɷɧɟɪɝɢɹ ɩɪɢɯɨɞɢɬɫɹ ɧɚ ɞɨɥɸ ɦɝɧɨɜɟɧɧɵɯ ɧɟɣɬɪɨɧɨɜ ɢ J -ɤɜɚɧɬɨɜ. ɉɪɨɰɟɫɫ ɞɟɥɟɧɢɹ ɹɞɪɚ ɫɜɹɡɚɧ ɫ ɩɟɪɟɫɬɪɨɣɤɨɣ ɫɨɫɬɨɹɧɢɣ ɜɫɟɯ ɧɭɤɥɨɧɨɜ ɷɬɨɝɨ ɹɞɪɚ, ɨɩɢɫɵɜɚɟɦɨɣ ɧɚ ɹɡɵɤɟ ɤɨɥɥɟɤɬɢɜɧɵɯ ɞɟɮɨɪɦɚɰɢɨɧɧɵɯ ɦɨɞ ɞɜɢɠɟɧɢɹ ɧɭɤɥɨɧɨɜ ɜ ɹɞɪɟ. ȼɫɥɟɞɫɬɜɢɟ ɦɚɥɨɣ ɫɠɢɦɚɟɦɨɫɬɢ ɹɞɟɪɧɨɝɨ ɜɟɳɟɫɬɜɚ ɤɨɥɥɟɤɬɢɜɧɵɟ ɞɟɮɨɪɦɚɰɢɨɧɧɵɟ ɞɜɢɠɟɧɢɹ ɹɞɪɚ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɫɢɥɶɧɵɦ ɨɬɤɥɨɧɟɧɢɹɦ ɮɨɪɦɵ ɹɞɪɚ ɨɬ ɫɮɟɪɢɱɟɫɤɨɣ ɢ ɨɩɢɫɵɜɚɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɜɜɟɞɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɞɟɮɨɪɦɚɰɢɢ EO , ɨɩɪɟɞɟɥɹɸɳɢɯ ɪɚɞɢɭɫ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɝɨ ɹɞɪɚ: § · RA T ,M RA0 ¨1 ¦ E OYO 0 T ,M ¦ E O2 4S ¸ , (1) ¨ ¸ O O © ¹ ɝɞɟ O 2, 3, 4,... – ɤɜɚɞɪɭɩɨɥɶɧɵɟ, ɨɤɬɭɩɨɥɶɧɵɟ ɢ ɝɟɤɫɚɞɟɤɚɩɨɥɶɧɵɟ ɢ ɬ. ɞ. ɞɟɮɨɪɦɚɰɢɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ȼɨɥɶɲɢɧɫɬɜɨ ɹɞɟɪ ɫ A t 220 ɞɚɠɟ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ ɨɤɚɡɵɜɚɸɬɫɹ ɞɟɮɨɪɦɢɪɨɜɚɧɧɵɦɢ, ɚ ɩɚɪɚɦɟɬɪ ɪɚɜɧɨɜɟɫɧɨɣ ɤɜɚɞɪɭɩɨɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ ɞɥɹ ɬɚɤɢɯ ɹɞɟɪ E 20 = 0,2 – 0,25. ȼ 1950– 1953 ɝɝ. Ɉ. Ȼɨɪ ɢ Ȼ. Ɇɨɬɬɟɥɶɫɨɧ ɩɨɫɬɪɨɢɥɢ ɨɛɨɛɳɟɧɧɭɸ ɦɨɞɟɥɶ ɹɞɪɚ [2], ɤɨɬɨɪɚɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɨɩɢɫɵɜɚɟɬ ɧɭɤɥɨɧɧɵɟ ɢ ɤɨɥɥɟɤɬɢɜɧɵɟ ɜɪɚɳɚɬɟɥɶɧɵɟ ɢ ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɦɨɞɵ ɞɜɢɠɟɧɢɹ ɚɬɨɦɧɵɯ ɹɞɟɪ. ȼ ɷɬɨɣ ɦɨɞɟɥɢ ɜ ɩɪɟɞɟɥɟ ɫɢɥɶɧɨɣ ɫɜɹɡɢ, ɤɨɝɞɚ ɹɞɪɨ ɦɨɠɟɬ ɢɦɟɬɶ ɨɬɥɢɱɧɵɟ ɨɬ ɧɭɥɹ ɫɬɚɬɢɱɟɫɤɢɟ ɞɟɮɨɪɦɚɰɢɢ, ɜ ɫɢɫɬɟɦɟ ɰɟɧɬɪɚ ɦɚɫɫ (ɫ. ɰ. ɦ.) ɨɛɨɥɨɱɟɱɧɚɹ
ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ
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ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ
ɫɨ ɫɩɢɧɨɦ J , ɟɝɨ ɩɪɨɟɤɰɢɟɣ M ɧɚ ɨɫɶ Z ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ (ɥ. ɫ.) ɢ ɩɪɨɟɤɰɢɟɣ K ɧɚ ɨɫɶ ɫɢɦɦɟɬɪɢɢ Z ' ɹɞɪɚ, ɱɟɬɧɨɫɬɶɸ S ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ V , ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ [2]
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2J 1 § 1 ·· § J K J J S DM K Z F S }, ¨1 G K ,0 ¨1 ¸ ¸{DMK Z FV K 1 VK 2 ¹¹ © 16S 2 ©
(2) ɝɞɟ Z – ɨɛɨɛɳɟɧɧɚɹ ɫɮɟɪɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ, ɡɚɜɢɫɹɳɚɹ ɨɬ ɭɝɥɨɜ ɗɣɥɟɪɚ Z { D ,E ,J ɢ ɨɩɢɫɵɜɚɸɳɚɹ ɜɪɚɳɚɬɟɥɶɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ ɹɞɪɚ; J DMK
FVS K –
ɜɧɭɬɪɟɧɧɹɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɹɞɪɚ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɢ ɧɭɤɥɨɧɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. ɉɨɫɤɨɥɶɤɭ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɫɨɯɪɚɧɹɟɬɫɹ ɚɤɫɢɚɥɶɧɚɹ ɫɢɦɦɟɬɪɢɹ, ɩɪɨɟɤɰɢɹ K ɹɜɥɹɟɬɫɹ ɢɧɬɟɝɪɚɥɨɦ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɤɨɥɥɟɤɬɢɜɧɵɯ ɜɪɚɳɚɬɟɥɶɧɵɯ ɢ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɹɞɪɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɨɟ ɩɪɢɛɥɢɠɟɧɢɟ, ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɬɨɦ ɮɚɤɬɟ, ɱɬɨ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ ɞɜɢɠɟɧɢɹ ɧɭɤɥɨɧɨɜ ɜ ɹɞɪɟ Tn ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧ, ɫɜɹɡɚɧɧɵɯ ɫ ɤɨɥɥɟɤɬɢɜɧɵɦɢ ɤɨɥɟɛɚɬɟɥɶɧɵɦɢ Tvib ɢ ɜɪɚɳɚɬɟɥɶɧɵɦɢ Trot ɞɜɢɠɟɧɢɹɦɢ: Tn Tvib Trot , ɬ. ɟ. ɧɭɤɥɨɧɵ ɭɫɩɟɜɚɸɬ «ɩɨɞɫɬɪɚɢɜɚɬɶɫɹ» ɩɨɞ ɢɡɦɟɧɟɧɢɟ ɮɨɪɦɵ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɉɨɬɟɧɰɢɚɥ ɞɟɮɨɪɦɚɰɢɢ ɹɞɪɚ V E O , ɤɨɬɨɪɵɣ ɫɨɜɩɚɞɚɟɬ ɫ ɷɧɟɪɝɢɟɣ ɫɜɹɡɢ ɹɞɪɚ ɩɪɢ ɞɟɮɨɪɦɚɰɢɢ E O , ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ (3) V EO E EO Eɨɛ EO , ɝɞɟ E E – ɷɧɟɪɝɢɹ ɫɜɹɡɢ ɹɞɪɚ, ɪɚɫɫɱɢɬɚɧɧɚɹ ɜ ɪɚɦɤɚɯ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɢ O
ɩɨ ɮɨɪɦɭɥɟ ȼɚɣɰɡɟɤɤɟɪɚ, Eɨɛ EO – ɨɛɨɥɨɱɟɱɧɚɹ ɩɨɩɪɚɜɤɚ, ɜɜɟɞɟɧɧɚɹ ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɢɦ. Ʉɨɥɟɛɚɬɟɥɶɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ ɹɞɪɚ ɨɩɢɫɵɜɚɸɬɫɹ ɩɨɬɟɧɰɢɚɥɨɦ ɞɟɮɨɪɦɚɰɢɢ ɹɞɪɚ V E O ɩɪɢ ɜɜɟɞɟɧɢɢ ɦɚɫɫɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ [2]. Ʉɚɩɟɥɶɧɚɹ ɷɧɟɪɝɢɹ E E O ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɚɪɚɦɟɬɪɚ ɤɜɚɞɪɭɩɨɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ E 2 ɢɦɟɟɬ ɜɢɞ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɧɚ ɪɢɫ. 2. ɗɧɟɪɝɢɹ E E ɢɦɟɟɬ ɦɢɧɢɦɭɦ ɩɪɢ E E , ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ O
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ɨɫɧɨɜɧɨɦɭ ɫɨɫɬɨɹɧɢɸ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɢ ɦɚɤɫɢɦɭɦ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɛɚɪɶɟɪɭ ɞɟɥɟɧɢɹ ɫ ɜɵɫɨɬɨɣ B ɞɥɹ ɞɟɥɟɧɢɹ ɹɞɪɚ ɢɡ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɜɨɡɧɢɤɚɸɳɢɣ ɩɪɢ E 2 E sd . Ɂɧɚɱɟɧɢɹ ɛɚɪɶɟɪɚ ɞɟɥɟɧɢɹ B ɩɨɱɬɢ ɞɥɹ ɜɫɟɯ ɬɹɠɟɥɵɯ ɹɞɟɪ ɫ A ! 220 ɡɚɤɥɸɱɟɧɵ ɜ ɢɧɬɟɪɜɚɥɟ 5.0–6.5 Ɇɷȼ. ȿɫɥɢ ɜɤɥɸɱɢɬɶ ɩɚɪɚɦɟɬɪɵ ɞɟɮɨɪɦɚɰɢɢ ɫ O 3, 4,... , ɬɨ ɛɚɪɶɟɪ ɞɟɥɟɧɢɹ ɩɟɪɟɯɨɞɢɬ ɜ ɫɟɞɥɨɜɭɸ ɬɨɱɤɭ. ɉɪɢ ɞɟɥɟɧɢɢ ɹɞɪɚ ɩɚɪɚɦɟɬɪ ɞɟɮɨɪɦɚɰɢɢ E 2 ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜɩɥɨɬɶ ɞɨ ɧɟɤɨɬɨɪɨɝɨ ɡɧɚɱɟɧɢɹ E sc , ɩɪɢ ɤɨɬɨɪɨɦ ɞɟɥɹɳɟɟɫɹ ɹɞɪɨ ɪɚɡɪɵɜɚɟɬɫɹ ɧɚ ɞɜɚ ɮɪɚɝɦɟɧɬɚ ɞɟɥɟɧɢɹ.
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Ɋɢɫ. 2. ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɟɮɨɪɦɚɰɢɢ ɹɞɪɚ ɜ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɢ ȼ ɪɚɦɤɚɯ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɢ, ɩɪɟɞɩɨɥɚɝɚɸɳɟɣ ɨɞɧɨɪɨɞɧɨɟ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɧɭɤɥɨɧɨɜ ɜ ɹɞɪɟ, ɧɟ ɭɞɚɥɨɫɶ ɨɛɴɹɫɧɢɬɶ ɬɚɤɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɧɚɛɥɸɞɚɟɦɵɟ ɫɜɨɣɫɬɜɚ ɞɟɥɟɧɢɹ, ɤɚɤ ɲɢɪɢɧɵ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɩɨɫɬɨɹɧɫɬɜɨ ɜɟɥɢɱɢɧ ɛɚɪɶɟɪɨɜ ɞɟɥɟɧɢɹ ɢ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɚɫɢɦɦɟɬɪɢɱɧɨɟ ɦɚɫɫɨɜɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɹɞɟɪ-ɚɤɬɢɧɢɞɨɜ. ɉɨɫɤɨɥɶɤɭ ɧɭɤɥɨɧɵ ɜ ɹɞɪɟ ɩɨ ɷɧɟɪɝɢɢ ɪɚɫɩɪɟɞɟɥɟɧɵ ɧɟɨɞɧɨɪɨɞɧɨ, ɞɥɹ ɪɚɫɱɟɬɚ V E O ɜɜɨɞɹɬɫɹ ɨɛɨɥɨɱɟɱɧɵɟ ɩɨɩɪɚɜɤɢ Eɨɛ E O . Ɉɛɨɥɨɱɟɱɧɚɹ ɩɨɩɪɚɜɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɡɧɨɫɬɶɸ ɫɭɦɦɵ ɨɛɨɥɨɱɟɱɧɵɯ ɷɧɟɪɝɢɣ EQ ɧɭɤɥɨɧɨɜ ɜ ɹɞɪɟ ɫ ɨɛɨɥɨɱɤɚɦɢ ɢ ɷɧɟɪɝɢɣ ɧɭɤɥɨɧɨɜ ɞɥɹ ɨɞɧɨɪɨɞɧɨɝɨ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɢ. Ɂɧɚɱɟɧɢɹ ɷɬɢɯ ɩɨɩɪɚɜɨɤ ɨɫɨɛɟɧɧɨ ɜɟɥɢɤɢ ɞɥɹ ɹɞɟɪ ɫ ɡɚɦɤɧɭɬɵɦɢ ɨɛɨɥɨɱɤɚɦɢ (ɦɚɝɢɱɟɫɤɢɯ ɹɞɟɪ), ɭ ɤɨɬɨɪɵɯ ɜɟɥɢɱɢɧɵ ɷɧɟɪɝɢɢ ɫɜɹɡɢ, ɩɪɢɯɨɞɹɳɟɣɫɹ ɧɚ ɨɞɢɧ ɧɭɤɥɨɧ – ɭɞɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɫɜɹɡɢ, ɛɨɥɶɲɟ, ɱɟɦ ɞɥɹ ɫɨɫɟɞɧɢɯ ɹɞɟɪ. Ɉɛɨɥɨɱɟɱɧɚɹ ɩɨɩɪɚɜɤɚ, ɡɚɜɢɫɹɳɚɹ ɨɬ ɞɟɮɨɪɦɚɰɢɢ ɹɞɪɚ, ɜɩɟɪɜɵɟ ɛɵɥɚ ɜɜɟɞɟɧɚ ɞɥɹ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɹɞɪɚ ɜ 1966 ɝ. Ɇɚɣɟɪɫɨɦ ɢ ɋɜɹɬɟɰɤɢɦ. Ƚɨɞɨɦ ɩɨɡɠɟ ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɢɣ ɩɪɟɞɥɨɠɢɥ ɫɩɨɫɨɛ ɭɫɪɟɞɧɟɧɢɹ ɩɥɨɬɧɨɫɬɢ ɨɞɧɨɱɚɫɬɢɱɧɵɯ ɭɪɨɜɧɟɣ ɩɨ ɷɧɟɪɝɢɢ, ɩɨɡɜɨɥɹɸɳɢɣ ɩɟɪɟɣɬɢ ɨɬ ɨɛɨɥɨɱɟɱɧɨɝɨ ɤ ɠɢɞɤɨɤɚɩɟɥɶɧɨɦɭ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɧɭɤɥɨɧɨɜ ɜ ɹɞɪɟ. Ʉɚɤ ɩɨɤɚɡɚɥɢ ɪɚɫɱɟɬɵ ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɨɝɨ, ɩɨɬɟɧɰɢɚɥ ɞɟɮɨɪɦɚɰɢɢ ɹɞɪɚ V E O (3) ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɨɫɰɢɥɥɢɪɭɟɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɚɜɢɫɢɦɨɫɬɢ, ɨɩɢɫɵɜɚɟɦɨɣ ɤɚɩɟɥɶɧɨɣ ɦɨɞɟɥɶɸ. ȼ ɤɪɢɜɨɣ V E 2 ɦɨɠɟɬ ɩɨɹɜɢɬɶɫɹ ɜɬɨɪɚɹ (ɢ ɞɚɠɟ ɬɪɟɬɶɹ) ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɹɦɚ ɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɜɬɨɪɨɣ (ɬɪɟɬɢɣ) ɛɚɪɶɟɪ ɫ ɜɵɫɨɬɨɣ B2 ɩɪɢ E 2 E sd 2 (ɪɢɫ. 3). ɉɨɞɨɛɧɵɣ ɩɨɬɟɧɰɢɚɥ V E 2 , ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɧɚ ɪɢɫ. 3, ɧɚɡɵɜɚɟɬɫɹ ɞɜɭɝɨɪɛɵɦ. 6
Ɋɢɫ. 3. ɉɨɬɟɧɰɢɚɥ ɞɟɮɨɪɦɚɰɢɢ ɹɞɪɚ ɜ ɦɨɞɟɥɢ ɞɜɭɝɨɪɛɨɝɨ ɛɚɪɶɟɪɚ ɞɟɥɟɧɢɹ Ⱦɚɧɧɵɟ ɨɛ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɜɵɫɨɬɟ ɛɚɪɶɟɪɨɜ ɞɟɥɟɧɢɹ ɢ ɝɥɭɛɢɧɚɯ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɹɦ ɩɨɥɭɱɚɸɬ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ [3]. ɉɨɫɤɨɥɶɤɭ ɝɥɭɛɢɧɚ ɜɬɨɪɨɣ ɹɦɵ ɦɟɧɶɲɟ ɝɥɭɛɢɧɵ ɩɟɪɜɨɣ ɹɦɵ, ɬɨ ɜɨ ɜɬɨɪɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɩɨɹɜɥɹɸɬɫɹ ɫɨɫɬɨɹɧɢɹ, ɜɨɡɛɭɠɞɟɧɧɵɟ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɫɧɨɜɧɨɦɭ ɫɨɫɬɨɹɧɢɸ ɹɞɪɚ ɜ ɩɟɪɜɨɣ ɹɦɟ ɢ ɢɦɟɸɳɢɟ ɦɚɥɵɟ J -ɲɢɪɢɧɵ ɞɥɹ ɩɟɪɟɯɨɞɨɜ ɜ ɨɫɧɨɜɧɨɟ ɢ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɩɟɪɜɨɣ ɹɦɵ ɢɡ-ɡɚ ɧɚɥɢɱɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ. Ɉɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɢ ɧɟɤɨɬɨɪɵɟ ɢɡ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɹɞɪɚ ɜɨ ɜɬɨɪɨɣ ɹɦɟ, ɢɦɟɸɳɢɟ ɦɚɥɵɟ J -ɲɢɪɢɧɵ ɞɥɹ ɩɟɪɟɯɨɞɨɜ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜɬɨɪɨɣ ɹɦɵ, ɜɵɫɬɭɩɚɸɬ ɤɚɤ ɢɡɨɦɟɪɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɧɚɡɜɚɧɧɵɟ ɢɡɨɦɟɪɚɦɢ ɮɨɪɦɵ. ɉɨɩɚɜ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɜɨ ɜɬɨɪɭɸ ɹɦɭ, ɹɞɪɨ ɦɨɠɟɬ ɪɚɡɞɟɥɢɬɶɫɹ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ: ɧɟ ɢɡɦɟɧɢɜ ɷɧɟɪɝɢɢ, ɬ. ɟ. ɦɝɧɨɜɟɧɧɨ, ɢɥɢ, ɢɫɩɵɬɚɜ ɪɚɞɢɚɰɢɨɧɧɵɟ ɩɟɪɟɯɨɞɵ ɜ ɫɨɫɬɨɹɧɢɹ ɢɡɨɦɟɪɨɜ ɮɨɪɦɵ, ɪɚɡɞɟɥɢɬɶɫɹ ɢɡ ɷɬɢɯ ɫɨɫɬɨɹɧɢɣ, ɬ. ɟ. ɫ ɡɚɩɚɡɞɵɜɚɧɢɟɦ. ȼɟɪɨɹɬɧɨɫɬɶ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɢɡ ɢɡɨɦɟɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ ɬɨɥɶɤɨ ɜɧɟɲɧɟɝɨ ɛɚɪɶɟɪɚ B2 ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ, ɢ ɩɨɷɬɨɦɭ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɜɟɪɨɹɬɧɨɫɬɢ ɞɟɥɟɧɢɹ ɹɞɪɚ ɢɡ ɛɥɢɡɤɨɝɨ ɩɨ ɷɧɟɪɝɢɢ ɫɨɫɬɨɹɧɢɹ ɹɞɪɚ ɜ ɩɟɪɜɨɣ ɹɦɟ. Ɍɚɤɨɟ ɫɩɨɧɬɚɧɧɨɟ ɞɟɥɟɧɢɟ ɹɞɪɚ ɢɡ ɢɡɨɦɟɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜɬɨɪɨɣ ɹɦɵ ɫ ɚɧɨɦɚɥɶɧɨ ɛɨɥɶɲɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɨɣ ɜɩɟɪɜɵɟ ɧɚɛɥɸɞɚɥɨɫɶ ɋ.Ɇ. ɉɨɥɢɤɚɧɨɜɵɦ ɢ ɟɝɨ ɫɨɬɪɭɞɧɢɤɚɦɢ ɞɥɹ ɹɞɟɪ 242Am. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɞɨɫɬɚɬɨɱɧɨ ɯɨɪɨɲɨ ɢɡɭɱɟɧɵ ɤɚɤ ɢɡɨɦɟɪɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɬɚɤ ɢ ɞɪɭɝɢɟ ɫɨɫɬɨɹɧɢɹ ɹɞɪɚ ɜɨ ɜɬɨɪɨɣ ɹɦɟ. ȼ ɫɟɞɥɨɜɨɣ ɬɨɱɤɟ ɜɧɟɲɧɟɝɨ ɛɚɪɶɟɪɚ ɞɟɥɟɧɢɹ, ɤɚɤ ɩɨɤɚɡɚɥɢ ɪɚɫɱɟɬɵ ɛɚɪɶɟɪɨɜ ɞɟɥɟɧɢɹ, ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɛɨɥɟɟ ɜɵɝɨɞɧɚ ɡɟɪɤɚɥɶɧɨ-ɚɫɢɦɦɟɬɪɢɱɧɚɹ ɝɪɭɲɟɜɢɞɧɚɹ ɮɨɪɦɚ ɹɞɪɚ, ɬ. ɟ. ɩɨɹɜɥɹɟɬɫɹ ɨɬɥɢɱɧɚɹ ɨɬ ɧɭɥɹ ɫɬɚɬɢɱɟɫɤɚɹ 7
ɨɤɬɭɩɨɥɶɧɚɹ ɞɟɮɨɪɦɚɰɢɹ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɚɹ ɩɚɪɚɦɟɬɪɨɦ ɞɟɮɨɪɦɚɰɢɢ E3 , ɩɪɢ ɤɨɬɨɪɨɣ ɹɞɪɨ ɫɨɯɪɚɧɹɟɬ ɚɤɫɢɚɥɶɧɭɸ ɫɢɦɦɟɬɪɢɸ. Ⱦɚɥɟɟ ɫɥɟɞɭɟɬ ɫɩɭɫɤ ɹɞɪɚ ɩɨ ɪɚɡɥɢɱɧɵɦ ɞɨɥɢɧɚɦ ɟɝɨ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɫ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ ɤ ɬɨɱɤɟ ɪɚɡɪɵɜɚ, ɝɞɟ ɮɨɪɦɢɪɭɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɦɨɞɵ ɞɟɥɟɧɢɹ. ɉɪɢ ɷɬɨɦ ɞɜɢɠɟɧɢɟ ɹɞɪɚ ɩɨ ɤɨɥɥɟɤɬɢɜɧɵɦ ɩɟɪɟɦɟɧɧɵɦ E O ɧɚ ɨɩɪɟɞɟɥɟɧɧɨɣ ɫɬɚɞɢɢ ɩɪɢ ɩɪɢɛɥɢɠɟɧɢɢ ɤ ɬɨɱɤɟ ɪɚɡɪɵɜɚ E O E sc ɫɬɚɧɨɜɢɬɫɹ ɨɱɟɧɶ ɛɵɫɬɪɵɦ, ɬɚɤ ɱɬɨ ɧɭɤɥɨɧɧɵɟ ɦɨɞɵ ɞɜɢɠɟɧɢɹ ɧɟ ɭɫɩɟɜɚɸɬ ɩɨɞɫɬɪɨɢɬɶɫɹ ɩɨɞ ɞɟɮɨɪɦɚɰɢɨɧɧɵɟ. ȼ ɦɨɦɟɧɬ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɧɭɤɥɨɧɨɜ Xn ɜ ɹɞɪɟ ɫɬɚɧɨɜɹɬɫɹ ɫɨɢɡɦɟɪɢɦɵɦɢ ɢɥɢ ɦɟɧɶɲɢɦɢ ɫɤɨɪɨɫɬɟɣ Xcol , ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɤɨɥɥɟɤɬɢɜɧɨɟ ɞɟɮɨɪɦɚɰɢɨɧɧɨɟ ɞɜɢɠɟɧɢɟ, ɧɚɪɭɲɚɟɬɫɹ ɭɫɥɨɜɢɟ ɚɞɢɚɛɚɬɢɱɧɨɫɬɢ. ɉɨɷɬɨɦɭ ɧɭɤɥɨɧɧɚɹ ɩɨɞɫɢɫɬɟɦɚ ɹɞɪɚ ɧɟ ɭɫɩɟɜɚɟɬ ɩɟɪɟɣɬɢ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɩɪɢ ɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɞɟɮɨɪɦɚɰɢɢ E O , ɬ. ɟ. ɹɞɪɨ ɨɤɚɡɵɜɚɟɬɫɹ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ȼ ɷɬɨɣ ɨɛɥɚɫɬɢ ɩɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ ɹɞɪɚ ɜ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɨɩɢɫɵɜɚɟɬɫɹ ɧɚ ɹɡɵɤɟ ɤɢɧɟɬɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ ɫ ɭɱɟɬɨɦ ɷɮɮɟɤɬɨɜ ɞɢɫɫɢɩɚɰɢɢ, ɤɨɝɞɚ ɜɜɟɞɟɧɢɟ ɜɧɭɬɪɟɧɧɟɝɨ «ɬɪɟɧɢɹ» ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɞɚɱɟ ɱɚɫɬɢ ɷɧɟɪɝɢɢ ɤɨɥɥɟɤɬɢɜɧɨɣ ɦɨɞɵ ɞɜɢɠɟɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɧɭɤɥɨɧɧɵɟ ɦɨɞɵ. ɉɪɢ ɬɚɤɨɦ ɩɨɞɯɨɞɟ ɨɛɵɱɧɨ ɩɪɢɧɢɦɚɟɬɫɹ, ɱɬɨ ɜɨɡɛɭɠɞɟɧɧɵɟ ɧɭɤɥɨɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɹɞɪɚ ɭɫɩɟɜɚɸɬ ɩɟɪɟɣɬɢ ɜ ɪɚɜɧɨɜɟɫɧɵɟ (ɬɟɪɦɚɥɢɡɨɜɚɧɧɵɟ) ɦɧɨɝɨɱɚɫɬɢɱɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɢ ɜ ɦɨɦɟɧɬ ɪɚɡɪɵɜɚ ɞɟɥɹɳɟɟɫɹ ɹɞɪɨ ɢɦɟɟɬ ɬɟɦɩɟɪɚɬɭɪɭ T | 1 Ɇɷȼ . ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ, ɦɚɫɫɨɜɵɟ ɢ ɡɚɪɹɞɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɜ ɪɚɦɤɚɯ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ [4], ɨɫɧɨɜɚɧɧɨɣ ɧɚ ɬɨɦ, ɱɬɨ ɹɞɪɨ, ɤɚɤ ɢ ɜɫɹɤɚɹ ɫɢɫɬɟɦɚ, ɫɬɪɟɦɢɬɫɹ ɩɟɪɟɣɬɢ ɜ ɤɨɧɟɱɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɵɟ ɧɚɢɛɨɥɶɲɟɣ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɶɸ. ȼ ɫɥɭɱɚɟ ɞɟɥɟɧɢɹ ɩɪɢɧɢɦɚɟɬɫɹ, ɱɬɨ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɢɦɟɸɬ ɬɟɦɩɟɪɚɬɭɪɭ, ɫɨɜɩɚɞɚɸɳɭɸ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ T ɜ ɦɨɦɟɧɬ ɪɚɡɪɵɜɚ, ɬɚɤ ɱɬɨ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɩɥɨɬɧɨɫɬɶ ɤɨɧɟɱɧɵɯ ɫɨɫɬɨɹɧɢɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦɢ ɩɥɨɬɧɨɫɬɹɦɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ, ɤɨɬɨɪɵɟ ɪɚɫɬɭɬ ɫ ɪɨɫɬɨɦ ɷɧɟɪɝɢɢ ɜɨɡɛɭɠɞɟɧɢɹ Eɜɨɡɛ ɷɬɢɯ ɮɪɚɝɦɟɧɬɨɜ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ~ exp Eɜɨɡɛ T . ɉɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ, ɨɛɥɚɞɚɸɳɢɟ ɜ ɦɨɦɟɧɬ ɨɛɪɚɡɨɜɚɧɢɹ ɧɟɪɚɜɧɨɜɟɫɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɞɟɮɨɪɦɚɰɢɢ, ɡɚ ɞɨɫɬɚɬɨɱɧɨ ɤɨɪɨɬɤɢɟ ɜɪɟɦɟɧɚ ( ~ 1021 ɫ) ɩɟɪɟɯɨɞɹɬ ɜ ɪɚɜɧɨɜɟɫɧɵɟ ɬɟɪɦɚɥɢɡɨɜɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ. ɇɚ ɫɥɟɞɭɸɳɢɯ ɫɬɚɞɢɹɯ ɩɪɨɰɟɫɫɚ ɞɟɥɟɧɢɹ ɡɚ ɜɪɟɦɟɧɚ ( ~ 1016 ɫ) ɢ ( ~ 1012 ɫ) ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɢɫɩɭɫɤɚɸɬ ɦɝɧɨɜɟɧɧɵɟ ɧɟɣɬɪɨɧɵ ɢ J -ɤɜɚɧɬɵ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɤɨɧɟɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɫɧɨɜɧɵɯ ɢɥɢ ɞɨɥɝɨɠɢɜɭɳɢɯ ɢɡɨɦɟɪɧɵɯ ɫɨɫɬɨɹɧɢɹɯ, ɤɨɬɨɪɵɟ ɢ ɪɟɝɢɫɬɪɢɪɭɸɬɫɹ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ. Ʉɨɧɟɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɦɨɝɭɬ ɢɫɩɵɬɵɜɚɬɶ E -ɪɚɫɩɚɞ ɫ ɜɵɯɨɞɨɦ ɡɚɞɟɪɠɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ ɢ J -ɤɜɚɧɬɨɜ. 8
Ⱦɟɥɟɧɢɟ ɚɬɨɦɧɵɯ ɹɞɟɪ ɫɜɹɡɚɧɨ ɫ ɩɨɹɜɥɟɧɢɟɦ ɨɝɪɨɦɧɨɝɨ ɱɢɫɥɚ ɮɢɡɢɱɟɫɤɢɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ ( | 1010 ), ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɪɚɡɥɢɱɧɵɦ ɩɨ ɫɨɫɬɚɜɭ, ɤɜɚɧɬɨɜɵɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɢ ɷɧɟɪɝɢɹɦ ɜɨɡɛɭɠɞɟɧɢɹ ɮɪɚɝɦɟɧɬɚɦ ɞɟɥɟɧɢɹ. ɍɞɢɜɢɬɟɥɶɧɨɣ ɱɟɪɬɨɣ ɞɟɥɟɧɢɹ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ, ɧɟɫɦɨɬɪɹ ɧɚ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɨɬɤɪɵɬɵɯ ɮɢɡɢɱɟɫɤɢɯ ɤɚɧɚɥɨɜ, ɤɨɬɨɪɵɟ, ɜ ɩɪɢɧɰɢɩɟ, ɦɨɝɭɬ ɢɦɟɬɶ ɫɥɭɱɚɣɧɵɦ ɨɛɪɚɡɨɦ ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɩɨ ɮɚɡɚɦ ɞɟɥɢɬɟɥɶɧɵɟ ɚɦɩɥɢɬɭɞɵ, ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ, ɛɟɡ ɜɵɞɟɥɟɧɢɹ ɤɨɧɤɪɟɬɧɨɣ ɫɬɪɭɤɬɭɪɵ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɧɚɛɥɸɞɚɸɬ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɵɟ ɷɮɮɟɤɬɵ. ɗɬɢ ɷɮɮɟɤɬɵ ɩɪɨɹɜɥɹɸɬɫɹ ɜ ɜɢɞɟ ɚɧɢɡɨɬɪɨɩɢɣ [5] ɢ Ɋ-ɧɟɱɟɬɧɵɯ [6–7], Ɋ-ɱɟɬɧɵɯ [8], Ɍ-ɧɟɱɟɬɧɵɯ [9] ɚɫɢɦɦɟɬɪɢɣ ɜ ɍɊɎ ɞɟɥɟɧɢɹ. Ⱦɥɹ ɨɛɴɹɫɧɟɧɢɹ ɦɟɯɚɧɢɡɦɚ ɩɨɹɜɥɟɧɢɹ ɚɧɢɡɨɬɪɨɩɢɣ ɜ ɍɊɎ ɞɟɥɟɧɢɹ ɜ ɪɚɛɨɬɚɯ Ɉ. Ȼɨɪɚ ɢ ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɨɝɨ ɛɵɥɨ ɢɫɩɨɥɶɡɨɜɚɧɨ ɤɚɱɟɫɬɜɟɧɧɨɟ ɮɢɡɢɱɟɫɤɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɜɫɟ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ, ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɢɯ ɫɨɫɬɚɜɚ ɢ ɫɬɪɭɤɬɭɪɵ, ɜɵɥɟɬɚɸɬ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɢɥɢ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ Z ' ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɗɬɨ ɞɨɩɭɳɟɧɢɟ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɨɛɟɫɩɟɱɢɜɚɟɬ ɤɨɝɟɪɟɧɬɧɨɫɬɶ ɞɟɥɢɬɟɥɶɧɵɯ ɚɦɩɥɢɬɭɞ ɞɥɹ ɜɫɟɯ ɮɢɡɢɱɟɫɤɢɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ. ɋɥɟɞɭɟɬ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɭɤɚɡɚɧɧɨɟ ɞɨɩɭɳɟɧɢɟ ɨ ɜɵɥɟɬɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɨ ɢɥɢ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɹɞɪɚ ɹɜɥɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦ, ɩɨɫɤɨɥɶɤɭ ɨɧɨ ɢɝɧɨɪɢɪɭɟɬ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɣ ɩɪɢɧɰɢɩ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɦɟɠɞɭ ɨɪɛɢɬɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ ɢ ɭɝɥɨɦ ɜɵɥɟɬɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɷɬɨɝɨ ɞɨɩɭɳɟɧɢɹ ɍɊɎ ɞɟɥɟɧɢɹ ɫɨɜɩɚɞɚɟɬ ɫ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɧɚɩɪɚɜɥɟɧɢɣ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɥ. ɫ., ɨɩɪɟɞɟɥɹɟɦɵɦ J ɡɧɚɱɟɧɢɹɦɢ ɨɛɨɛɳɟɧɧɵɯ ɫɮɟɪɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ DMK Ȧ ɢ DMJ K Ȧ ɩɪɢ ɭɝɥɚɯ ɗɣɥɟɪɚ Z D , E , J , ɩɪɢɱɟɦ ɭɝɥɵ E ɢ D ɫɨɜɩɚɞɚɸɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫ ɭɝɥɚɦɢ T ɢ M , ɡɚɞɚɸɳɢɦɢ ɧɚɩɪɚɜɥɟɧɢɟ ɜɵɥɟɬɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɜ ɥ. ɫ. ȼ ɫɥɭɱɚɟ ɨɬɫɭɬɫɬɜɢɹ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ ɫ ɪɚɡɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɫɩɢɧɨɜ ɢ ɱɟɬɧɨɫɬɟɣ, ɩɪɢ ɭɱɟɬɟ ɩɨɥɹɪɢɡɚɰɢɨɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɟɥɟɧɢɹ ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɨɛɪɚɡɨɦ ɞɥɹ ɜɫɟɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ: dP J S : 2 J 1 J J '* J J '* ª J º ¦ UMM ' g K ¬ DMK Ȧ DM ' K Ȧ DM K Ȧ DM ' K Ȧ ¼. 8S MM ' K t0 d: (4) ȼ ɷɬɨɣ ɮɨɪɦɭɥɟ ɨɬɫɭɬɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɬɪɟɬɶɟɝɨ ɭɝɥɚ ɗɣɥɟɪɚ J , J U MM ' – ɫɩɢɧɨɜɚɹ ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ, ɡɚɜɢɫɹɳɚɹ ɨɬ ɨɪɢɟɧɬɚɰɢɣ ɫɩɢɧɚ
ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɞɥɹ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɢ ɨɬ ɨɪɢɟɧɬɚɰɢɢ ɫɩɢɧɨɜ ɹɞɪɚɦɢɲɟɧɢ ɢ ɧɚɥɟɬɚɸɳɟɣ ɱɚɫɬɢɰɵ ɞɥɹ ɢɧɞɭɰɢɪɨɜɚɧɧɨɝɨ ɞɟɥɟɧɢɹ, ɬɟɥɟɫɧɵɣ ɭɝɨɥ : { T ,M . Ʉɨɷɮɮɢɰɢɟɧɬ g K ɨɩɪɟɞɟɥɹɟɬ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɹɜɥɟɧɢɹ ɞɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɩɪɨɟɤɰɢɢ K ɜ ɩɪɟɞɪɚɡɪɵɜɧɵɯ ɫɨɫɬɨɹɧɢɹɯ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɫɜɹɡɚɧɧɵɯ ɫ ɦɨɞɚɦɢ ɞɟɥɟɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ: 9
* JK f
2 G K ,0 , ɝɞɟ * J – ɩɨɥɧɚɹ ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ ɫɨɫɬɨɹɧɢɹ *J ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɜɨ ɜɫɟ ɨɬɤɪɵɬɵɟ ɤɚɧɚɥɵ, ɚ * JK f – ɞɟɥɢɬɟɥɶɧɚɹ ɲɢɪɢɧɚ. ȼ ɫɥɭɱɚɟ ɞɢɚɝɨɧɚɥɶɧɨɫɬɢ ɫɩɢɧɨɜɨɣ gK
J J J ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ U MM ' ɩɨ ɩɪɨɟɤɰɢɹɦ M , M ' : U MM ' G MM 'aM , ɝɞɟ J aM – ɩɚɪɚɦɟɬɪ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɡɚɫɟɥɟɧɧɨɫɬɢ ɩɨɞɭɪɨɜɧɟɣ J S M ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ (4) ɩɪɢɧɢɦɚɟɬ ɜɢɞ [2]: JS dP J S : dP J S : J dPMK : g K aM gK K , (5) ¦ ¦ d: d: d: MK t 0 K t0
ɝɞɟ JS dPMK : d:
2 2º 2J 1 ª J J (6) . DMK Ȧ DM K Ȧ » « 8S ¬ ¼E T ȿɫɥɢ ɫɨɫɬɨɹɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɩɪɨɟɤɰɢɹɦɢ M ɫɩɢɧɚ J ɧɚ ɨɫɶ Z ɥ. ɫ. 1 J G MM ' , ɡɚɫɟɥɟɧɵ ɨɞɧɨɪɨɞɧɨ, ɬ. ɟ. ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ U MM ' 2J 1 ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɵɪɚɠɟɧɢɸ ɮɨɪɦɭɥɚ (4) 2 2 1 ª J º Ȧ DMJ K Ȧ » , ɤɨɬɨɪɨɟ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ¦ g K «¬ DMK 8S MK t0 ¼ M BK
J* DM DJM B K Z , ɬɟɨɪɟɦɵ ɭɦɧɨɠɟɧɢɹ ɮɨɪɦɭɥɵ r K Z 1 D -ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ ɢ ɫɭɦɦɢɪɨɜɚɧɢɢ ɩɨ ɩɪɨɟɤɰɢɹɦ M ɨɤɚɡɵɜɚɟɬɫɹ ɧɟ ɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɨɜ T ɢ M , ɬ. ɟ. ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɨɬɪɨɩɧɨɦɭ ɍɊɎ ɞɟɥɟɧɢɹ. Ⱥɧɚɥɨɝɢɱɧɨ, ɟɫɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɟɣ g K ɹɜɥɹɟɬɫɹ ɨɞɧɨɪɨɞɧɵɦ,
ɬ. ɟ. g K ~
2 G K ,0 ,
ɜɵɪɚɠɟɧɢɟ: 1 8S
2J 1
¦
MM ' K
ɬɨ ɜ ɮɨɪɦɭɥɟ (4) ɞɥɹ ɍɊɎ ɞɟɥɟɧɢɹ ɩɨɹɜɥɹɟɬɫɹ
J J* J J* ª J º U MM ' DMK Ȧ DM ' K Ȧ DM K Ȧ DM ' K Ȧ ,
¬
¼
ɤɨɬɨɪɨɟ ɩɪɢ ɫɭɦɦɢɪɨɜɚɧɢɢ ɩɨ ɩɪɨɟɤɰɢɹɦ K ɬɚɤɠɟ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɨɜ T ɢ M , ɱɬɨ ɨɡɧɚɱɚɟɬ ɢɡɨɬɪɨɩɢɸ ɍɊɎ ɞɟɥɟɧɢɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɹɜɥɟɧɢɟ ɚɧɢɡɨɬɪɨɩɢɣ ɜ ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɨɟɤɰɢɣ M ɢ K ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ J ɜɛɥɢɡɢ ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɹɞɪɚ ɧɟɨɞɧɨɪɨɞɧɵ. ɇɟɨɞɧɨɪɨɞɧɨɫɬɶ M -ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ J ɩɥɨɬɧɨɫɬɢ U MM ' , ɞɨɫɬɢɝɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɭɬɟɦ ɨɪɢɟɧɬɚɰɢɢ ɫɩɢɧɚ J ɫɩɨɧɬɚɧɧɨ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɥ. ɫ., ɧɚɩɪɢɦɟɪ, ɜ ɫɢɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ 10
ɗɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ, Ɇɷȼ
ɩɨɥɹɯ ɩɪɢ ɫɜɟɪɯɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ, ɢɥɢ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɯ ɹɞɟɪ ɢ (ɢɥɢ) ɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɱɚɫɬɢɰ, ɜɵɡɵɜɚɸɳɢɯ ɞɟɥɟɧɢɟ.
Ɋɢɫ. 4. ɋɯɟɦɚ ɭɪɨɜɧɟɣ ɱɟɬɧɨ-ɱɟɬɧɨɝɨ ɹɞɪɚ ɩɪɢ ɫɬɚɛɢɥɶɧɨɣ ɤɜɚɞɪɭɩɨɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ E 20 ɇɟɨɞɧɨɪɨɞɧɨɫɬɶ K -ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ g K ɜ ɮɨɪɦɭɥɚɯ (4)–(5), ɞɥɹ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɢɧɞɭɰɢɪɨɜɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ɛɵɥɚ ɫɜɹɡɚɧɚ ɜ ɪɚɛɨɬɟ [2] ɫ ɩɨɹɜɥɟɧɢɟɦ ɧɟɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɩɟɪɟɯɨɞɧɵɯ ɞɟɥɢɬɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɣ (ɉȾɋ) ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɱɟɪɟɡ ɤɨɬɨɪɵɟ ɩɪɨɢɫɯɨɞɢɬ ɩɪɨɰɟɫɫ ɞɟɥɟɧɢɹ ɢ ɤɨɬɨɪɵɟ ɮɨɪɦɢɪɭɸɬɫɹ ɩɪɢ E O E sd1 ɢ E O E sd 2 , ɡɧɚɱɟɧɢɹɯ ɩɚɪɚɦɟɬɪɨɜ ɞɟɮɨɪɦɚɰɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɟɞɥɨɜɵɦ ɬɨɱɤɚɦ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ. ɉȾɋ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ J S K , ɚ ɢɯ ɫɩɟɤɬɪ ɫɬɪɨɢɬɫɹ ɩɨ ɚɧɚɥɨɝɢɢ ɫɨ ɫɩɟɤɬɪɨɦ ɧɢɡɤɨɥɟɠɚɳɢɯ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɪɚɜɧɨɜɟɫɧɨɝɨ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɚ ɞɟɮɨɪɦɚɰɢɢ E 2 E 20 , ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɦɢɧɢɦɭɦɭ ɩɟɪɜɨɣ ɹɦɵ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ. ȼ ɷɬɨɦ ɫɩɟɤɬɪɟ ɜɵɞɟɥɹɸɬɫɹ ɜɪɚɳɚɬɟɥɶɧɵɟ ɩɨɥɨɫɵ ɫ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ J S K , ɝɞɟ J t K , ɩɨɫɬɪɨɟɧɧɵɟ ɧɚ ɛɚɡɟ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɷɬɨɣ ɩɨɥɨɫɵ ɫ J K . ȼɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ ɉȾɋ ɫɨɨɬɜɟɬɫɬɜɭɸɬ «ɯɨɥɨɞɧɨɦɭ» ɞɟɥɹɳɟɦɭɫɹ ɹɞɪɭ ɢ ɨɩɢɫɵɜɚɸɬɫɹ ɮɨɪɦɭɥɨɣ (5), ɜ ɤɨɬɨɪɨɣ ɜɧɭɬɪɟɧɧɢɟ ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ FVS K ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɪɨɫɬɟɣɲɢɦɢ ɬɢɩɚɦɢ ɤɨɥɥɟɤɬɢɜɧɵɯ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɜɨɡɛɭɠɞɟɧɢɣ ɹɞɪɚ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ, ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ (ɪɢɫ. 4) ɫɬɪɭɤɬɭɪɭ ɉȾɋ ɞɥɹ ɱɟɬɧɨ-ɱɟɬɧɵɯ ɹɞɟɪ-ɚɤɬɢɧɢɞɨɜ. ɉɪɢ ɡɧɚɱɟɧɢɹɯ ɤɜɚɧɬɨɜɵɯ ɱɢɫɟɥ K S 0 ɩɨɹɜɥɹɟɬɫɹ ɜɪɚɳɚɬɟɥɶɧɚɹ ɩɨɥɨɫɚ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɱɟɬɧɨɫɬɢ ɫ 11
J 0,2,4,... , ɚ ɩɪɢ K S 0 – ɩɨɥɨɫɚ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɱɟɬɧɨɫɬɢ ɫ J 1,3,5,... , ɪɚɫɩɨɥɨɠɟɧɧɚɹ ɩɨ ɷɧɟɪɝɢɢ ɩɪɢɦɟɪɧɨ ɧɚ 0,5–0,7 Ɇɷȼ ɜɵɲɟ ɩɟɪɜɨɣ ɩɨɥɨɫɵ. Ȼɨɥɟɟ ɫɥɨɠɧɵɦ ɬɢɩɚɦ ɉȾɋ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɪɚɳɚɬɟɥɶɧɵɟ ɩɨɥɨɫɵ ɫ K z 0 , ɧɚɯɨɞɹɳɢɟɫɹ ɟɳɟ ɜɵɲɟ ɩɨ ɷɧɟɪɝɢɢ (ɧɚ ɜɟɥɢɱɢɧɭ § 1 Ɇɷȼ), ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɩɨɥɨɫɟ ɫ K S 0 . ɉɨɫɤɨɥɶɤɭ ɮɚɤɬɨɪɵ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɞɟɥɢɬɟɥɶɧɵɯ ɛɚɪɶɟɪɨɜ ɞɥɹ ɉȾɋ ɫ ɨɬɥɢɱɚɸɳɢɦɢɫɹ ɡɧɚɱɟɧɢɹɦɢ J S K ɨɤɚɡɵɜɚɸɬɫɹ ɪɚɡɥɢɱɧɵɦɢ, ɭɤɚɡɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɪɚɛɨɬɚɸɬ ɤɚɤ ɮɢɥɶɬɪɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɧɟɨɞɧɨɪɨɞɧɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɦɨɞ ɞɟɥɟɧɢɹ ɩɨ K . ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɨɩɢɫɚɧɢɟ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɵɯ ɷɮɮɟɤɬɨɜ ɜ ɍɊɎ ɞɟɥɟɧɢɹ ɬɪɟɛɭɟɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɧɹɬɢɣ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧ ɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ. Ʉɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɟ ɜɚɪɢɚɧɬɵ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɛɵɥɢ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɪɹɞɟ ɪɚɛɨɬ, ɧɚɩɪɢɦɟɪ [10–13], ɝɞɟ ɜ ɪɚɦɤɚɯ R-ɦɚɬɪɢɱɧɨɣ ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ [14] ɛɵɥɢ ɩɨɫɬɪɨɟɧɵ ɮɨɪɦɭɥɵ ɞɥɹ ɨɩɢɫɚɧɢɹ ɚɧɢɡɨɬɪɨɩɢɣ, Ɋ-ɧɟɱɟɬɧɵɯ, Ɋ-ɱɟɬɧɵɯ ɢ Ɍ-ɧɟɱɟɬɧɵɯ ɚɫɢɦɦɟɬɪɢɣ ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. Ɉɞɧɚɤɨ ɧɢɤɚɤɢɯ ɮɨɪɦɭɥ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧ ɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ ɜ ɷɬɢɯ ɪɚɛɨɬɚɯ ɧɟ ɜɜɨɞɢɥɨɫɶ, ɚ ɭɤɚɡɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɤɚɤ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ. ɗɬɨ ɩɪɢɜɟɥɨ ɤ ɫɟɪɶɟɡɧɵɦ ɬɪɭɞɧɨɫɬɹɦ, ɩɨɫɤɨɥɶɤɭ, ɟɫɥɢ ɢɧɮɨɪɦɚɰɢɸ ɨ ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧɚɯ ɦɨɠɧɨ ɜ ɤɚɤɨɣ-ɬɨ ɮɨɪɦɟ ɩɨɥɭɱɢɬɶ ɢɯ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɬɨ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɚɹ ɢɧɮɨɪɦɚɰɢɹ ɨ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡɚɯ ɨɬɫɭɬɫɬɜɭɟɬ. ȼ ɪɚɛɨɬɚɯ [10, 13] ɩɪɢ ɨɩɢɫɚɧɢɢ Ɋ-ɱɟɬɧɵɯ ɢ Ɋ-ɧɟɱɟɬɧɵɯ ɚɫɢɦɦɟɬɪɢɣ ɜ ɍɊɎ ɞɟɥɟɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɫɹ ɨɛɨɛɳɟɧɧɵɣ ɜɚɪɢɚɧɬ ɮɨɪɦɭɥɵ (4), ɭɱɢɬɵɜɚɸɳɢɣ ɜɨɡɦɨɠɧɨɫɬɶ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɪɚɡɥɢɱɧɵɦɢ ɫɩɢɧɚɦɢ ɢ ɱɟɬɧɨɫɬɹɦɢ. Ɉɞɧɚɤɨ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɢɫɩɨɥɶɡɨɜɚɧɧɨɟ ɢ ɜ ɷɬɢɯ ɪɚɛɨɬɚɯ ɞɨɩɭɳɟɧɢɟ ɨ ɜɵɥɟɬɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɨ ɢɥɢ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢɦɟɟɬ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ ɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɪɟɞɫɬɚɜɥɟɧɢɸ ɨ ɩɨɹɜɥɟɧɢɢ ɛɟɫɤɨɧɟɱɧɨ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɢɝɧɨɪɢɪɨɜɚɧɢɸ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ, ɩɨɫɤɨɥɶɤɭ ɤɚɤ ɫɩɢɧɵ ɨɛɪɚɡɭɸɳɢɯɫɹ ɮɪɚɝɦɟɧɬɨɜ, ɬɚɤ ɢ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɨɪɛɢɬɚɥɶɧɵɟ ɦɨɦɟɧɬɵ ɞɨɥɠɧɵ ɢɦɟɬɶ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ. ȼ ɫɜɹɡɢ ɫ ɭɤɚɡɚɧɧɵɦɢ ɩɪɨɛɥɟɦɚɦɢ ɨɩɢɫɚɧɢɹ ɹɜɥɟɧɢɹ ɞɟɥɟɧɢɹ ɜ ɪɚɦɤɚɯ ɬɪɚɞɢɰɢɨɧɧɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɫ ɭɱɟɬɨɦ R-ɦɚɬɪɢɱɧɵɯ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɞɯɨɞɨɜ, ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɦ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɨɦ ɨɩɢɫɚɧɢɢ ɷɬɨɝɨ ɹɜɥɟɧɢɹ, ɤɨɬɨɪɨɟ, ɢɫɩɨɥɶɡɭɹ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɹɯ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɹɜɧɵɦ ɨɛɪɚɡɨɦ ɨɩɪɟɞɟɥɹɟɬ ɚɦɩɥɢɬɭɞɵ ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧ ɢ
12
ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ ɫ ɭɱɟɬɨɦ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. 2. Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ
Ɉɛɳɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ ɞɟɥɟɧɢɹ, ɛɚɡɢɪɭɸɳɚɹɫɹ ɧɚ ɫɬɚɰɢɨɧɚɪɧɨɦ ɮɨɪɦɚɥɢɡɦɟ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ [15] ɢ ɬɟɨɪɢɢ ɨɬɤɪɵɬɵɯ ɮɟɪɦɢ-ɫɢɫɬɟɦ [16], ɢɫɩɨɥɶɡɭɸɳɚɹ ɨɫɧɨɜɧɵɟ ɞɨɫɬɢɠɟɧɢɹ ɬɪɚɞɢɰɢɨɧɧɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɢ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɞɯɨɞɨɜ ɪɚɛɨɬ [10–13] ɢ ɨɩɢɪɚɸɳɚɹɫɹ ɧɚ ɩɨɧɹɬɢɹ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɚɦɩɥɢɬɭɞ ɩɚɪɰɢɚɥɶɧɵɯ ɞɟɥɢɬɟɥɶɧɵɯ ɲɢɪɢɧ ɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ, ɛɵɥɚ ɪɚɡɜɢɬɚ ɜ ɪɚɛɨɬɚɯ [17–19]. ȼ ɪɚɦɤɚɯ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ [17–19] ɞɟɥɟɧɢɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɪɚɫɩɚɞ ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɨɩɢɫɵɜɚɟɦɨɝɨ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ ȌVJ S M , ɤɨɬɨɪɚɹ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ:
H A EVJ ȌVJS M
(7)
0,
ɝɞɟ H A – ɝɚɦɢɥɶɬɨɧɢɚɧ ɹɞɪɚ A ɜ ɫ. ɰ. ɦ., EVJ
EVJ i*VJS 2 ,
EVJ
ɫɨɜɩɚɞɚɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɡɧɚɤɚ ɫ ɷɧɟɪɝɢɟɣ ɫɜɹɡɢ ɹɞɪɚ, *VJ S – ɩɨɥɧɚɹ ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ ɹɞɪɚ ɜɨ ɜɫɟ ɨɬɤɪɵɬɵɟ ɤɚɧɚɥɵ. ɋ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɟɯɧɢɤɢ ɩɪɨɟɤɰɢɨɧɧɵɯ ɨɩɟɪɚɬɨɪɨɜ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ ɬɟɨɪɢɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ ɢ ɬɟɨɪɢɢ ɨɬɤɪɵɬɵɯ Ɏɟɪɦɢ-ɫɢɫɬɟɦ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ȌVJ S M ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ: < J S M W Pˆ < J S M W Qˆ < J S M W , (8) V
V
V
ɝɞɟ ɨɩɟɪɚɬɨɪ Pˆ ɩɪɨɟɤɬɢɪɭɟɬ ɫɨɫɬɨɹɧɢɹ ɹɞɪɚ A ɧɚ ɜɧɭɬɪɟɧɧɸɸ (ɨɛɨɥɨɱɟɱɧɭɸ) ɨɛɥɚɫɬɶ ɤɨɧɮɢɝɭɪɚɰɢɨɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɫɜɹɡɚɧɧɭɸ ɫ ɩɨɥɧɵɦ ɧɚɛɨɪɨɦ ɤɨɨɪɞɢɧɚɬ W ɹɞɪɚ ɜ ɫ. ɰ. ɦ. ȼ ɷɬɨɣ ɨɛɥɚɫɬɢ ɹɞɪɨ A ɢɦɟɟɬ ɨɞɧɨɫɜɹɡɧɭɸ ɮɨɪɦɭ ɢ ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɨ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɨɝɨ, ɧɨ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɛɚɡɢɫɚ Ȍ nJ S M W ɦɧɨɝɨɱɚɫɬɢɱɧɵɯ ɨɛɨɥɨɱɟɱɧɵɯ ɮɭɧɤɰɢɣ, ɫɬɪɨɹɳɢɯɫɹ ɜ ɪɚɦɤɚɯ ɨɛɨɛɳɟɧɧɨɣ ɦɨɞɟɥɢ ɹɞɪɚ [20] ɫ ɭɱɟɬɨɦ ɧɨɪɦɚɥɶɧɵɯ ɢ ɫɜɟɪɯɬɟɤɭɱɢɯ ɧɭɤɥɨɧ-ɧɭɤɥɨɧɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɢ ɤɨɥɥɟɤɬɢɜɧɵɯ ɦɨɞ ɞɜɢɠɟɧɢɹ, ɝɞɟ ɢɧɞɟɤɫ n ɩɪɢɧɢɦɚɟɬ ɞɢɫɤɪɟɬɧɵɣ ɢ ɤɨɧɟɱɧɵɣ ɪɹɞ ɡɧɚɱɟɧɢɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɟɪɚɬɨɪ Pˆ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ Pˆ op ¦ < J S M < J S M . (9) n
n
n
13
ȼɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ Pˆ
V
VK
sh
ɩɪɨɟɤɰɢɹ K ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɫɧɨɜɧɨɦɭ ɫɨɫɬɨɹɧɢɸ K J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ, ɩɨɫɤɨɥɶɤɭ ɩɪɨɟɤɰɢɹ K ɫɨɯɪɚɧɹɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ. ȼ ɫɥɭɱɚɟ ɜɵɧɭɠɞɟɧɧɨɝɨ ɨɤɨɥɨɩɨɪɨɝɨɜɨɝɨ ɞɟɥɟɧɢɹ, ɤɨɝɞɚ ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɨɛɪɚɡɭɟɬɫɹ ɫɨɫɬɚɜɧɨɟ ɹɞɪɨ ɫ ɛɨɥɶɲɨɣ ɷɧɟɪɝɢɟɣ ɜɨɡɛɭɠɞɟɧɢɹ ( Eɜɨɡɛ ~ B1 ), ɨɛɨɥɨɱɟɱɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Pˆ < J S M W ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ V
ɞɟɮɨɪɦɚɰɢɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɩɟɪɩɨɡɢɰɢɸ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ
(10)
ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɚKJ ɭɱɢɬɵɜɚɸɬ Ʉɨɪɢɨɥɢɫɨɜɨ ɫɦɟɲɢɜɚɧɢɟ [21] ɩɪɨɟɤɰɢɣ ɫɩɢɧɚ K ɞɥɹ ɜɵɫɨɤɨɥɟɠɚɳɢɯ ɩɨ ɷɧɟɪɝɢɢ ɢ ɫɥɨɠɧɵɯ ɩɨ ɫɜɨɟɣ ɤɜɚɡɢɱɚɫɬɢɱɧɨɣ ɫɬɪɭɤɬɭɪɟ ɫɨɫɬɨɹɧɢɣ ɹɞɪɚ. Ɉɛɨɥɨɱɟɱɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Pˆ
ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬ bVJ SqK ɭɱɢɬɵɜɚɟɬ ɞɢɧɚɦɢɤɭ ɩɟɪɟɯɨɞɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɩɪɢ ɫɨɯɪɚɧɟɧɢɢ ɤɜɚɧɬɨɜɵɯ ɱɢɫɟɥ J S K ɢɡ ɫɨɫɬɨɹɧɢɹ ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ V ɜ ɩɟɪɜɨɣ ɹɦɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ ɜ ɫɨɫɬɨɹɧɢɟ ɞɟɥɢɬɟɥɶɧɨɣ ɦɨɞɵ q ɩɪɢ ɭɱɟɬɟ ɉȾɋ ɧɚ ɜɧɭɬɪɟɧɧɟɣ ɢ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɵɯ ɬɨɱɤɚɯ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ. Ɉɩɟɪɚɬɨɪ Qˆ 1 Pˆ ɩɪɨɟɤɬɢɪɭɟɬ ɫɨɫɬɨɹɧɢɟ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɨɛɥɚɫɬɶ ɤɨɧɮɢɝɭɪɚɰɢɨɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ (ɤɥɚɫɬɟɪɧɭɸ ɨɛɥɚɫɬɶ), ɝɞɟ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɭɠɟ ɫɮɨɪɦɢɪɨɜɚɧɵ. ȼɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ˆ J S M (8) ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫ * J E J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ QȌ V V V ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ [20] ɮɨɪɦɭɥɨɣ Qˆ < J S M W G JM W ,W ' Qˆ H E J Pˆ < J S M W ' , (12)
V
14
A
V
V
ɝɞɟ G JM W ,W ' – ɦɧɨɝɨɱɚɫɬɢɱɧɚɹ ɮɭɧɤɰɢɹ Ƚɪɢɧɚ ɜ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ, ɤɨɬɨɪɚɹ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ: ˆ JM W ,W ' G W W ' . Qˆ H A EVJ QG (13)
ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ Qˆ
^
`
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɨɪɛɢɬɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ L , ɡɚɜɢɫɢɬ ɨɬ ɬɟɥɟɫɧɨɝɨ ɭɝɥɚ : { T , M , ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R R1 R 2 ɜ ɥ. ɫ., ɩɪɢɱɟɦ R1 ɢ R 2 – ɤɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɨɜ ɬɹɠɟɫɬɢ ɮɪɚɝɦɟɧɬɨɜ ɫ JS M
ɦɚɫɫɨɜɵɦɢ ɱɢɫɥɚɦɢ A1 ɢ A2 ( A2 t A1 ); ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ
G JM W ,W '
GD iFD R FD R , !
(16)
ɝɞɟ ɢɧɞɟɤɫ R! ( R ) ɜɤɥɸɱɚɟɬ ɛɨɥɶɲɟɟ (ɦɟɧɶɲɟɟ) ɢɡ ɡɧɚɱɟɧɢɣ ɦɨɞɭɥɟɣ ɪɚɞɢɭɫɨɜ ɜɟɤɬɨɪɨɜ R ɢ R ' , ɜɯɨɞɹɳɢɯ ɜ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɥɧɨɝɨ ɧɚɛɨɪɚ W ɢ W ' ɤɨɨɪɞɢɧɚɬ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, FD ɢ GD – ɪɟɝɭɥɹɪɧɵɟ ɢ ɧɟɪɟɝɭɥɹɪɧɵɟ ɮɭɧɤɰɢɢ, ɧɨɪɦɢɪɨɜɚɧɧɵɟ ɧɚ G -ɮɭɧɤɰɢɸ ɩɨ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
15
UDJ S M fDJ S R UDJ S M gDJ S R , GD . (17) R R ȼ ɮɨɪɦɭɥɟ (17) ɪɚɞɢɚɥɶɧɵɟ ɮɨɪɦɮɚɤɬɨɪɵ fDJ S R ɢ gDJ S R ɹɜɥɹɸɬɫɹ ɪɟɲɟɧɢɹɦɢ ɪɚɞɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧɝɟɪɚ, ɨɩɢɫɵɜɚɸɳɟɝɨ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɷɧɟɪɝɢɟɣ FD
Qc
EVJ EVJ1 EVJ 2 : 1 2 § d 2 L L 1 · 2M kc2 ¸ fDJ S R 2 ɫ VDD R fDJ S R 0, ¨¨ 2 2 ¸ = R © dR ¹
(18)
ɝɞɟ =k c , (19) Mc = ɩɪɢɱɟɦ Xɫ – ɫɤɨɪɨɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ;
VD 'D '' R
2 M cQc
UDJ S'' M V UDJ S' M , kc
2
, Xc
M ɫ – ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ ɮɪɚɝɦɟɧɬɨɜ. Ɏɨɪɦɮɚɤɬɨɪɵ fDJ S R ɢ gDJ S R ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɟ ɚɫɢɦɩɬɨɬɢɤɢ ɩɪɢ R o f : LS § · (20) fDJ S R o sin ¨ kc R GDJ S ¸ , 2 © ¹ LS § · (21) gDJ S R o cos ¨ kc R GDJ S ¸ , 2 © ¹ ɝɞɟ GDJ S – ɩɨɬɟɧɰɢɚɥɶɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ. ˆ J S M ɦɨɞɵ ɞɟɥɟɧɢɹ q , Ɉɛɨɥɨɱɟɱɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ PȌ qK
ɨɩɢɫɵɜɚɸɳɟɣ ɩɪɟɞɪɚɡɪɵɜɧɭɸ ɤɨɧɮɢɝɭɪɚɰɢɸ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɜ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɮɨɪɦɢɪɭɸɬɫɹ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ, JS M ɩɟɪɟɯɨɞɢɬ ɜ ɮɭɧɤɰɢɸ Qˆ < qK , ɚɫɢɦɩɬɨɬɢɤɚ ɤɨɬɨɪɨɣ ɩɪɢ ɛɨɥɶɲɢɯ R ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ [10]: JS M Qˆ < qK o UDJ S M
ɝɞɟ
LS § · i ¨ kc R GDJ S ¸ 2 © ¹ e
JS * qK D
R
=Xc
,
(22)
JS * qK D – ɚɦɩɥɢɬɭɞɚ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ, ɨɩɪɟɞɟɥɹɟɦɚɹ
ɤɚɤ JS * qK D
f JS R HA 2S UD D R
JS M Pˆ < qK
.
(23)
ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɱɟɬɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧɚ JS * qK D ɨɬɥɢɱɧɚ ɨɬ ɧɭɥɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ:
16
1 L SS1S 2 .
ɉɪɢ
ɭɱɟɬɟ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɤɚɧɚɥɨɜɵɯ ɮɭɧɤɰɢɣ (14), ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɪɚɡɥɢɱɧɵɦ ɞɟɥɢɬɟɥɶɧɵɦ ɦɨɞɚɦ q ɢ ɡɧɚɱɟɧɢɹɦ ɩɪɨɟɤɰɢɣ K , ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɨɥɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ *VJ S ɩɪɢɧɢɦɚɟɬ ɜɢɞ: *VJ S
JS aKJ ¦ *VJ Sɫ ¦ * qKɫ ɫ
2
bVJ SqK
2
JS J ¦ *qK D aK
2
2
bVJ SqK .
(24)
D qK
ɫqK
Ⱦɥɹ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɨɟ ɩɪɢɛɥɢɠɟɧɢɟ, ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɬɨɦ, ɱɬɨ ɪɚɞɢɚɥɶɧɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɛɵɫɬɪɟɟ, ɱɟɦ ɢɯ ɭɝɥɨɜɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɢ ɜɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɩɪɢɦɟɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɞɨɥɠɧɵ ɜɵɩɨɥɧɹɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ. ȼɨ-ɩɟɪɜɵɯ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ Eckin Rsc ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Rsc ɞɥɹ ɜɫɟɯ ɨɬɤɪɵɬɵɯ ɤɚɧɚɥɨɜ c ɞɨɥɠɧɚ ɛɵɬɶ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɫɜɹɡɚɧɧɨɝɨ ɫɨ ɜɫɟɦɢ ɜɨɡɦɨɠɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ:
Eckin Rsc !!
= 2 L L 1
. (25) 2 2 M c Rsc ȼɵɩɨɥɧɟɧɢɟ ɞɚɧɧɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢɜɨɞɢɬ ɤ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ GDJ S ɨɬ ɜɟɥɢɱɢɧɵ L . ȼɨ-ɜɬɨɪɵɯ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ Eckin Rsc ɞɨɥɠɧɚ ɛɵɬɶ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɜɪɚɳɚɬɟɥɶɧɵɯ ɷɧɟɪɝɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ J i ɮɪɚɝɦɟɧɬɨɜ = 2 J i J i 1 (26) , 2 Ji ɝɞɟ J i – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ i -ɝɨ ɮɪɚɝɦɟɧɬɚ. ɗɬɨ ɭɫɥɨɜɢɟ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ Eckin Rsc !!
ɩɨɬɟɧɰɢɚɥɶɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɮɚɡɵ GDJ S ɧɟ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɫɩɢɧɨɜ J i ɢ ɫɭɦɦɚɪɧɨɝɨ ɫɩɢɧɚ F ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɇɚɤɨɧɟɰ, ɜɪɟɦɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ t0 ɞɨɥɠɧɨ ɛɵɬɶ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɩɟɪɢɨɞɨɜ ɜɪɚɳɟɧɢɹ tirot [21] ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ J i ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ 'Rc 2S J i t0 tirot , (27) =J i Xc ɝɞɟ 'Rc – ɨɛɥɚɫɬɶ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬ ɭɝɥɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɨɧɟɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɗɬɨ ɭɫɥɨɜɢɟ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɨ ɜɫɟɣ 17
ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫɨɜɩɚɞɚɸɬ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɤɨɝɞɚ Z Z1 Z2 . ɍɫɥɨɜɢɹ (25)–(27) ɪɟɚɥɢɡɭɸɬɫɹ ɞɥɹ ɞɟɥɟɧɢɹ ɚɤɬɢɧɢɞɧɵɯ ɹɞɟɪ ɩɪɢ Eckin ! 10 Ɇɷȼ, M c | 60mn , Rsc | 15 ɮɦ, 'Rc 5 ɮɦ ɢ ɦɚɤɫɢɦɚɥɶɧɵɯ ɡɧɚɱɟɧɢɹɯ L ɢ J i ɪɚɜɧɵɯ 30 ɢ 15 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɇɟɡɚɜɢɫɢɦɨɫɬɶ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ GDJ S ɨɬ L , J1 , J 2 , F ɩɪɢɜɨɞɢɬ ɤ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɫɨɫɬɨɹɧɢɣ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ L , J1 , J 2 , F ɜ ɚɦɩɥɢɬɭɞɚɯ ɍɊɎ ɞɟɥɟɧɢɹ ɫ ɮɢɤɫɢɪɨɜɚɧɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ V1K1V 2 K 2 . ɗɬɨɬ ɪɟɡɭɥɶɬɚɬ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɪɚɛɨɬɵ ȼ.Ɇ. ɋɬɪɭɬɢɧɫɤɨɝɨ, ɝɞɟ ɩɪɟɧɟɛɪɟɝɚɟɬɫɹ ɢɧɬɟɪɮɟɪɟɧɰɢɟɣ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɣ L . Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɧɨɪɦɢɪɨɜɚɧɧɨɟ ɧɚ ɟɞɢɧɢɰɭ ɍɊɎ ɞɜɨɣɧɨɝɨ JS dPMK : ɢɡ ɫɨɫɬɨɹɧɢɹ J S MK ɬɪɚɞɢɰɢɨɧɧɨ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɪɢ ɞɟɥɟɧɢɹ d: ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɮɨɪɦɭɥɵ (6), ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɭɧɢɜɟɪɫɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɞɥɹ ɜɫɟɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ cJ1J 2 FL . ȼ ɨɫɧɨɜɟ ɷɬɨɣ ɮɨɪɦɭɥɵ ɥɟɠɢɬ ɤɚɱɟɫɬɜɟɧɧɨɟ ɮɢɡɢɱɟɫɤɨɟ ɞɨɩɭɳɟɧɢɟ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɜɵɥɟɬɚɸɬ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɢɥɢ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ Z ' ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɍɊɎ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ. ɢɦɟɟɬ G -ɨɛɪɚɡɧɵɣ ɯɚɪɚɤɬɟɪ ɜɢɞɚ G ([ ' B 1) , ɝɞɟ T ' – ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɨɦ R ɢ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Z ' , ɚ [ ' ɮɭɧɤɰɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
G ([ ' B 1)
lm
Lm
l 0
L 0
¦ 2S Yl 0 ([ ' )YL0 ( r 1) ¦ 2L 1 S
cosT ' . ɍɤɚɡɚɧɧɵɟ G -
( 1) LYL 0 ([ ' ),
(28)
ɝɞɟ ɜɟɥɢɱɢɧɚ Lm ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɜ ɩɪɟɞɟɥɟ Lm o f . Ɏɨɪɦɭɥɚ (28) ɨɬɪɚɠɚɟɬ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɦɟɠɞɭ ɨɪɛɢɬɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ L ɢ ɭɝɥɨɦ ɜɵɥɟɬɚ ɱɚɫɬɢɰɵ T ' , ɢɡ ɤɨɬɨɪɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɡɚɞɚɧɢɟ ɬɨɱɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɵɥɟɬɚ ɱɚɫɬɢɰɵ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɩɪɢ ɩɨɥɧɨɣ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɜ ɡɧɚɱɟɧɢɹɯ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ L ɱɚɫɬɢɰɵ ( 0 d L d f ). ɉɨɫɤɨɥɶɤɭ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɹɞɟɪ ɦɨɝɭɬ ɩɨɹɜɢɬɶɫɹ ɬɨɥɶɤɨ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ ɫɩɢɧɨɜ J i ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɬɨ ɮɨɪɦɭɥɚ (6) ɦɨɠɟɬ ɢɦɟɬɶ ɥɢɲɶ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɮɨɪɦɭɥɚ (6) ɭɫɩɟɲɧɨ ɨɩɢɫɵɜɚɟɬ ɲɢɪɨɤɢɣ ɤɥɚɫɫ ɹɜɥɟɧɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɞɟɥɟɧɢɟɦ ɹɞɟɪ, ɱɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɟɟ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɢ. ɉɨɧɹɬɶ ɷɬɨɬ
18
ɪɟɡɭɥɶɬɚɬ ɦɨɠɧɨ, ɟɫɥɢ ɜɦɟɫɬɨ G ([ ' B 1) (28) ɞɥɹ ɨɩɢɫɚɧɢɹ ɍɊɎ ɜɨ ɜ. ɫ. ɢɫɩɨɥɶɡɨɜɚɬɶ ɪɚɡɦɚɡɚɧɧɵɟ G -ɮɭɧɤɰɢɢ ɜɢɞɚ 2S FL2 ([ ' ) : m
FL ([ ' ) { FL m
m
:' ¦ aL L 0
m
L YL0 [ ' ,
(29)
ɝɞɟ Lm ɩɪɢɧɢɦɚɟɬ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ, 2L +1 4 Lm L p L b(Lm ), (30) 4S ɩɪɢɱɟɦ ɮɚɤɬɨɪ p L ª1 SS1S 2 ( 1) L º / 2 ɭɱɢɬɵɜɚɟɬ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ¬ ¼ ɱɟɬɧɨɫɬɢ, 4 Lm L – ɮɭɧɤɰɢɹ ɏɟɜɢɫɚɣɞɚ, ɚ b(Lm ) – ɧɨɪɦɢɪɨɜɨɱɧɚɹ ɤɨɧɫɬɚɧɬɚ, ɪɚɜɧɚɹ aLm L =
1/ 2
° b(Lm ) ® ¯° L
½° 2L +1 (31) . 4 Lm L p 2 L ¾ 4S 0 ¿° ([ ' ) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɍɊɎ, ɨɬɥɢɱɧɵɦ ɨɬ ɧɭɥɹ ɜɧɭɬɪɢ
¦
Ɏɭɧɤɰɢɹ 2S FL2
m
ɤɨɧɭɫɚ ɫ ɨɫɶɸ, ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɞɨɥɶ ɨɫɢ Z ' ɢ ɪɚɫɬɜɨɪɨɦ ɭɝɥɚ 'T ' ɩɪɢ ɜɟɪɲɢɧɟ ɤɨɧɭɫɚ 'T ' | 1 L . Ⱦɥɹ ɩɪɢɛɥɢɠɟɧɧɨɣ ɫɩɪɚɜɟɞɥɢɜɨɫɬɢ ɮɨɪɦɭɥɵ m
(28) ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɜɟɥɢɱɢɧɚ 'T ' ɛɵɥɚ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ, ɱɬɨ ɨɡɧɚɱɚɟɬ ɩɨɹɜɥɟɧɢɟ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ Lm ɜ ɮɨɪɦɭɥɟ (29). ɉɪɢ ɭɱɟɬɟ ɤɨɧɟɱɧɵɯ ɡɧɚɱɟɧɢɣ Lm ɮɨɪɦɭɥɚ (6) ɞɥɹ ɧɨɪɦɢɪɨɜɚɧɧɨɝɨ ɧɚ ɟɞɢɧɢɰɭ ɍɊɎ ɞɟɥɟɧɢɹ (6) ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɤ ɜɢɞɭ: JS 2º 2 dPMK : 2J 1 u ª D J Ȧ 2 DJ ' Ȧ (32) MK M K « » FLm ([ )dZ. 2 d: 16S ¬ ¼ ȿɫɬɟɫɬɜɟɧɧɨ, ɱɬɨ ɮɨɪɦɭɥɚ (32) ɩɟɪɟɯɨɞɢɬ ɜ ɮɨɪɦɭɥɭ (6) ɩɪɢ Lm o f . Ⱦɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɩɨɥɭɱɟɧɢɹ ɮɨɪɦɭɥɵ (32) ɤɚɧɚɥɨɜɚɹ ɮɭɧɤɰɢɹ JS M UD (14) ɜ ɥ. ɫ. ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜɨ ɜ. ɫ. ɩɪɢ ɭɱɟɬɟ, ɱɬɨ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɮɪɚɝɦɟɧɬɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɢ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ȼɢɝɧɟɪɚ [2]. ɋ ɩɪɢɦɟɧɟɧɢɟɦ ɩɨɥɭɱɟɧɧɵɯ ɤɚɧɚɥɨɜɵɯ ɮɭɧɤɰɢɣ UDJ S M ɜɨ ɜ. ɫ. ɚɦɩɥɢɬɭɞɚ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ
³
ɲɢɪɢɧɵ
JS * qK D ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɩɪɨɢɡɜɟɞɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ Ʉɥɟɛɲɚ-
Ƚɨɪɞɚɧɚ ɧɚ ɢɧɬɟɝɪɚɥ ɩɟɪɟɤɪɵɬɢɹ AqKD : ' ɜɧɭɬɪɟɧɧɟɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ S ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ F qK ɫ ɜɧɭɬɪɟɧɧɢɦɢ ɜɨɥɧɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ ɮɪɚɝɦɟɧɬɨɜ
19
ɞɟɥɟɧɢɹ FVSi K ɢ ɪɚɞɢɚɥɶɧɵɦɢ ɮɨɪɦɮɚɤɬɨɪɚɦɢ fDJ S R . Ɍɨɝɞɚ ɡɚɜɢɫɢɦɨɫɬɶ ɚɦɩɥɢɬɭɞɵ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ
JS * qK D ɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ
ɦɨɦɟɧɬɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɧɬɟɝɪɚɥɨɦ ³ AqKD : ' YLK L : ' d : ' { BqKD LK L , ɝɞɟ ɫɮɟɪɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ YLK L : ' ɜɯɨɞɢɬ ɜ ɨɩɪɟɞɟɥɟɧɢɟ ɤɚɧɚɥɨɜɨɣ ɮɭɧɤɰɢɢ UDJ S M ɜɨ ɜ. ɫ. ɂɫɩɨɥɶɡɭɹ ɩɪɢɛɥɢɠɟɧɢɟ, ɱɬɨ ɞɥɹ ɜɫɟɯ ɤɚɧɚɥɨɜ ɞɟɥɟɧɢɹ ɫ ɍɊɎ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ. ɢɦɟɸɬ ɭɧɢɜɟɪɫɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ, ɩɪɢɛɥɢɠɟɧɧɨ ɨɩɢɫɵɜɚɟɦɵɣ ɪɚɡɦɚɡɚɧɧɨɣ G ɮɭɧɤɰɢɟɣ (29) ɜɟɥɢɱɢɧɭ BqKɫLK L ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ BqKcLK L
DqKc aLm L G K L ,0 . ɉɨɞɫɬɚɜɥɹɹ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ
ɚɦɩɥɢɬɭɞɵ
JS * qK D ɜ ɮɨɪɦɭɥɭ (22) ɢ ɩɪɨɜɨɞɹ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ L , J1 , J 2 , F
ɩɪɢ ɭɱɟɬɟ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɞɟɥɢɬɟɥɶɧɵɯ ɚɦɩɥɢɬɭɞ ɫ ɪɚɡɥɢɱɧɵɦɢ L , J1 , J 2 , F ɢ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ GDJ S ɨɬ ɭɤɚɡɚɧɧɵɯ ɤɜɚɧɬɨɜɵɯ ɱɢɫɟɥ, ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɚɫɢɦɩɬɨɬɢɤɭ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ JS M ȌVJ S M , ɨɩɪɟɞɟɥɹɟɦɭɸ ɚɫɢɦɩɬɨɬɢɤɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ Ȍ qK (22) ɦɨɞɵ ɞɟɥɟɧɢɹ q , ɤɚɤ ȌVJ S M o
¦
qKcL
1
J K
aKJ bVJ SqK
eikc R R
2J 1 ª J DMK Z FVS1K1 [1 FVS 2 K 2 [ 2 16S 2 ¬
^
S S J DM K Z FV K [1 FV 1 1
`a
[ 2 2 K2
Lm
L YL0 : '
JS * qKɫ
=X c
, (33)
ɝɞɟ ɚɦɩɥɢɬɭɞɚ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ
JS * qKɫ
e
iG ɫJ S
JS * qKɫ
.
ɂɫɩɨɥɶɡɭɹ ɮɭɧɤɰɢɸ (33) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɦɧɨɝɨɱɚɫɬɢɱɧɨɣ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ jVJ S M ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɜ ɥ. ɫ. ɢ ɩɪɨɢɡɜɨɞɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɷɬɨɣ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɩɨ ɭɝɥɚɦ ɗɣɥɟɪɚ Z ɢ ɩɨ ɜɧɭɬɪɟɧɧɢɦ ɤɨɨɪɞɢɧɚɬɚɦ [1 , [ 2 ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɫ ɭɱɟɬɨɦ ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɨɫɬɢ ɜɧɭɬɪɟɧɧɢɯ ɮɭɧɤɰɢɣ
FVS1K1 ɢ FVS 2 K 2 , ɦɨɠɧɨ
ɩɨɥɭɱɢɬɶ ɨɞɧɨɱɚɫɬɢɱɧɭɸ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɮɪɚɝɦɟɧɬɨɜ ɧɚɩɪɚɜɥɟɧɢɢ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɜ ɥ. ɫ. [10]:
20
jVJ S M R ɜ
jVJ S M R u¦ qc
1 R
2
2J 1 ª
J Z ¦ ³ dZ 16S 2 «¬ DMK
2 2 aKJ bVJ SqK
K
JS * qKɫ
=
2
2º 2 J DM K Z »FLm [ ' u ¼
(34) .
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɥɧɨɟ ɱɢɫɥɨ ɥɟɝɤɢɯ ɢ ɬɹɠɟɥɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɪɟɝɢɫɬɪɢɪɭɟɦɨɟ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɞɟɬɟɤɬɨɪɚɦɢ, ɡɚɩɨɥɧɹɸɳɢɦɢ 4S ɫɮɟɪɭ, ɜ ɤɚɧɚɥɟ ɫ , ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɢɧɬɟɝɪɚɥɨɦ ɨɬ jVJ S M R ɩɨ d: ' ɢ ɪɚɜɧɨ, ɤɚɤ ɢ ɫɥɟɞɨɜɚɥɨ ɨɠɢɞɚɬɶ, *VJ Sc = , ɝɞɟ *VJ Sc – ɞɟɥɢɬɟɥɶɧɚɹ ɲɢɪɢɧɚ ɪɨɞɢɬɟɥɶɫɤɨɝɨ ɹɞɪɚ ɜ ɤɚɧɚɥɟ ɫ . ɂɡ ɮɨɪɦɭɥɵ (34) ɫɥɟɞɭɟɬ, ɱɬɨ JS dPMK : ɜ ɥ. ɫ. ɜɵɪɚɠɚɟɬɫɹ ɧɨɪɦɢɪɨɜɚɧɧɨɟ ɧɚ ɟɞɢɧɢɰɭ ɍɊɎ ɞɟɥɟɧɢɹ d: ɮɨɪɦɭɥɨɣ (32). Ɇɟɯɚɧɢɡɦ ɝɟɧɟɪɚɰɢɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ȼ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ ɛɵɥɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɞɥɹ ɩɪɢɛɥɢɠɟɧɧɨɣ ɫɩɪɚɜɟɞɥɢɜɨɫɬɢ ɮɨɪɦɭɥɵ ɋɬɪɭɬɢɧɫɤɨɝɨ – Ȼɨɪɚ (6) ɧɟɨɛɯɨɞɢɦɨ ɩɨɹɜɥɟɧɢɟ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ L d Lm . ɇɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɢɡ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ J F L, (35) ɝɞɟ F J1 J 2 – ɫɭɦɦɚɪɧɵɣ ɫɩɢɧ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɫɥɟɞɭɟɬ, ɱɬɨ ɟɫɥɢ ɫɩɢɧ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ J ɩɪɢɧɢɦɚɟɬ ɦɚɥɵɟ ɡɧɚɱɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɜɟɥɢɱɢɧɨɣ Lm , ɬɨ ɜɨɡɧɢɤɚɟɬ ɩɪɢɛɥɢɠɟɧɧɨɟ ɪɚɜɟɧɫɬɜɨ F L . ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɪɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ L ɫɭɦɦɚɪɧɵɣ ɫɩɢɧ F ɩɪɢɧɢɦɚɟɬ ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ. ȼɨɡɧɢɤɧɨɜɟɧɢɟ ɠɟ ɛɨɥɶɲɨɝɨ ɡɧɚɱɟɧɢɹ F ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ ɩɨɹɜɥɟɧɢɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ J i ( i 1,2 ). ɗɬɨ ɩɪɟɞɫɤɚɡɚɧɢɟ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɦɢ ɩɨ ɢɡɦɟɪɟɧɢɸ ɦɭɥɶɬɢɩɨɥɶɧɨɫɬɟɣ ɢ ɦɧɨɠɟɫɬɜɟɧɧɨɫɬɟɣ ɦɝɧɨɜɟɧɧɵɯ J -ɤɜɚɧɬɨɜ, ɢɫɩɭɫɤɚɟɦɵɯ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ, ɝɞɟ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ J i ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɨɰɟɧɢɜɚɸɬɫɹ ɤɚɤ J i | (6 8)= . Ʉɚɤ ɛɭɞɟɬ ɩɨɤɚɡɚɧɨ ɧɢɠɟ, ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ Lm ɨɤɚɡɵɜɚɸɬɫɹ ɪɚɜɧɵɦɢ Lm > 20 , ɨɬɤɭɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɫɩɢɧɵ ɮɪɚɝɦɟɧɬɨɜ J i , ɨɛɧɚɪɭɠɟɧɧɵɟ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ, ɞɨɥɠɧɵ ɛɵɬɶ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɩɚɪɚɥɥɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɭ ɢ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨɦɭ ɨɪɛɢɬɚɥɶɧɨɦɭ ɦɨɦɟɧɬɭ ɮɪɚɝɦɟɧɬɨɜ L . ɉɨɫɤɨɥɶɤɭ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ L ɧɚɩɪɚɜɥɟɧ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɵɥɟɬɚ ɮɪɚɝɦɟɧɬɨɜ, ɬɨ ɫɩɢɧɵ J1 ɢ J 2 ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ 21
ɬɚɤɠɟ ɫ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɶɸ ɧɚɩɪɚɜɥɟɧɵ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɜɵɥɟɬɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɱɬɨ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɪɟɡɭɥɶɬɚɬɚɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ. ȼɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ, ɨɬɤɭɞɚ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɦɨɝɭɬ ɩɨɹɜɢɬɶɫɹ ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɢ ɫɩɢɧɨɜ J i ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ? ȼ ɪɹɞɟ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɩɨɞɯɨɞɨɜ (Ɇ.Ɇ. ɏɨɮɮɦɚɧ, Ⱦɠ.Ɋ. ɇɢɤɫ) ɫɱɢɬɚɥɨɫɶ, ɱɬɨ ɩɪɢɱɢɧɨɣ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɹɜɥɹɟɬɫɹ ɞɢɧɚɦɢɱɟɫɤɚɹ ɝɟɧɟɪɚɰɢɹ ɤɨɥɥɟɤɬɢɜɧɵɯ ɜɨɡɛɭɠɞɟɧɢɣ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɩɨɹɜɥɟɧɢɟɦ ɤɨɥɥɟɤɬɢɜɧɵɯ ɜɪɚɳɚɬɟɥɶɧɵɯ ɬɨɤɨɜ ɜɧɭɬɪɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɜɛɥɢɡɢ ɬɨɱɤɢ ɪɚɡɪɵɜɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ. Ɉɞɧɚɤɨ ɪɚɫɫɱɢɬɚɧɧɵɟ ɜ ɷɬɢɯ ɪɚɛɨɬɚɯ ɡɧɚɱɟɧɢɹ ɷɧɟɪɝɢɢ ɧɭɥɟɜɵɯ ɤɨɥɟɛɚɧɢɣ ɩɨɞɨɛɧɨɝɨ ɬɢɩɚ ɨɤɚɡɵɜɚɸɬɫɹ ɨɱɟɧɶ ɛɨɥɶɲɢɦɢ ɢ ɫɭɳɟɫɬɜɟɧɧɨ ɩɪɟɜɨɫɯɨɞɹɳɢɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɨɰɟɧɤɢ ɷɧɟɪɝɢɢ ɜɨɡɛɭɠɞɟɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɬɨɱɤɟ ɪɚɡɪɵɜɚ. ȼ ɪɚɛɨɬɟ ɂ.ɇ. Ɇɢɯɚɣɥɨɜɚ ɢ ɉ. Ʉɜɟɧɬɢɧɚ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɦɟɯɚɧɢɡɦ «ɨɪɢɟɧɬɚɰɢɨɧɧɨɣ ɧɚɤɚɱɤɢ» ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɫɜɹɡɚɧɧɵɣ ɫ ɫɢɥɶɧɨɣ ɧɟɫɮɟɪɢɱɧɨɫɬɶɸ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ. Ɉɞɧɚɤɨ ɤɨɧɤɪɟɬɧɵɣ ɪɚɫɱɟɬ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɭɤɚɡɚɧɧɵɦ ɦɟɯɚɧɢɡɦɨɦ, ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɧɟ ɩɪɢɜɨɞɢɥɫɹ. ȼ ɪɚɛɨɬɟ Ɍ.Ɇ. ɒɧɟɣɞɟɦɚɧɚ ɢ ɞɪ. ɛɵɥ ɢɫɫɥɟɞɨɜɚɧ ɦɟɯɚɧɢɡɦ ɝɟɧɟɪɚɰɢɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɫɜɹɡɚɧɧɵɣ ɫ ɢɡɝɢɛɧɵɦɢ ɤɨɥɟɛɚɧɢɹɦɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɭ R , ɨɩɢɫɵɜɚɸɳɟɦɭ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ, ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɝɨ ɜ ɭɤɚɡɚɧɧɨɣ ɪɚɛɨɬɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɞɨɩɭɳɟɧɢɟɦ ɋɬɪɭɬɢɧɫɤɨɝɨ – Ȼɨɪɚ ɩɪɢɧɢɦɚɥɨɫɶ ɫɨɜɩɚɞɚɸɳɢɦ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ȼ ɪɚɛɨɬɟ [21] ɜ ɪɚɦɤɚɯ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɦɟɯɚɧɢɡɦ «ɧɚɤɚɱɤɢ» ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɢ ɫɩɢɧɨɜ J i ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɫɜɹɡɚɧɧɵɣ ɫ ɫɢɥɶɧɨɣ ɧɟɫɮɟɪɢɱɧɨɫɬɶɸ ɩɨɬɟɧɰɢɚɥɚ V R, Z1, Z2 ɤɭɥɨɧɨɜɫɤɨɝɨ ɢ ɹɞɟɪɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɍɤɚɡɚɧɧɵɣ ɩɨɬɟɧɰɢɚɥ ɫɬɪɨɢɬɫɹ ɜ ɦɨɞɟɥɢ ɞɜɨɣɧɨɝɨ ɮɨɥɞɢɧɝɚ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ i ɩɚɪɚɦɟɬɪɨɜ ɞɟɮɨɪɦɚɰɢɢ E ɢ ɭɝɥɨɜ ɗɣɥɟɪɚ Z , ɨɩɪɟɞɟɥɹɸɳɢɯ i
2
ɨɪɢɟɧɬɚɰɢɸ ɨɫɟɣ ɫɢɦɦɟɬɪɢɢ ɮɪɚɝɦɟɧɬɨɜ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɥ. ɫ. ȿɫɥɢ ɩɨɬɟɧɰɢɚɥ V R, Z1, Z2 ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɪɚɡɥɨɠɟɧɢɹ ɩɨ ɩɚɪɚɦɟɬɪɚɦ i ɞɟɮɨɪɦɚɰɢɢ E , ɬɨ ɧɟɫɮɟɪɢɱɟɫɤɢɟ ɱɥɟɧɵ ɷɬɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɜɨ ɜɫɟɯ 2
ɩɨɪɹɞɤɚɯ ɬɟɨɪɢɢ i N (i ) E 2 Y2 m :'R(i )
ɜɨɡɦɭɳɟɧɢɣ ɛɭɞɭɬ ɫɜɹɡɚɧɵ ɫ ɜɟɥɢɱɢɧɚɦɢ i E 2 ¦ Dm2*0 Zi Y2m : R , ɝɞɟ ɬɟɥɟɫɧɵɟ ɭɝɥɵ :R ɢ m
22
:'R(i ) , ɨɩɪɟɞɟɥɹɸɬ ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɜ ɥ. ɫ. ɢ ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ i -ɝɨ ɮɪɚɝɦɟɧɬɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɬɪɭɤɬɭɪɚ ɩɨɬɟɧɰɢɚɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɬɨɥɶɤɨ ɤ ɩɨɹɜɥɟɧɢɸ ɦɟɯɚɧɢɡɦɚ ɨɞɧɨɜɪɟɦɟɧɧɨɣ «ɨɪɢɟɧɬɚɰɢɨɧɧɨɣ ɧɚɤɚɱɤɢ» ɫɩɢɧɨɜ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɉɨɫɤɨɥɶɤɭ ɩɨɬɟɧɰɢɚɥ V R, Z1, Z2 ɹɜɥɹɟɬɫɹ ɫɤɚɥɹɪɨɦ, ɬɨ
ɧɟɫɮɟɪɢɱɟɫɤɢɟ ɱɥɟɧɵ ɷɬɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɟɥɢɱɢɧɚɦɢ N (i ) , ɧɟ ɦɟɧɹɸɬ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɣɫɹ ɫɢɫɬɟɦɵ J ɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ (35), ɧɨ ɦɨɝɭɬ ɢɡɦɟɧɢɬɶ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ L ɢ ɫɩɢɧɵ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ J i ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɹɦ ɢ ɪɚɜɧɵɟ ɩɨ ɚɛɫɨɥɸɬɧɵɦ ɡɧɚɱɟɧɢɹɦ ɜɟɥɢɱɢɧɵ. ɉɪɢ ɷɬɨɦ ɧɟɫɮɟɪɢɱɟɫɤɢɟ ɱɥɟɧɵ ɩɨɬɟɧɰɢɚɥɚ V R, Z1, Z2 ɢɡɦɟɧɹɸɬ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɵ 'L , ɢɦɟɸɳɢɟ ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɱɟɬɧɨɫɬɶ, ɩɨɫɤɨɥɶɤɭ ɜ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧ N (i ) ɜɯɨɞɹɬ ɫɮɟɪɢɱɟɫɤɢɟ ɮɭɧɤɰɢɢ ɫɨ ɡɧɚɱɟɧɢɟɦ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ L 2 . Ɉɞɧɨɜɪɟɦɟɧɧɨ ɜɟɥɢɱɢɧɵ N (i ) ɧɟ ɦɟɧɹɸɬ ɩɪɨɟɤɰɢɢ Ki ɫɩɢɧɚ ɮɪɚɝɦɟɧɬɚ ɞɟɥɟɧɢɹ J i ɧɚ ɟɝɨ ɨɫɶ ɫɢɦɦɟɬɪɢɢ, ɬɚɤ ɤɚɤ ɭɤɚɡɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɡɚɜɢɫɹɬ ɨɬ D – ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ Dm2*0 Zi ɫ ɧɭɥɟɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɪɨɟɤɰɢɣ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɜ ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɮɪɚɝɦɟɧɬɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ( Z Z1 Z2 ), ɩɨɬɟɧɰɢɚɥ V R, Z1, Z2 ɦɨɠɧɨ
ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ V R, Z , Z V R,T ' , ɝɞɟ T ' – ɭɝɨɥ ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɟɦ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɢ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ȼ ɩɨɬɟɧɰɢɚɥɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ V R,T ' ɢɡ-ɡɚ ɫɥɨɠɟɧɢɹ ɹɞɟɪɧɨɝɨ ɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɩɨɹɜɥɹɟɬɫɹ ɤɭɥɨɧɨɜɫɤɢɣ ɛɚɪɶɟɪ ɩɪɢ ɡɧɚɱɟɧɢɹɯ 1 2 ɪɚɞɢɭɫɚ R T ' R 0 1 E Y T ' R 0 1 E Y T ' s , ɝɞɟ B
A1
2
20
A2
2
20
ɜɟɥɢɱɢɧɚ s ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɩɨɪɹɞɤɚ ɪɚɞɢɭɫɚ ɹɞɟɪɧɵɯ ɫɢɥ s | 2 ɮɦ, ɚ ɪɚɞɢɭɫ ɹɞɪɚ RA0i
1
1.4 Ai
3
ɮɦ. Ⱦɥɹ ɦɚɥɵɯ ɭɝɥɨɜ T ' ɜɟɥɢɱɢɧɚ ɦɚɤɫɢɦɭɦɚ
ɤɭɥɨɧɨɜɫɤɨɝɨ ɛɚɪɶɟɪɚ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ: 2
B T '
B 0
C T ' , 2
(36)
ɝɞɟ ɤɨɧɫɬɚɧɬɵ B 0 ɢ ɋ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɚɦɢ ɞɟɮɨɪɦɚɰɢɢ E 2 ɢ i
ɪɚɞɢɭɫɚɦɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ RA0i . ɍɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ ɞɥɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ. ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɞɥɹ ɦɚɥɵɯ ɭɝɥɨɜ T ' ɜ 23
ɨɤɪɟɫɬɧɨɫɬɢ ɦɚɤɫɢɦɭɦɚ ɤɭɥɨɧɨɜɫɤɨɝɨ ɛɚɪɶɟɪɚ (36) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ª º 2 2 C T ' =2 1 w § 1 w · w2 « = H » < H T ',M ' 0, (37) T' « 2 MR 2 T ' wT ' ©¨ wT ' ¹¸ 2 MR 2 T ' 2 w M ' 2 » 2 ¬ ¼ ɝɞɟ – ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ ɮɪɚɝɦɟɧɬɨɜ. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (37) ɨɩɢɫɵɜɚɟɬ ɤɨɥɟɛɚɧɢɹ ɧɚɩɪɚɜɥɟɧɢɹ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɩɨ ɭɝɥɚɦ T ' . ȼɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ < 0 T ',M ' ɨɫɧɨɜɧɨɝɨ ɤɨɥɟɛɚɬɟɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫ ɷɧɟɪɝɢɟɣ ɫɜɹɡɢ H 0 , ɹɜɥɹɸɳɚɹɫɹ ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ (37), ɨɬɥɢɱɧɚ ɨɬ ɧɭɥɹ ɜ ɭɡɤɨɦ ɞɢɚɩɚɡɨɧɟ ɭɝɥɨɜ ɦɟɠɞɭ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɵɥɟɬɚ ɮɪɚɝɦɟɧɬɨɜ ɢ ɢɦɟɟɬ ɜɢɞ: ª J T ' 2 º J », < 0 T ',M ' (38) exp « S 2 » «¬ ¼ MC R = ɩɪɢ ɝɞɟ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ J , ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɤɚɤ J R RB 0 ɞɥɹ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɹɞɟɪ-ɚɤɬɢɧɢɞɨɜ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɵɦ J 196 [21]. Ɋɚɡɥɨɠɟɧɢɟ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ < 0 T ',M ' ɜ ɪɹɞ ɩɨ ɲɚɪɨɜɵɦ ɮɭɧɤɰɢɹɦ < 0 T ',M ' ¦ aLYL 0 [ ' L
ɩɪɢɜɨɞɢɬ ɤ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ aL ɨɬ L , ɤɨɬɨɪɭɸ ɦɨɠɧɨ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɜɜɟɞɟɧɧɨɣ ɪɚɧɟɟ ɮɭɧɤɰɢɟɣ aLm L (30) ɫɨ ɡɧɚɱɟɧɢɟɦ Lm 2 J ~ 25 . ɍɤɚɡɚɧɧɨɟ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ Lm ɩɨɞɬɜɟɪɠɞɚɟɬ ɩɨɥɭɱɟɧɧɨɟ ɜɵɲɟ ɡɚɤɥɸɱɟɧɢɟ ɨ ɩɨɹɜɥɟɧɢɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ J i ɢ ɢɯ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɩɚɪɚɥɥɟɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɞɪɭɝ ɤ ɞɪɭɝɭ ɢ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɬɧɨɫɢɬɟɥɶɧɨɦɭ ɨɪɛɢɬɚɥɶɧɨɦɭ ɦɨɦɟɧɬɭ L . ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɨ «ɯɨɥɨɞɧɨɫɬɢ» ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ Ʉɚɤ ɛɵɥɨ ɨɬɦɟɱɟɧɨ ɜɵɲɟ, ɚɧɢɡɨɬɪɨɩɢɢ, Ɋ-ɱɟɬɧɵɟ, Ɋ-ɧɟɱɟɬɧɵɟ ɢ Ɍ-ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ ɜ ɍɊɎ ɞɟɥɟɧɢɹ ɜɨɡɧɢɤɚɸɬ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɡɧɚɱɟɧɢɹ ɩɪɨɟɤɰɢɢ K ɫɩɢɧɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ J ɜ ɬɨɱɤɟ ɪɚɡɪɵɜɚ ɹɞɪɚ ɪɚɫɩɪɟɞɟɥɟɧɵ ɧɟɨɞɧɨɪɨɞɧɨ. ɇɟɨɞɧɨɪɨɞɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ K ɜɨɡɦɨɠɧɚ ɬɨɥɶɤɨ ɩɪɢ ɫɨɯɪɚɧɟɧɢɢ ɩɪɨɟɤɰɢɣ K , ɨɬɨɛɪɚɧɧɵɯ ɉȾɋ, ɧɚ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɯ ɫɬɚɞɢɹɯ ɞɟɥɟɧɢɹ, ɩɪɟɞɲɟɫɬɜɭɸɳɢɯ ɪɚɡɪɵɜɭ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɢ ɜɵɡɵɜɚɸɳɢɯ ɩɟɪɟɯɨɞ ɷɬɨɝɨ ɹɞɪɚ ɜ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ. ȿɫɥɢ ɭɤɚɡɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɭɫɩɟɜɚɸɬ ɬɟɪɦɚɥɢɡɨɜɚɬɶɫɹ, ɬɨ ɞɥɹ ɧɢɯ ɜɨɡɧɢɤɚɟɬ ɷɮɮɟɤɬ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɭɫɢɥɟɧɢɹ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɩɪɢɜɨɞɹɳɢɣ ɤ ɪɚɜɧɨɦɟɪɧɨɦɭ ɫɬɚɬɢɫɬɢɱɟɫɤɨɦɭ ɫɦɟɲɢɜɚɧɢɸ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɩɪɨɟɤɰɢɣ K [21]. 24
Ɇɧɨɝɢɟ ɞɟɥɢɬɟɥɶɧɵɟ ɦɨɞɟɥɢ, ɪɚɡɭɦɧɨ ɨɩɢɫɵɜɚɸɳɢɟ ɦɚɫɫɨɜɵɟ ɢ ɡɚɪɹɞɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɩɪɢɜɨɞɹɬ ɤ ɩɪɟɞɫɬɚɜɥɟɧɢɸ, ɱɬɨ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ ɫɩɭɫɤɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ ɜɵɡɵɜɚɟɬ ɧɚɝɪɟɜɚɧɢɟ ɷɬɨɝɨ ɹɞɪɚ ɢ ɩɨɹɜɥɟɧɢɟ ɭ ɧɟɝɨ ɜɛɥɢɡɢ ɬɨɱɤɢ ɟɝɨ ɪɚɡɪɵɜɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ T | 1 Ɇɷȼ, ɤɨɬɨɪɨɣ ɞɥɹ ɹɞɟɪ ɫ ɚɬɨɦɧɵɦ ɜɟɫɨɦ A | 240 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ E * | 30 Ɇɷȼ [2]. ɉɪɢ ɫɬɨɥɶ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɜ ɞɟɥɹɳɟɦɫɹ ɹɞɪɟ ɩɨɹɜɥɹɸɬɫɹ ɫɥɨɠɧɵɟ ɦɧɨɝɨɤɜɚɡɢɱɚɫɬɢɱɧɵɟ ɫɨɫɬɨɹɧɢɹ ɫ ɛɨɥɶɲɨɣ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɶɸ, ɤɨɬɨɪɵɟ ɹɜɥɹɸɬɫɹ ɢɞɟɚɥɶɧɵɦ ɨɛɴɟɤɬɨɦ ɞɥɹ ɩɪɨɹɜɥɟɧɢɹ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. Ɋɚɜɧɨɦɟɪɧɨɟ ɫɬɚɬɢɫɬɢɱɟɫɤɨɟ ɫɦɟɲɢɜɚɧɢɟ ɩɪɨɟɤɰɢɣ K ɫɩɢɧɚ J ɧɚ ɨɫɶ ɫɢɦɦɟɬɪɢɢ ɹɞɪɚ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ Ʉɨɪɢɨɥɢɫɨɜɵɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ, ɞɥɹ ɩɨɞɨɛɧɵɯ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɟɝɨ ɪɚɡɪɵɜɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ ɪɚɛɨɬɟ [21], ɩɪɢɜɨɞɢɬ ɤ «ɡɚɛɵɜɚɧɢɸ» ɞɟɥɹɳɢɦɫɹ ɹɞɪɨɦ ɡɧɚɱɟɧɢɣ K , ɜɵɞɟɥɹɟɦɵɯ ɉȾɋ, ɢ ɤ ɩɨɥɧɨɦɭ ɢɫɱɟɡɧɨɜɟɧɢɸ ɥɸɛɨɝɨ ɪɨɞɚ ɚɧɢɡɨɬɪɨɩɢɣ, ɜɤɥɸɱɚɹ P -ɧɟɱɟɬɧɵɟ, P -ɱɟɬɧɵɟ ɢ T -ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ, ɜ ɍɊɎ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɉɨɫɤɨɥɶɤɭ ɩɨɞɨɛɧɵɟ ɚɧɢɡɨɬɪɨɩɢɢ ɞɥɹ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɞɟɥɟɧɢɹ, ɢɧɞɭɰɢɪɨɜɚɧɧɨɝɨ ɜ ɪɟɚɤɰɢɹɯ ɫ ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ, J -ɤɜɚɧɬɚɦɢ ɢ ɞɪɭɝɢɦɢ ɱɚɫɬɢɰɚɦɢ, ɧɚɞɟɠɧɨ ɭɫɬɚɧɨɜɥɟɧɵ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ [5í9], ɦɨɠɧɨ ɩɪɢɞɬɢ ɤ ɩɪɢɧɰɢɩɢɚɥɶɧɨɦɭ ɡɚɤɥɸɱɟɧɢɸ, ɱɬɨ ɞɟɥɹɳɚɹɫɹ ɫɢɫɬɟɦɚ ɨɫɬɚɟɬɫɹ «ɯɨɥɨɞɧɨɣ» ɧɚ ɜɫɟɯ ɫɬɚɞɢɹɯ ɞɟɥɟɧɢɹ, ɧɚɱɢɧɚɸɳɢɯɫɹ ɫɨ ɫɩɭɫɤɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ ɢ ɡɚɤɚɧɱɢɜɚɸɳɢɯɫɹ ɮɨɪɦɢɪɨɜɚɧɢɟɦ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ. ɗɬɨ ɫɪɚɡɭ ɩɪɢɜɨɞɢɬ ɤ ɩɪɟɞɫɬɚɜɥɟɧɢɸ ɨ ɬɨɦ, ɱɬɨ ɜ ɞɟɥɹɳɟɦɫɹ ɹɞɪɟ ɢɡ-ɡɚ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɯɚɪɚɤɬɟɪɚ ɟɝɨ ɤɨɥɥɟɤɬɢɜɧɨɝɨ ɞɟɮɨɪɦɚɰɢɨɧɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɝɭɬ ɜɨɡɛɭɠɞɚɬɶɫɹ ɬɨɥɶɤɨ «ɜɯɨɞɧɵɟ» ɫɨɫɬɨɹɧɢɹ, ɢɦɟɸɳɢɟ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɭɸ (ɦɚɥɨɤɜɚɡɢɱɚɫɬɢɱɧɭɸ) ɫɬɪɭɤɬɭɪɭ ɢ ɨɛɥɚɞɚɸɳɢɟ ɞɨɫɬɚɬɨɱɧɨ ɧɢɡɤɨɣ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɶɸ, ɤɨɬɨɪɵɟ ɧɟ ɭɫɩɟɜɚɸɬ ɡɚ ɜɪɟɦɹ ɩɪɨɬɟɤɚɧɢɹ ɷɬɨɣ ɫɬɚɞɢɢ ɬɪɚɧɫɮɨɪɦɢɪɨɜɚɬɶɫɹ ɜ ɫɥɨɠɧɵɟ (ɦɧɨɝɨɤɜɚɡɢɱɚɫɬɢɱɧɵɟ) ɫɨɫɬɨɹɧɢɹ, ɨɬɜɟɱɚɸɳɢɟ ɩɨɥɧɨɣ ɬɟɪɦɚɥɢɡɚɰɢɢ ɷɧɟɪɝɢɢ ɜɨɡɛɭɠɞɟɧɢɹ ɹɞɪɚ ɢ ɨɛɥɚɞɚɸɳɢɟ ɜɵɫɨɤɨɣ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɶɸ. Ⱦɥɹ ɭɤɚɡɚɧɧɵɯ «ɜɯɨɞɧɵɯ» ɫɨɫɬɨɹɧɢɣ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ Ʉɨɪɢɨɥɢɫɨɜɵɦ ɫɦɟɲɢɜɚɧɢɟɦ ɩɪɨɟɤɰɢɣ K ɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɷɬɢ ɩɪɨɟɤɰɢɢ ɞɥɹ ɭɤɚɡɚɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɤɚɤ ɢɧɬɟɝɪɚɥɵ ɞɜɢɠɟɧɢɹ. ȼɟɥɢɱɢɧɵ K ɞɥɹ ɚɧɚɥɢɡɢɪɭɟɦɵɯ «ɜɯɨɞɧɵɯ» ɫɨɫɬɨɹɧɢɣ ɛɭɞɭɬ ɫɨɜɩɚɞɚɬɶ ɫ ɜɟɥɢɱɢɧɚɦɢ K ɞɥɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɟɪɟɯɨɞɧɵɯ ɞɟɥɢɬɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɣ ɧɚ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɟ ɩɨɬɟɧɰɢɚɥɚ ɞɟɮɨɪɦɚɰɢɢ, ɩɨɫɤɨɥɶɤɭ ɮɨɪɦɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɫɨɯɪɚɧɹɟɬ ɚɤɫɢɚɥɶɧɭɸ ɫɢɦɦɟɬɪɢɸ. «ɏɨɥɨɞɧɨɫɬɶ» ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɦɨɦɟɧɬ ɟɝɨ ɪɚɡɪɵɜɚ ɢ «ɯɨɥɨɞɧɨɫɬɶ» ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɪɢɜɨɞɹɬ ɤ ɫɨɯɪɚɧɟɧɢɸ ɫɜɟɪɯɬɟɤɭɱɢɯ ɧɭɤɥɨɧ-ɧɭɤɥɨɧɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɜ ɞɟɥɹɳɟɦɫɹ ɹɞɪɟ ɢ ɮɪɚɝɦɟɧɬɚɯ ɞɟɥɟɧɢɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɚɥɶɮɚ- ɢ ɤɥɚɫɬɟɪɧɵɦ ɪɚɫɩɚɞɚɦɢ ɬɹɠɟɥɵɯ ɹɞɟɪ 25
ɦɨɠɧɨ ɨɠɢɞɚɬɶ, ɱɬɨ ɫ ɧɚɢɛɨɥɶɲɟɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɛɭɞɭɬ ɩɪɨɢɫɯɨɞɢɬɶ ɨɛɥɟɝɱɟɧɧɵɟ ɞɟɥɢɬɟɥɶɧɵɟ ɩɟɪɟɯɨɞɵ, ɞɥɹ ɤɨɬɨɪɵɯ ɩɟɪɜɢɱɧɵɟ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɮɨɪɦɢɪɭɸɬɫɹ ɛɟɡ ɪɚɡɪɵɜɚ ɤɭɩɟɪɨɜɫɤɢɯ ɩɚɪ ɧɭɤɥɨɧɨɜ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɩɪɟɞɪɚɡɪɵɜɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɉɪɢ ɷɬɨɦ ɨɛɦɟɧ ɧɭɤɥɨɧɚɦɢ ɦɟɠɞɭ ɧɚɱɚɥɶɧɵɦɢ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ ɫ ɧɚɢɛɨɥɶɲɟɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɛɭɞɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɩɭɬɟɦ ɜɡɚɢɦɧɨɣ ɩɟɪɟɞɚɱɢ ɧɟ ɨɬɞɟɥɶɧɵɯ ɧɭɤɥɨɧɨɜ, ɚ ɢɯ ɤɭɩɟɪɨɜɫɤɢɯ ɩɚɪ, ɱɬɨ ɢɦɟɟɬ ɨɩɪɟɞɟɥɟɧɧɭɸ ɚɧɚɥɨɝɢɸ ɫ ɷɮɮɟɤɬɨɦ Ⱦɠɨɡɟɮɫɨɧɚ ɞɥɹ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ. ɉɨɫɤɨɥɶɤɭ ɤɭɩɟɪɨɜɫɤɢɟ ɩɚɪɵ ɧɭɤɥɨɧɨɜ ɢɦɟɸɬ ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɱɟɬɧɨɫɬɶ ɢ ɪɚɜɧɵɟ ɧɭɥɸ ɩɪɨɟɤɰɢɢ ɢɯ ɩɨɥɧɵɯ ɫɩɢɧɨɜ ɧɚ ɨɫɶ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɬɨ ɞɥɹ ɨɛɥɟɝɱɟɧɧɵɯ ɞɟɥɢɬɟɥɶɧɵɯ ɩɟɪɟɯɨɞɨɜ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɨɪɛɢɬɚɥɶɧɵɟ ɦɨɦɟɧɬɵ L , ɱɟɬɧɨɫɬɢ S i ɢ ɩɪɨɟɤɰɢɢ Ki ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɞɨɥɠɧɵ ɢɦɟɬɶ ɡɧɚɱɟɧɢɹ, ɫɨɝɥɚɫɭɸɳɢɟɫɹ ɫ ɩɪɨɹɜɥɟɧɢɟɦ ɫɜɟɪɯɬɟɤɭɱɢɯ ɤɨɪɪɟɥɹɰɢɣ ɢ ɫ ɡɚɤɨɧɚɦɢ ɫɨɯɪɚɧɟɧɢɹ ɱɟɬɧɨɫɬɢ S ɢ ɩɪɨɟɤɰɢɢ K ɞɥɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. Ʉɚɤ ɢ ɜ ɫɥɭɱɚɟ D - ɢ ɤɥɚɫɬɟɪɧɨɝɨ ɪɚɫɩɚɞɨɜ ɹɞɟɪ, ɜɟɪɨɹɬɧɨɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɧɚɱɚɥɶɧɵɯ ɢ ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɪɢ ɪɚɡɪɵɜɟ ɨɞɧɨɣ ɤɭɩɟɪɨɜɫɤɨɣ ɩɚɪɵ ɜ ɩɪɟɞɪɚɡɪɵɜɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ (ɷɬɨɬ ɫɥɭɱɚɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɞɟɥɢɬɟɥɶɧɨɦɭ ɩɟɪɟɯɨɞɭ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɡɚɩɪɟɬɚ) ɞɨɥɠɧɵ ɛɵɬɶ ɭɦɟɧɶɲɟɧɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɥɹ ɨɛɥɟɝɱɟɧɧɨɝɨ ɞɟɥɢɬɟɥɶɧɨɝɨ ɩɟɪɟɯɨɞɚ. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɞɟɥɢɬɟɥɶɧɵɯ ɩɟɪɟɯɨɞɨɜ ɩɨ ɫɬɟɩɟɧɢ ɢɯ ɡɚɩɪɟɳɟɧɧɨɫɬɢ ɩɨɡɜɨɥɹɟɬ, ɩɨ-ɜɢɞɢɦɨɦɭ, ɨɛɴɹɫɧɢɬɶ ɱɟɬɧɨ-ɧɟɱɟɬɧɵɟ ɷɮɮɟɤɬɵ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɚɪɹɞɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɤɨɧɟɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɉɨɥɭɱɟɧɧɨɟ ɡɚɤɥɸɱɟɧɢɟ ɩɪɢɜɨɞɢɬ ɤ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɨ-ɧɨɜɨɦɭ ɜɡɝɥɹɧɭɬɶ ɧɚ ɮɢɡɢɤɭ ɩɪɨɰɟɫɫɚ ɞɟɥɟɧɢɹ ɢ ɧɚ ɫɜɹɡɶ ɤɜɚɧɬɨɜɵɯ ɢ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɟɥɹɳɟɣɫɹ ɫɢɫɬɟɦɵ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɫɬɚɞɢɣ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ.
3. Ɉɛɳɢɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ əɜɥɟɧɢɟ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ɫ ɜɵɥɟɬɨɦ D -ɱɚɫɬɢɰ ɜɩɟɪɜɵɟ ɧɚɛɥɸɞɚɥɨɫɶ ɜ 1943 ɝ., ɩɟɪɜɵɟ ɩɭɛɥɢɤɚɰɢɢ ɩɨɹɜɢɥɢɫɶ ɜ 1947 ɝ. ɏɨɬɹ ɜɟɪɨɹɬɧɨɫɬɶ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɧɟɜɟɥɢɤɚ (2–3 ɫɥɭɱɚɹ ɬɪɨɣɧɨɝɨ ɧɚ 1000 ɫɥɭɱɚɟɜ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ) ɡɚ ɩɪɨɲɟɞɲɢɟ ɝɨɞɵ ɛɵɥɨ ɧɚɤɨɩɥɟɧɨ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɜ ɨɫɧɨɜɧɨɦ ɞɥɹ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ 235U ɬɟɩɥɨɜɵɦɢ ɧɟɣɬɪɨɧɚɦɢ ɢ ɞɥɹ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ 244Cm ɢ 252ɋf, ɫɜɹɡɚɧɧɵɯ ɫ ɜɵɥɟɬɨɦ ɧɟ ɬɨɥɶɤɨ D -, ɧɨ ɢ ɛɨɥɟɟ ɬɹɠɟɥɵɯ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɪɨɞɭɤɬɨɜ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ɪɚɫɫɦɨɬɪɢɦ ɜ ɧɚɱɚɥɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɭɤɚɡɚɧɧɨɝɨ ɜɢɞɚ ɞɟɥɟɧɢɹ, ɩɪɢɜɟɞɟɧɧɵɟ, 26
ɧɚɩɪɢɦɟɪ, ɜ ɨɛɡɨɪɟ [22]. ȼ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɪɨɞɢɬɟɥɶɫɤɨɝɨ ɹɞɪɚ ɜɨɡɧɢɤɚɸɬ ɞɜɚ ɞɨɫɬɚɬɨɱɧɨ ɬɹɠɟɥɵɯ ɮɪɚɝɦɟɧɬɚ A1 , Z1 ɢ A2 , Z 2 ( A2 t A1 , Z 2 t Z1 ) ɢ ɬɪɟɬɶɹ ɥɟɝɤɚɹ ɱɚɫɬɢɰɚ ɫ ɚɬɨɦɧɵɦ ɜɟɫɨɦ A3 A1, A2 ɢ ɡɚɪɹɞɨɦ Z3 Z1, Z 2 . ȼɟɪɨɹɬɧɨɫɬɶ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɜɟɪɨɹɬɧɨɫɬɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɬɨɝɨ ɠɟ ɫɚɦɨɝɨ ɹɞɪɚ ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ d 4 103 , ɩɪɢɱɟɦ ɧɚɢɛɨɥɶɲɭɸ ɜɟɪɨɹɬɧɨɫɬɶ ɢɦɟɸɬ ɤɚɧɚɥɵ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɫ ɜɵɥɟɬɨɦ D -ɱɚɫɬɢɰ. Ɇɚɫɫɨɜɵɟ ɢ ɡɚɪɹɞɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɜɭɯ ɬɹɠɟɥɵɯ ɮɪɚɝɦɟɧɬɨɜ A1 , Z1 ɢ A2 , Z 2 ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɢɦɟɸɬ ɜ ɚɤɬɢɧɢɞɧɨɣ ɨɛɥɚɫɬɢ ɡɚɦɟɬɧɭɸ ɚɫɢɦɦɟɬɪɢɸ ɢ ɛɥɢɡɤɢ ɤ ɚɧɚɥɨɝɢɱɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹɦ ɩɪɢ ɞɜɨɣɧɨɦ ɞɟɥɟɧɢɢ ɬɟɯ ɠɟ ɹɞɟɪ. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɭɦɦɚɪɧɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɨɬ ɦɚɫɫɵ ɮɪɚɝɦɟɧɬɨɜ ɜ ɞɜɨɣɧɨɦ ɢ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɩɪɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɸɬ, ɯɨɬɹ ɜɟɥɢɱɢɧɚ ɫɭɦɦɚɪɧɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɮɪɚɝɦɟɧɬɨɜ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɞɜɨɣɧɨɦ ɧɚ ɜɟɥɢɱɢɧɭ, ɩɪɢɦɟɪɧɨ ɪɚɜɧɭɸ ɩɨɥɨɜɢɧɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɥɟɝɤɨɣ ɱɚɫɬɢɰɵ. ɗɧɟɪɝɟɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɧɟ ɱɭɜɫɬɜɢɬɟɥɶɧɵ ɤɚɤ ɤ ɫɩɢɧɭ J ɢ ɬɢɩɭ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɬɚɤ ɢ ɤ ɯɚɪɚɤɬɟɪɭ ɩɪɨɰɟɫɫɚ, ɜɵɡɵɜɚɸɳɟɝɨ ɬɪɨɣɧɨɟ ɞɟɥɟɧɢɟ, ɢ ɯɨɪɨɲɨ ɚɩɩɪɨɤɫɢɦɢɪɭɸɬɫɹ ɲɢɪɨɤɢɦɢ ɝɚɭɫɫɨɜɫɤɢɦɢ ɮɭɧɤɰɢɹɦɢ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ ɷɧɟɪɝɢɢ E3m ɢ ɲɢɪɢɧɨɣ 'E3 . ȼ ɫɥɭɱɚɟ D -ɱɚɫɬɢɰ ɜɟɥɢɱɢɧɚ E3m ɞɥɹ ɜɫɟɯ ɚɤɬɢɧɢɞɨɜ ɨɤɚɡɵɜɚɟɬɫɹ ɛɥɢɡɤɨɣ ɤ 16 Ɇɷȼ, ɚ ɜɟɥɢɱɢɧɚ 'E3 ɥɟɠɢɬ ɜ ɭɡɤɨɦ ɢɧɬɟɪɜɚɥɟ ɨɬ 9,6 Ɇɷȼ ɞɨ 10,9 Ɇɷȼ, ɜɨɡɪɚɫɬɚɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɚɬɨɦɧɨɝɨ ɜɟɫɚ A ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɍɝɥɨɜɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɜɵɥɟɬɚ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɫɥɚɛɨ ɡɚɜɢɫɹɬ ɨɬ ɫɩɢɧɚ J ɢ ɬɢɩɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɢ ɯɚɪɚɤɬɟɪɚ ɩɪɨɰɟɫɫɚ, ɜɵɡɵɜɚɸɳɟɝɨ ɬɪɨɣɧɨɟ ɞɟɥɟɧɢɟ, ɢ ɨɩɢɫɵɜɚɸɬɫɹ ɲɢɪɨɤɢɦɢ ɝɚɭɫɫɨɜɫɤɢɦɢ ɮɭɧɤɰɢɹɦɢ, ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɭɝɥɚ T3' ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɜɵɥɟɬɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ ɞɟɥɟɧɢɹ, ɫ
ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ ɭɝɥɟ T3'
m
ɢ ɲɢɪɢɧɨɣ 'T3' . ɍɝɨɥ T3'
m
ɨɤɚɡɵɜɚɟɬɫɹ
ɛɥɢɡɤɢɦ ɤ 90D , ɱɬɨ ɭɤɚɡɵɜɚɟɬ ɧɚ ɷɤɜɚɬɨɪɢɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɪɨɠɞɟɧɢɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢɡ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɪɚɡɞɟɥɹɸɳɟɣ ɬɹɠɟɥɵɟ ɩɪɟɞɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɜ ɩɪɟɞɪɚɡɪɵɜɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɷɬɨɝɨ ɹɞɪɚ. ȼ ɫɥɭɱɚɟ D -ɱɚɫɬɢɰ ɲɢɪɢɧɚ 'T3' ɫɥɚɛɨ ɦɟɧɹɟɬɫɹ ɨɬ 19,3D ɞɨ 18,6D ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ
236
Uɤ
Cf, ɚ ɜɟɥɢɱɢɧɚ T3'
252
m
ɦɟɧɹɟɬɫɹ ɞɥɹ
252
Cf ɨɬ 90D ɩɪɢ G
1 ɞɨ
82D ɩɪɢ G 2 , ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɜɨɣ ɚɫɢɦɦɟɬɪɢɢ G ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ G A2 A1 . ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɪɚɫɱɟɬ ɭɝɥɨɜɵɯ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ, ɤɚɤ ɩɪɚɜɢɥɨ, ɩɪɨɜɨɞɢɬɫɹ ɜ ɪɚɦɤɚɯ ɦɟɬɨɞɚ ɬɪɚɟɤɬɨɪɧɵɯ ɪɚɫɱɟɬɨɜ, ɨɫɧɨɜɚɧɧɨɝɨ ɧɚ ɤɥɚɫɫɢɱɟɫɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɢ ɡɚɤɥɸɱɚɸɳɟɝɨɫɹ ɜ 27
ɩɨɫɬɪɨɟɧɢɢ ɧɚɱɚɥɶɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɫɢɫɬɟɦɵ ɮɪɚɝɦɟɧɬɨɜ ɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɜɨ ɜɧɟɲɧɟɣ ɨɛɥɚɫɬɢ, ɤɨɝɞɚ ɭɠɟ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɞɟɣɫɬɜɢɟɦ ɹɞɟɪɧɵɯ ɫɢɥ ɦɟɠɞɭ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɟɣ ɢ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ, ɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɪɚɡɥɟɬ ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɬɨɥɶɤɨ ɫɢɥ ɤɭɥɨɧɨɜɫɤɨɝɨ ɨɬɬɚɥɤɢɜɚɧɢɹ. ɇɚɱɚɥɶɧɚɹ ɤɨɧɮɢɝɭɪɚɰɢɹ (ɩɨɥɨɠɟɧɢɟ ɢ ɫɤɨɪɨɫɬɢ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ) ɩɨɞɛɢɪɚɟɬɫɹ ɬɚɤɨɣ, ɱɬɨɛɵ ɜ ɤɨɧɰɟ ɪɚɡɥɟɬɚ ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɪɚɫɱɟɬɧɵɟ ɜɟɥɢɱɢɧɵ ɫɨɜɩɚɥɢ ɫ ɧɚɛɥɸɞɚɟɦɵɦɢ: ɪɚɫɩɪɟɞɟɥɟɧɢɹɦɢ ɦɚɫɫ ɢ ɩɨɥɧɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɪɨɞɭɤɬɨɜ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ, ɭɝɥɨɜɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɪɚɛɨɬ ɩɨ ɬɪɚɟɤɬɨɪɧɵɦ ɪɚɫɱɟɬɚɦ ɪɚɡɭɦɧɨ ɨɩɢɫɵɜɚɸɬɫɹ ɭɝɥɨɜɵɟ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ, ɨɞɧɚɤɨ ɫɭɳɟɫɬɜɭɟɬ ɛɨɥɶɲɨɣ ɪɚɡɛɪɨɫ ɢɫɩɨɥɶɡɭɟɦɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɧɚɱɚɥɶɧɵɯ ɤɨɧɮɢɝɭɪɚɰɢɣ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜɵɛɨɪ ɧɚɱɚɥɶɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɞɥɹ ɬɪɚɟɤɬɨɪɧɵɯ ɪɚɫɱɟɬɨɜ ɞɨɥɠɟɧ ɨɩɢɪɚɬɶɫɹ ɧɚ ɮɢɡɢɤɭ ɪɨɠɞɟɧɢɹ ɢ ɞɜɢɠɟɧɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɜɨ ɜɧɭɬɪɟɧɧɟɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɫɭɳɟɫɬɜɟɧɧɵ ɹɞɟɪɧɵɟ ɫɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɷɬɨɣ ɱɚɫɬɢɰɵ ɫ ɨɫɬɨɜɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɉɪɢɦɟɪ ɬɚɤɨɣ ɫɢɬɭɚɰɢɢ ɪɟɚɥɢɡɨɜɚɧ ɜ ɪɚɛɨɬɟ [25], ɝɞɟ ɭɱɢɬɵɜɚɟɬɫɹ ɦɟɯɚɧɢɡɦ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɞɢɧɚɦɢɤɚ ɞɜɢɠɟɧɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɜɨ ɜɧɭɬɪɟɧɧɟɣ ɨɛɥɚɫɬɢ. Ȼɵɥɨ ɛɵ ɬɚɤɠɟ ɜɚɠɧɨ ɩɪɨɜɟɫɬɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɟ ɪɚɫɱɟɬɵ ɞɜɢɠɟɧɢɹ ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɜɨ ɜɧɟɲɧɟɣ ɨɛɥɚɫɬɢ, ɱɬɨ ɩɨɡɜɨɥɢɥɨ ɛɵ ɨɩɪɟɞɟɥɢɬɶ ɫɬɪɭɤɬɭɪɭ ɞɟɥɢɬɟɥɶɧɵɯ ɮɚɡ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɨɱɟɧɶ ɜɚɠɧɵɯ ɞɥɹ ɨɩɢɫɚɧɢɹ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɵɯ ɷɮɮɟɤɬɨɜ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ, ɧɚɩɪɢɦɟɪ, Ɍ-ɧɟɱɟɬɧɵɯ ɚɫɢɦɦɟɬɪɢɣ ɜ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɜɵɯɨɞɨɜ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɛɵɥɨ ɩɪɟɞɥɨɠɟɧɨ ɧɟɫɤɨɥɶɤɨ ɩɨɞɯɨɞɨɜ. ȼ ɪɚɦɤɚɯ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ Ɏɨɧɝɨɦ [4] ɛɵɥɢ ɜɵɱɢɫɥɟɧɵ ɜɟɪɨɹɬɧɨɫɬɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɫ ɜɵɥɟɬɨɦ D -ɱɚɫɬɢɰ. ȼ ɫɥɭɱɚɟ ɞɟɥɟɧɢɹ 235U ɬɟɩɥɨɜɵɦɢ ɧɟɣɬɪɨɧɚɦɢ, ɩɨɥɭɱɟɧɧɨɟ ɜ ɪɚɛɨɬɟ [4] ɡɧɚɱɟɧɢɟ ɨɬɧɨɲɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɤ ɞɜɨɣɧɨɦɭ ɯɨɪɨɲɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɞɥɹ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ 252 Cf ɡɧɚɱɟɧɢɟ ɷɬɨɝɨ ɨɬɧɨɲɟɧɢɹ ɩɪɢɦɟɪɧɨ ɜ 2 ɪɚɡɚ ɛɨɥɶɲɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɣ ɢɫɩɚɪɢɬɟɥɶɧɵɣ ɦɟɯɚɧɢɡɦ ɜɵɛɪɨɫɚ ɥɟɝɤɨɣ ɱɚɫɬɢɰɵ ɢɡ ɧɚɝɪɟɬɨɣ ɥɨɤɚɥɢɡɨɜɚɧɧɨɣ ɨɛɥɚɫɬɢ ɦɟɠɞɭ ɨɫɤɨɥɤɚɦɢ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɜ ɪɚɛɨɬɟ Ƚ.ȼ. ȼɚɥɶɫɤɨɝɨ. ɇɨ ɢ ɷɬɨɬ ɦɟɯɚɧɢɡɦ ɧɟ ɥɢɲɟɧ ɧɟɞɨɫɬɚɬɤɨɜ. Ⱥɜɬɨɪ ɪɚɛɨɬɵ ɨɬɦɟɱɚɟɬ, ɱɬɨ ɜɜɟɞɟɧɧɵɟ ɢɦ ɜɟɥɢɱɢɧɵ ɷɧɟɪɝɢɢ ɨɬɞɟɥɟɧɢɹ ɧɟɣɬɪɨɧɨɜ ɢ ɩɪɨɬɨɧɨɜ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɜɵɜɨɞɚ ɷɬɢɯ ɧɭɤɥɨɧɨɜ ɢɡ ɲɟɣɤɢ ɧɚ ɜɟɪɲɢɧɭ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ, ɨɤɚɡɵɜɚɸɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɢɦɢ ɡɧɚɱɟɧɢɣ, ɫɥɟɞɭɸɳɢɯ ɢɡ ɫɢɫɬɟɦɚɬɢɤɢ ɷɧɟɪɝɢɣ ɫɜɹɡɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ ɪɚɛɨɬ, ɜ ɤɨɬɨɪɵɯ ɜɵɥɟɬ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɨɩɢɫɵɜɚɟɬɫɹ ɢɫɩɚɪɢɬɟɥɶɧɵɦ ɦɟɯɚɧɢɡɦɨɦ, ɫɭɳɟɫɬɜɭɟɬ ɩɪɨɬɢɜɨɪɟɱɢɟ ɫ 28
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɮɚɤɬɨɦ – ɜɟɪɨɹɬɧɨɫɬɶ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɜɨɡɛɭɠɞɟɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ȼ ɪɚɛɨɬɟ ȼ.Ⱥ. Ɋɭɛɱɟɧɢ ɩɪɟɞɥɨɠɟɧɚ ɞɢɧɚɦɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɫɜɹɡɚɧɧɚɹ ɫ ɞɜɨɣɧɵɦ ɪɚɡɪɵɜɨɦ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ɗɬɢ ɪɚɡɪɵɜɵ ɫɬɚɬɢɫɬɢɱɟɫɤɢ ɧɟɡɚɜɢɫɢɦɵ ɢ ɫɥɟɞɭɸɬ ɨɞɢɧ ɡɚ ɞɪɭɝɢɦ ɡɚ ɜɪɟɦɟɧɚ ɩɨɪɹɞɤɚ ɩɟɪɢɨɞɨɜ ɨɞɧɨɱɚɫɬɢɱɧɨɝɨ ɞɜɢɠɟɧɢɹ. ɑɚɫɬɶ ɲɟɣɤɢ, ɡɚɤɥɸɱɟɧɧɚɹ ɦɟɠɞɭ ɞɜɭɦɹ ɪɚɡɪɵɜɚɦɢ, ɩɪɢɜɨɞɢɬ ɤ ɮɨɪɦɢɪɨɜɚɧɢɸ ɥɟɝɤɨɣ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ, ɫɨɩɪɨɜɨɠɞɚɸɳɟɣ ɞɟɥɟɧɢɟ. ɇɚ ɨɫɧɨɜɟ ɭɩɪɨɳɟɧɧɨɝɨ ɩɨɥɭɤɥɚɫɫɢɱɟɫɤɨɝɨ ɪɚɫɫɦɨɬɪɟɧɢɹ ɩɪɨɰɟɫɫɚ ɫɩɭɫɤɚ ɹɞɪɚ ɫ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ ɫ ɭɱɟɬɨɦ ɞɢɫɫɢɩɚɬɢɜɧɵɯ ɫɢɥ ɩɨɥɭɱɟɧɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɨɬɧɨɲɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɤ ɞɜɨɣɧɨɦɭ, ɤɨɬɨɪɨɟ ɪɚɡɭɦɧɨ ɨɩɢɫɵɜɚɟɬ ɨɩɵɬɧɵɟ ɞɚɧɧɵɟ. Ƚɥɚɜɧɨɣ ɠɟ ɩɪɨɛɥɟɦɨɣ ɨɩɢɫɚɧɧɵɯ ɜɵɲɟ ɪɚɛɨɬ ɹɜɥɹɟɬɫɹ ɩɨɥɭɱɚɟɦɚɹ ɜ ɧɢɯ ɬɟɦɩɟɪɚɬɭɪɚ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ T ~ 1 2 Ɇɷȼ, ɱɬɨ ɩɪɨɬɢɜɨɪɟɱɢɬ ɨɛɫɭɠɞɚɟɦɨɦɭ ɜɵɲɟ ɩɪɟɞɫɬɚɜɥɟɧɢɸ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɨ «ɯɨɥɨɞɧɨɫɬɢ» ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɬɨɱɤɟ ɪɚɡɪɵɜɚ. ɍɤɚɡɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɪɢɜɨɞɢɬ ɤ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜɜɟɞɟɧɢɹ ɢɧɨɝɨ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɫɩɚɪɢɬɟɥɶɧɵɦ, ɦɟɯɚɧɢɡɦɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ. ɉɨɞɨɛɧɵɟ ɦɟɯɚɧɢɡɦɵ ɛɵɥɢ ɩɪɟɞɥɨɠɟɧɵ ɜ ɪɚɛɨɬɚɯ ɇ. Ʉɚɪɠɚɧɚ, Ⱥ. ɋɚɧɞɭɥɟɫɤɭ, ȼ.ȼ. ɉɚɲɤɟɜɢɱɚ ɢ Ɉ. Ɍɚɧɢɦɭɪɵ ɢ Ɍ. Ɏɥɢɫɫɛɚɯɚ [25] ɞɥɹ ɫɥɭɱɚɹ, ɤɨɝɞɚ ɜ ɤɚɱɟɫɬɜɟ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɞɟɣɬɪɨɧ, ɬɪɢɬɨɧ ɢ D -ɱɚɫɬɢɰɚ, ɢ ɨɫɧɨɜɚɧ ɧɚ ɩɟɪɟɯɨɞɚɯ ɭɤɚɡɚɧɧɵɯ ɱɚɫɬɢɰ ɢɡ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɤɥɚɫɬɟɪɧɵɯ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɜɵɫɨɤɨɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɫɨɫɬɨɹɧɢɹ ɷɬɢɯ ɱɚɫɬɢɰ ɩɨɞ ɜɥɢɹɧɢɟɦ ɷɮɮɟɤɬɨɜ ɬɢɩɚ «ɜɫɬɪɹɫɤɢ», ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɦ ɯɚɪɚɤɬɟɪɨɦ ɤɨɥɥɟɤɬɢɜɧɨɝɨ ɞɟɮɨɪɦɚɰɢɨɧɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɫɬɚɞɢɢ ɟɝɨ ɫɩɭɫɤɚ ɫ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ.
4. Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ȼ ɪɚɛɨɬɚɯ [21, 19, 23] ɛɵɥɚ ɪɚɡɜɢɬɚ ɤɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɨɛɨɛɳɚɸɳɚɹ ɪɟɡɭɥɶɬɚɬɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ. Ⱦɢɧɚɦɢɤɚ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ
Ɋɚɫɫɦɨɬɪɢɦ ɫɥɭɱɚɣ ɞɟɥɟɧɢɹ ɚɬɨɦɧɨɝɨ ɹɞɪɚ ɫ ɦɚɫɫɨɜɵɦ ɱɢɫɥɨɦ A ɢ ɡɚɪɹɞɨɦ Z ɧɚ ɞɜɚ ɮɪɚɝɦɟɧɬɚ A1 , Z1 ; A2 , Z 2 ɢ ɬɪɟɬɶɸ ɱɚɫɬɢɰɭ A3 , Z3 ( A3 A1, A2 , Z3 Z1, Z 2 ). ȼɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ
ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ
ɫɨɨɬɧɨɲɟɧɢɟɦ Qc
EV K EV1K1 EV 2 K 2 EV 3 , ɝɞɟ EV K , EV1K1 , EV 2 K 2 ɢ 3
J
EV 3 – ɷɧɟɪɝɢɢ ɫɨɫɬɨɹɧɢɣ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɢ ɬɪɟɬɶɟɣ 3
ɱɚɫɬɢɰɵ. Ɋɚɞɢɚɥɶɧɚɹ ɪɟɝɭɥɹɪɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ \ Ll R,r , ɨɩɢɫɵɜɚɸɳɚɹ ɞɜɢɠɟɧɢɟ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ ɜ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɩɨɬɟɧɰɢɚɥɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ, ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ: ª = 2 1 d § 2 d · = 2 1 d § 2 d · = 2 L L 1 = 2l l 1 « ¨R ¸ ¨r ¸ 2 2 2M a R 2 2M br 2 (39) «¬ 2 M a R dR © dR ¹ 2 M b r dr © dr ¹ Qc @ \ Ll R,r 0, AA A1 A2 , M b m 3 a – ɩɪɢɜɟɞɟɧɧɵɟ ɦɚɫɫɵ A1 A2 Aa A3 ɩɪɨɞɭɤɬɨɜ; m – ɦɚɫɫɚ ɧɭɤɥɨɧɚ, L – ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, l – ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ. Ɉɬ ɤɨɨɪɞɢɧɚɬ R ɢ r ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɧɨɜɵɦ ɝɢɩɟɪɫɮɟɪɢɱɟɫɤɢɦ ɤɨɨɪɞɢɧɚɬɚɦ U ɢ H :
ɝɞɟ
Ma
mAa
m
R
Mɫ U sin H ; r Ma
Mɫ U cos H , Mb
(40)
ɝɞɟ ɭɝɨɥ H ɦɟɧɹɟɬɫɹ ɜ ɢɧɬɟɪɜɚɥɟ 0 d H d S , M ɫ M a M b . ɉɪɢ ɷɬɨɦ 2 ɮɚɡɨɜɵɣ ɨɛɴɟɦ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɤɚɤ R 2dR r 2dr =U 5 sin 2 H cos 2 H d U d H . (41) ȼ ɧɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ ɭɪɚɜɧɟɧɢɟ (39) ɩɪɢɧɢɦɚɟɬ ɜɢɞ
30
ª 1 d § 5 d · d § 2 1 2 d · L L 1 U 2 2 « 5 ¨ sin H cos H ¸ ¨ ¸ 2 d H ¹ U 2 sin 2 H ¬ U d U © d U ¹ U sin H cos H d H © l l 1
2º
(42)
2M ɫQc / = » \ Ll U ,H 0. ¼ Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (42) ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɮɨɪɦɟ P L, l , O , H RcL0 U , (43) \ Ll U ,H U 5 2 sin H cos H ɝɞɟ O 0, 1, 2, ... , L0 L l 2O 3 2 , ɚ ɮɭɧɤɰɢɢ P L, l , O , H ɜɵɪɚɠɚɸɬɫɹ ɱɟɪɟɡ ɩɨɥɢɧɨɦɵ əɤɨɛɢ ɢ ɨɛɪɚɡɭɸɬ ɩɨɥɧɵɣ ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɵɣ ɛɚɡɢɫ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɟɪɟɦɟɧɧɵɯ H . ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ ɮɭɧɤɰɢɹ RcL0 U
U 2 cos 2 H
ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ: ª d2 L0 L0 1 º kc2 » RcL0 U 0, « 2 2 ¼ U U d «¬ i k U L S / 2 ɢ ɢɦɟɟɬ ɚɫɢɦɩɬɨɬɢɤɭ ɩɪɢ U o f ɜɢɞɚ R U oe c 0 cL0
(44)
Xc , ɝɞɟ
kc2 2 MQc / = 2 , Xɫ =kc / M ɫ . ɉɨɫɤɨɥɶɤɭ ɜ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ V ɦɟɠɞɭ ɩɪɨɞɭɤɬɚɦɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɫɬɚɧɨɜɢɬɫɹ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɵɦ, ɜɫɟ ɮɪɚɝɦɟɧɬɵ ɞɜɢɠɭɬɫɹ ɫ ɮɢɤɫɢɪɨɜɚɧɧɵɦɢ Xa , ɬɨ ɢɡ ɨɬɧɨɫɢɬɟɥɶɧɵɦɢ ɢɦɩɭɥɶɫɚɦɢ ɢ ɫɤɨɪɨɫɬɹɦɢ, ɬɚɤ ɱɬɨ R r Xb ɫɨɨɬɧɨɲɟɧɢɹ (40) ɢ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɫɥɟɞɭɟɬ: M b Xa M aXa2 M bXb2 tgD Qc . , (45) M a Xb 2 2 Ɍɨɝɞɚ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɤɢɧɟɬɢɱɟɫɤɢɟ ɷɧɟɪɝɢɢ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ E1 , E2 , E3 ɜ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɨɛɥɚɫɬɢ ɱɟɪɟɡ ɭɝɨɥ H : E1 Qc
A1 A3 cos 2 H A2 sin 2 H A1 A2 A1 A2 A1 A2 A3
E2 Qc
A2 A3 cos 2 H A1 sin 2 H A1 A2 A1 A2 A1 A2 A3
A1 A2 A3 cos H sin H cosTrR
A1 A2
A1 A2 A3
A1 A2 A3 cos H sin H cosTrR
A1 A2
A1 A2 A3
; ;
(46)
2 E3 A1 A2 cos H , Qc A1 A2 A3 ɝɞɟ TrR – ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ r ɢ R . Ɍɨɝɞɚ ɭɝɨɥ H ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɤɚɤ:
31
H
arccos
E3 E3m ,
(47)
A1 A2 . A1 A2 A3 Ɋɚɫɫɦɨɬɪɢɦ ɜɨɩɪɨɫ ɨ ɩɪɢɦɟɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ (25)–(27), ɢɫɩɨɥɶɡɨɜɚɧɧɨɝɨ ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɤ ɬɪɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɹɞɟɪ. Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚ [22], ɩɨɹɜɥɟɧɢɟ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɷɧɟɪɝɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɧɚɥɨɝɢɱɧɨɣ ɷɧɟɪɝɢɟɣ ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɭ ɩɪɢɦɟɪɧɨ ɪɚɜɧɭɸ ɩɨɥɨɜɢɧɟ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ E3 . ȼɟɥɢɱɢɧɚ E3 ɞɥɹ ɜɫɟɯ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɦɟɬɧɨ ɦɟɧɶɲɟ ( E3 < 30 Ɇɷȼ) ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ( E1 E2 ! 200 Ɇɷȼ). Ⱦɥɹ ɜɵɩɨɥɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ (25)–(27) ɞɥɹ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɮɪɚɝɦɟɧɬɨɜ ɜ ɦɨɦɟɧɬ 3 ɪɚɡɪɵɜɚ ( R R ) ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ ɞɨɥɠɧɚ ɛɵɬɶ
ɝɞɟ E3m – ɦɚɤɫɢɦɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ E3m
Qc
sc
! 10 Ɇɷȼ. ɉɨɫɤɨɥɶɤɭ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ: Eckin Rsc 3
ɜɵɲɟ, ɷɧɟɪɝɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ 3 ɞɜɨɣɧɨɦ ɞɟɥɟɧɢɢ, ɬɨ ɷɬɨ ɭɫɥɨɜɢɟ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ, ɱɬɨ R ɞɥɹ ɬɪɨɣɧɨɝɨ sc
2 ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ ɞɟɥɟɧɢɹ ɛɨɥɶɲɟ Rsc ɚɞɢɚɛɚɬɢɱɧɨɫɬɢ (25) ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɨɩɭɳɟɧɢɟ, ɱɬɨ ɭɝɥɵ ɗɣɥɟɪɚ, ɨɩɪɟɞɟɥɹɸɳɢɟ ɨɪɢɟɧɬɚɰɢɸ ɨɫɟɣ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɫɨɜɩɚɞɚɸɬ ɜ ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ. ɉɨɫɤɨɥɶɤɭ ɚɬɨɦɧɵɣ ɜɟɫ A3 ɢ ɡɚɪɹɞ Z3 ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɚɬɨɦɧɵɯ ɜɟɫɨɜ Ai ɢ ɡɚɪɹɞɨɜ Z i ( i 1,2 ) ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɬɨ ɜɟɥɢɱɢɧɵ ɹɞɟɪɧɵɯ ɢ ɤɭɥɨɧɨɜɫɤɢɯ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ ɛɭɞɭɬ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɜɟɥɢɱɢɧ ɹɞɟɪɧɨɝɨ ɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɭɤɚɡɚɧɧɵɯ ɮɪɚɝɦɟɧɬɨɜ. ɉɨɷɬɨɦɭ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɩɪɚɤɬɢɱɟɫɤɢ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɛɭɞɟɬ ɫɨɯɪɚɧɹɬɶɫɹ ɦɟɯɚɧɢɡɦ ɧɚɤɚɱɤɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɢ ɫɩɢɧɨɜ J i ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɩɨɫɬɪɨɟɧɧɵɣ ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɗɬɨɬ ɜɵɜɨɞ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɪɟɡɭɥɶɬɚɬɚɦɢ, ɞɟɦɨɧɫɬɪɢɪɭɸɳɢɦɢ ɨɬɫɭɬɫɬɜɢɟ ɢɡɦɟɧɟɧɢɣ ɜ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɢɫɩɭɫɤɚɟɦɵɯ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ ɦɝɧɨɜɟɧɧɵɯ J -ɤɜɚɧɬɨɜ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɞɜɨɣɧɨɝɨ ɤ ɬɪɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɢ 32
ɨɬɫɭɬɫɬɜɢɟ ɤɨɪɪɟɥɹɰɢɣ ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɜɵɥɟɬɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢ J -ɤɜɚɧɬɨɜ. əɞɟɪɧɵɣ ɢ ɤɭɥɨɧɨɜɫɤɢɣ ɩɨɬɟɧɰɢɚɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢ ɞɜɭɯ ɮɪɚɝɦɟɧɬɨɜ ɜ ɫɥɭɱɚɟ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ, ɩɨɦɢɦɨ ɫɮɟɪɢɱɟɫɤɢ ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɱɥɟɧɚ, ɫɨɞɟɪɠɚɬ ɤɜɚɞɪɭɩɨɥɶɧɵɣ ɢ ɞɢɩɨɥɶɧɵɣ ɱɥɟɧɵ, ɡɚɜɢɫɹɳɢɟ ɨɬ ɭɝɥɚ TrR ɦɟɠɞɭ ɪɚɞɢɭɫɚɦɢ-ɜɟɤɬɨɪɚɦɢ R ɢ r . ɉɨɷɬɨɦɭ ɷɬɢ ɩɨɬɟɧɰɢɚɥɵ ɧɟ ɜɥɢɹɸɬ ɧɚ ɫɩɢɧɵ ɮɪɚɝɦɟɧɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɧɟ ɦɨɝɭɬ ɦɟɧɹɬɶ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɨɪɛɢɬɚɥɶɧɵɟ ɦɨɦɟɧɬɵ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ L ɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ l ɧɚ ɜɟɥɢɱɢɧɵ 'L 'l , ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɢ ɪɚɜɧɵɟ ɩɨ ɚɛɫɨɥɸɬɧɵɦ ɡɧɚɱɟɧɢɹɦ. ɂɡɦɟɧɟɧɢɟ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɱɟɬɭ ɜɥɢɹɧɢɹ ɧɚ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɷɮɮɟɤɬɨɜ ɨɬɞɚɱɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɜɵɥɟɬɨɦ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ. ɉɨ ɚɧɚɥɨɝɢɢ ɫ ɞɜɨɣɧɵɦ ɞɟɥɟɧɢɟɦ ɜ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ, ɝɞɟ ɩɪɨɞɭɤɬɵ ɞɟɥɟɧɢɹ ɭɠɟ ɫɮɨɪɦɢɪɨɜɚɧɵ, ɦɨɠɧɨ ɜɜɟɫɬɢ ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ UDJ S M , ɩɪɟɞɫɬɚɜɥɹɟɦɵɟ ɜ ɜɢɞɟ [23]: ½° °° u UDJ S M [ ®®
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P l, l, O,H , sin H cos H ( i 1,2 ) – ɜɨɥɧɨɜɵɟ
Yl 0 TrR
ɬɪɨɣɧɨɝɨ
ɞɟɥɟɧɢɹ,
ɮɭɧɤɰɢɢ
ɨɩɢɫɵɜɚɟɦɵɟ
ɞɟɮɨɪɦɢɪɨɜɚɧɧɵɯ ɮɨɪɦɭɥɨɣ
(14),
ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɬɪɟɬɶɟɣ (ɥɟɝɤɨɣ) ɱɚɫɬɢɰɵ, ɤɨɬɨɪɚɹ, ɤɚɤ
ɩɪɚɜɢɥɨ, ɢɦɟɟɬ ɫɮɟɪɢɱɟɫɤɭɸ ɮɨɪɦɭ; ɮɢɝɭɪɧɵɟ ɫɤɨɛɤɢ ɨɛɨɡɧɚɱɚɸɬ ɜɟɤɬɨɪɧɭɸ ɫɜɹɡɶ ɦɨɦɟɧɬɨɜ; ɤɚɧɚɥɨɜɵɣ ɢɧɞɟɤɫ D ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ D cE Ll , c { S1V1S 2V 2S 3V 3 J 3 ɢ E J1J 2 J 0 j j3 j , J 0 , j3 – ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɫɩɢɧɵ, ɚ ɲɚɪɨɜɵɟ ɮɭɧɤɰɢɢ YLM L : R ɢ Yl 0 TrR ɨɩɢɫɵɜɚɸɬ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɨɪɛɢɬɚɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɢ ɭɝɥɨɜɨɟ ɞɜɢɠɟɧɢɟ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɜɟɤɬɨɪɭ R , ɩɪɢɱɟɦ TrR í ɭɝɨɥ ɦɟɠɞɭ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɚɦɢ r ɢ R . ɂɧɞɟɤɫɚɦɢ [1 , [ 2 , [3 ɨɛɨɡɧɚɱɟɧɵ ɩɨɥɧɵɟ ɧɚɛɨɪɵ ɜɧɭɬɪɟɧɧɢɯ ɤɨɨɪɞɢɧɚɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ ɜ ɢɯ ɫɨɛɫɬɜɟɧɧɵɯ ɜ. ɫ.. ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɮɨɪɦɭɥɵ (48) ɢɫɩɨɥɶɡɨɜɚɧ ɮɚɤɬ, ɱɬɨ ɢɡ-ɡɚ ɜɥɢɹɧɢɹ ɷɮɮɟɤɬɨɜ ɫɜɟɪɯɬɟɤɭɱɢɯ ɧɭɤɥɨɧ-ɧɭɤɥɨɧɧɵɯ ɤɨɪɪɟɥɹɰɢɣ D -ɱɚɫɬɢɰɚ ɫ ɧɚɢɛɨɥɶɲɟɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɮɨɪɦɢɪɭɟɬɫɹ ɜ ɞɟɥɹɳɟɦɫɹ ɹɞɪɟ ɜ ɫɨɫɬɨɹɧɢɢ ɫ l 0 ( Kl = 0). ɉɨɫɤɨɥɶɤɭ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɨɪɛɢɬɚɥɶɧɵɟ ɦɨɦɟɧɬɵ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ l , ɫɜɹɡɚɧɧɵɟ ɫ ɦɟɯɚɧɢɡɦɚɦɢ ɟɟ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɜɵɥɟɬɚ ɢɡ ɨɛɥɚɫɬɢ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɫ ɭɱɟɬɨɦ ɭɤɚɡɚɧɧɵɯ ɫɜɨɣɫɬɜ ɩɨɬɟɧɰɢɚɥɨɜ 33
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ, ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɷɮɮɟɤɬɨɦ ɧɚɤɚɱɤɢ ɢ ɢɦɟɸɳɢɯ ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ, ɜ ɮɨɪɦɭɥɟ (48) ɜ ɮɢɝɭɪɧɵɯ ɫɤɨɛɤɚɯ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɡɧɚɱɟɧɢɟ L , ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɞɜɨɣɧɨɦɭ ɞɟɥɟɧɢɸ ɹɞɟɪ, ɚ ɜ ɩɨɥɢɧɨɦɟ əɤɨɛɢ ɜ ɤɚɱɟɫɬɜɟ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ L ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɡɧɚɱɟɧɢɟ l , ɩɨɫɤɨɥɶɤɭ ɷɬɨ ɡɧɚɱɟɧɢɟ ɩɟɪɟɞɚɟɬɫɹ ɮɪɚɝɦɟɧɬɚɦɢ ɞɟɥɟɧɢɹ ɢɡ-ɡɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɟɣ. Ɍɨɝɞɚ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ
(49)
JS *VD ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɨɣ, Ⱥɦɩɥɢɬɭɞɚ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ ɚɧɚɥɨɝɢɱɧɨɣ ɮɨɪɦɭɥɟ (23) ɞɥɹ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɲɢɪɢɧɵ ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ: JS *VD
2S
JS J S M fD U U H Pˆ
D
U
(50)
,
2
ɝɞɟ GDJ S – ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɮɚɡɚ. Ɋɚɞɢɚɥɶɧɵɟ ɮɨɪɦɮɚɤɬɨɪɵ
fDJ S U ,
JS ɜɯɨɞɹɳɢɟ ɜ ɨɩɪɟɞɟɥɟɧɢɟ *VD ɢ ɧɨɪɦɢɪɨɜɚɧɧɵɟ ɧɚ G -ɮɭɧɤɰɢɸ ɩɨ ɷɧɟɪɝɢɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɪɚɜɧɟɧɢɸ ɜɢɞɚ (18) ɫ ɡɚɦɟɧɨɣ ɩɟɪɟɦɟɧɧɨɣ R ɧɚ U ɢ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ L ɧɚ L0 . Ɉɫɭɳɟɫɬɜɥɹɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɜɨ ɜ. ɫ. ɤɚɧɚɥɨɜɨɣ ɮɭɧɤɰɢɢ (48),
ɚɦɩɥɢɬɭɞɭ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ
JS * qK D
ɩɨ ɚɧɚɥɨɝɢɢ ɫ
ɞɜɨɣɧɵɦ ɞɟɥɟɧɢɟɦ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɱɟɪɟɡ ɩɪɨɢɡɜɟɞɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ Ʉɥɟɛɲɚ-Ƚɨɪɞɚɧɚ ɧɚ ɢɧɬɟɝɪɚɥ ɩɟɪɟɤɪɵɬɢɹ AqKD ɜɧɭɬɪɟɧɧɟɣ ɮɭɧɤɰɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ F qK ɫ ɜɧɭɬɪɟɧɧɢɦɢ ɜɨɥɧɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ ɮɪɚɝɦɟɧɬɨɜ J S
ɞɟɥɟɧɢɹ FV i K , ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ
fDJ S U . Ɂɚɜɢɫɢɦɨɫɬɶ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ ɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ L ɢ ɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ l ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ
JS * qK D ~ acl O aLm L AqKc .
Ɍɨɝɞɚ,
ɩɨɞɫɬɚɜɥɹɹ
ɜɵɪɚɠɟɧɢɟ
ɞɥɹ
ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ ɲɢɪɢɧɵ ɜ ɮɨɪɦɭɥɭ (49) ɢ ɩɪɨɜɨɞɹ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ J1 , J 2 , J 0 , j , j3 ɚɫɢɦɩɬɨɬɢɤɚ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ȌVJ S M , ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ 34
ȌVJ S M o
2J 1 ª J Z F [ F [ < J 3S 3 [ ' ...` u D 2 ¬ MK V1K1 1 V 2 K 2 2 V 3 K3 3 qKcl O 16S
^
¦
uaKJ bVJ SqK FLm
eikc U
* qKc
Qq TrR ,H sin H cos HU 5 2 : R'
=Xc
(51)
,
K K1 K 2 , [3' – ɜɧɭɬɪɟɧɧɹɹ ɤɨɨɪɞɢɧɚɬɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɜɨ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, Qq TrR , H ¦ acl OYl 0 TrR P l , l , O , H , ɝɞɟ
ɝɞɟ K3 ɜ. ɫ.
lO
ɤɨɷɮɮɢɰɢɟɧɬɵ acl O , ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɤɨɦɩɥɟɤɫɧɵɟ ɢ ɜɤɥɸɱɚɸɳɢɟ ɞɟɥɢɬɟɥɶɧɭɸ ɮɚɡɭ G lSO , ɫɥɚɛɨ ɡɚɜɢɫɹɬ ɨɬ ɢɧɞɟɤɫɚ c ɞɥɹ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɵɯ ɤɚɧɚɥɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɢ ɨɩɪɟɞɟɥɹɸɬ ɮɨɪɦɢɪɨɜɚɧɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ. ɂɫɩɨɥɶɡɭɹ ɬɟɯɧɢɤɭ, ɪɚɡɜɢɬɭɸ ɞɥɹ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɮɨɪɦɭɥɵ (51), ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɦɧɨɝɨɱɚɫɬɢɱɧɭɸ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɩɪɨɞɭɤɬɨɜ ɞɟɥɟɧɢɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɝɢɩɟɪɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ ȡ . ɂɧɬɟɝɪɢɪɭɹ ɷɬɭ ɩɥɨɬɧɨɫɬɶ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɦɧɨɝɨɦɟɪɧɨɣ ɫɮɟɪɵ U 5 sin 2 H cos 2 H d H , ɩɨ ɧɚɛɨɪɭ ɜɧɭɬɪɟɧɧɢɯ ɤɨɨɪɞɢɧɚɬ [1 , [ 2 , [3 ɢ ɩɨ ɭɝɥɚɦ ɗɣɥɟɪɚ Z ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɩɨɥɧɭɸ ɜɟɪɨɹɬɧɨɫɬɶ ɪɟɝɢɫɬɪɚɰɢɢ ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɪɚɜɧɭɸ *VJ / = . ɉɪɢ ɷɬɨɦ ɧɨɪɦɢɪɨɜɚɧɧɨɟ ɧɚ ɟɞɢɧɢɰɭ ɭɝɥɨɜɨɟ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ
dPMJ : R , :r , H ɩɪɨɞɭɤɬɨɜ d : R d :r d H
ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɜ ɥ. ɫ. ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɤɚɤ 2 2º dPMJ : R , :r , H 1 2J 1 ª J *VJ SK dZ « DMK Ȧ DMJ K Ȧ » ¦ J 2 S d : R d :r d H *V K 16S ¬ ¼
³
2
u ¦ aLm L L
YL 0 :'R
¦^alOYl 0 TrR `P l , l , O , H
u
2
.
lO
(52) ɝɞɟ ɭɝɨɥ H ɫɜɹɡɚɧ ɫ ɷɧɟɪɝɢɟɣ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨɨɬɧɨɲɟɧɢɟɦ (47). Ɋɚɫɫɦɨɬɪɟɧɧɨɟ ɜ ɪɚɡɞɟɥɟ 1.2. ɡɚɤɥɸɱɟɧɢɟ ɨ «ɯɨɥɨɞɧɨɫɬɢ» ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɜɫɟɯ ɷɬɚɩɚɯ ɟɝɨ ɷɜɨɥɸɰɢɢ ɢ ɨ «ɯɨɥɨɞɧɨɫɬɢ» ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɩɨɥɧɨɫɬɶɸ ɫɨɯɪɚɧɹɟɬɫɹ ɢ ɜ ɫɥɭɱɚɟ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ [23]. ɗɬɨ ɡɚɤɥɸɱɟɧɢɟ ɨ ɯɨɥɨɞɧɨɫɬɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɩɪɢɜɨɞɢɬ ɤ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜɜɟɞɟɧɢɹ ɢɧɨɝɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɫɩɚɪɢɬɟɥɶɧɵɦ ɦɟɯɚɧɢɡɦɨɦ ɮɨɪɦɢɪɨɜɚɧɢɹ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ. ɉɨɞɨɛɧɵɣ ɦɟɯɚɧɢɡɦ, ɪɚɫɫɦɨɬɪɟɧɧɵɣ ɜɵɲɟ, ɨɛɨɛɳɚɟɬɫɹ ɜ ɪɚɦɤɚɯ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ɧɚ ɫɥɭɱɚɣ ɩɨɹɜɥɟɧɢɹ ɜ ɬɪɨɣɧɨɦ 35
ɞɟɥɟɧɢɢ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ, ɨɬɥɢɱɧɵɯ ɩɨ ɫɜɨɟɣ ɫɬɪɭɤɬɭɪɟ ɨɬ ɞɟɣɬɪɨɧɨɜ, ɬɪɢɬɨɧɨɜ ɢ D -ɱɚɫɬɢɰ. ɉɪɟɞɫɬɚɜɥɹɟɬɫɹ ɩɪɚɜɞɨɩɨɞɨɛɧɵɦ, ɱɬɨ ɧɭɤɥɨɧɵ, ɮɨɪɦɢɪɭɸɳɢɟ ɲɟɣɤɭ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɞɨɫɬɚɬɨɱɧɨ ɢɡɨɥɢɪɨɜɚɧɵ ɨɬ ɧɭɤɥɨɧɨɜ, ɮɨɪɦɢɪɭɸɳɢɯ ɩɪɟɞɮɪɚɝɦɟɧɬɵ ɞɟɥɟɧɢɹ, ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɟɠɞɭ ɤɨɬɨɪɵɦɢ ɨɛɪɚɡɭɟɬɫɹ ɞɚɧɧɚɹ ɲɟɣɤɚ. Ɍɨɝɞɚ, ɟɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɱɢɫɥɨ ɧɭɤɥɨɧɨɜ, ɮɨɪɦɢɪɭɸɳɢɯ ɲɟɣɤɭ, ɧɟ ɫɥɢɲɤɨɦ ɜɟɥɢɤɨ, ɭɤɚɡɚɧɧɭɸ ɲɟɣɤɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɚɧɚɥɨɝ ɥɟɝɤɨɝɨ ɹɞɪɚ, ɡɚɦɟɬɧɨ ɨɛɨɝɚɳɟɧɧɨɝɨ ɧɟɣɬɪɨɧɚɦɢ. ɋɩɟɤɬɪɨɫɤɨɩɢɱɟɫɤɢɟ ɮɚɤɬɨɪɵ ɞɟɣɬɪɨɧɧɵɯ, ɬɪɢɬɨɧɧɵɯ, D -ɱɚɫɬɢɱɧɵɯ ɢ ɛɨɥɟɟ ɬɹɠɟɥɵɯ ɤɥɚɫɬɟɪɨɜ ɜ ɥɟɝɤɢɯ ɹɞɪɚɯ ( A d 16 ) ɢɦɟɸɬ ɡɧɚɱɟɧɢɹ, ɧɟ ɫɢɥɶɧɨ ɨɬɥɢɱɚɸɳɢɟɫɹ ɨɬ ɟɞɢɧɢɰɵ, ɚ ɢɯ ɮɨɪɦɮɚɤɬɨɪɵ ɢɦɟɸɬ ɨɛɴɟɦɧɵɣ ɯɚɪɚɤɬɟɪ. ɉɨɷɬɨɦɭ ɜɟɪɨɹɬɧɨɫɬɢ ɨɛɪɚɡɨɜɚɧɢɹ ɬɪɟɬɶɢɯ (ɥɟɝɤɢɯ) ɱɚɫɬɢɰ ɫ ɚɬɨɦɧɵɦ ɜɟɫɨɦ A3 ɜ ɨɛɥɚɫɬɢ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɢ, ɡɚɦɟɬɧɨ ɭɦɟɧɶɲɚɹɫɶ ɥɢɲɶ ɩɪɢ ɩɟɪɟɯɨɞɟ ɤ ɬɪɟɬɶɢɦ ɱɚɫɬɢɰɚɦ ɫ A3 ! 20 , ɤɨɝɞɚ ɜ ɢɯ ɮɨɪɦɢɪɨɜɚɧɢɢ ɭɱɚɫɬɜɭɸɬ ɧɭɤɥɨɧɵ ɧɟ ɬɨɥɶɤɨ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɧɨ ɢ ɩɪɟɞɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ. ɉɪɢ ɷɬɨɦ ɫɩɟɤɬɪɨɫɤɨɩɢɱɟɫɤɢɟ ɮɚɤɬɨɪɵ ɞɥɹ ɞɨɫɬɚɬɨɱɧɨ ɥɟɝɤɢɯ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɟ ɬɨɥɶɤɨ ɜ ɨɫɧɨɜɧɵɯ, ɧɨ ɢ ɜ ɧɢɡɤɨɥɟɠɚɳɢɯ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹɯ, ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɨɞɧɨ- ɢ ɞɜɭɯ-ɧɭɤɥɨɧɧɵɦɢ ɩɟɪɟɯɨɞɚɦɢ ɜ ɞɚɧɧɵɯ ɱɚɫɬɢɰɚɯ, ɨɤɚɡɵɜɚɸɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɛɥɢɡɤɢɦɢ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɨɛɴɹɫɧɢɬɶ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɢɟ ɜɵɯɨɞɵ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɹɞɟɪ 5 He , 7 He ɢ 8 Li ɞɥɹ ɬɪɨɣɧɨɝɨ ɫɩɨɧɬɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɪɚ 252 Cf . ɉɨɫɤɨɥɶɤɭ ɞɟɥɹɳɟɟɫɹ ɹɞɪɨ ɧɚ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɯ ɭɱɚɫɬɤɚɯ ɟɝɨ ɫɩɭɫɤɚ ɫ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ ɨɤɚɡɵɜɚɟɬɫɹ ɯɨɥɨɞɧɵɦ, ɬɨ ɜɚɠɧɭɸ ɪɨɥɶ ɜ ɮɨɪɦɢɪɨɜɚɧɢɢ ɮɪɚɝɦɟɧɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɢ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɤɚɤ ɤɥɚɫɬɟɪɨɜ, ɨɛɪɚɡɨɜɚɧɧɵɯ ɢɡ ɧɭɤɥɨɧɨɜ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɞɨɥɠɧɵ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ, ɢɝɪɚɬɶ ɫɜɟɪɯɬɟɤɭɱɢɟ ɢ ɩɚɪɧɵɟ ɧɭɤɥɨɧɧɭɤɥɨɧɧɵɟ ɤɨɪɪɟɥɹɰɢɢ. ɍɱɟɬ ɭɤɚɡɚɧɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ ɱɟɬɧɨ-ɧɟɱɟɬɧɵɟ ɡɚɪɹɞɨɜɵɟ ɢ ɦɚɫɫɨɜɵɟ ɷɮɮɟɤɬɵ ɜ ɜɵɯɨɞɚɯ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɞɥɹ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ [22]. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɜɤɥɸɱɢɬɶ ɦɟɯɚɧɢɡɦ ɬɢɩɚ «ɜɫɬɪɹɫɤɢ», ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɧɟɚɞɢɚɛɚɬɢɱɟɫɤɢɦ ɯɚɪɚɤɬɟɪɨɦ ɢɡɦɟɧɟɧɢɹ ɤɨɥɥɟɤɬɢɜɧɵɯ ɞɟɮɨɪɦɚɰɢɨɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɡɚɤɥɸɱɢɬɟɥɶɧɵɯ ɫɬɚɞɢɹɯ ɟɝɨ ɫɩɭɫɤɚ ɫ ɜɧɟɲɧɟɣ ɫɟɞɥɨɜɨɣ ɬɨɱɤɢ, ɤɨɬɨɪɵɣ ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɯɨɞɚɦ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɢɡ ɤɥɚɫɬɟɪɧɵɯ ɫɨɫɬɨɹɧɢɣ ɲɟɣɤɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɜ ɫɨɫɬɨɹɧɢɹ ɫ ɷɧɟɪɝɢɹɦɢ, ɞɨɫɬɚɬɨɱɧɵɦɢ ɞɥɹ ɩɪɟɨɞɨɥɟɧɢɹ ɷɬɢɦɢ ɱɚɫɬɢɰɚɦɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɛɚɪɶɟɪɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɹɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɨɩɢɫɚɬɶ ɜɵɯɨɞɵ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ ɩɪɢ ɭɱɟɬɟ ɦɟɧɹɸɳɟɝɨɫɹ ɜɨ ɜɪɟɦɟɧɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɛɚɪɶɟɪɚ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɫɥɨɠɟɧɢɟɦ ɤɭɥɨɧɨɜɫɤɢɯ ɢ ɹɞɟɪɧɵɯ ɩɨɬɟɧɰɢɚɥɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɫ ɪɚɡɥɟɬɚɸɳɢɦɢɫɹ ɮɪɚɝɦɟɧɬɚɦɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ. 36
ɉɪɢ ɭɱɟɬɟ ɫɜɟɪɯɬɟɤɭɱɢɯ ɢ ɩɚɪɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɢ ɫɨɯɪɚɧɟɧɢɹ ɚɤɫɢɚɥɶɧɨɣ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɣɫɹ ɫɢɫɬɟɦɵ ɩɪɢ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɦɨɠɧɨ ɩɪɢɞɬɢ ɤ ɜɵɜɨɞɭ, ɱɬɨ ɜɟɞɭɳɢɦɢ ɡɧɚɱɟɧɢɹɦɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢ ɢɯ ɩɪɨɟɤɰɢɣ Kl ɧɚ ɨɫɶ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɛɭɞɭɬ ɡɧɚɱɟɧɢɹ, ɪɚɜɧɵɟ ɧɭɥɸ. ɋɬɪɭɤɬɭɪɚ ɧɟɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢ ɩɨɬɟɧɰɢɚɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫ ɮɪɚɝɦɟɧɬɚɦɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ [21] ɩɪɢɜɨɞɢɬ ɤ ɫɨɯɪɚɧɟɧɢɸ ɩɪɨɟɤɰɢɢ Kl 0 ɢ ɜɟɞɟɬ ɤ ɦɟɯɚɧɢɡɦɭ ɧɚɤɚɱɤɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ, ɨɛɭɫɥɨɜɥɟɧɧɨɦɭ ɮɨɤɭɫɢɪɭɸɳɢɦ ɯɚɪɚɤɬɟɪɨɦ ɭɤɚɡɚɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɢ ɪɨɞɫɬɜɟɧɧɨɦɭ ɦɟɯɚɧɢɡɦɭ ɧɚɤɚɱɤɢ [21] ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ L ɢ ɫɩɢɧɨɜ J i ( i 1, 2 ) ɮɪɚɝɦɟɧɬɨɜ ɤɚɤ ɞɜɨɣɧɨɝɨ, ɬɚɤ ɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɍɱɟɬ ɭɤɚɡɚɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɩɨɡɜɨɥɹɟɬ ɨɛɴɹɫɧɢɬɶ ɫɬɪɭɤɬɭɪɭ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ɢ ɩɪɢɪɨɞɭ P -ɧɟɱɟɬɧɵɯ, P -ɱɟɬɧɵɯ ɢ T -ɧɟɱɟɬɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ.
5. Ɍ-ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ ɋɨɜɫɟɦ ɧɟɞɚɜɧɨ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɫɟɱɟɧɢɣ ɪɟɚɤɰɢɢ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ n, f ɩɪɨɞɨɥɶɧɨ-ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɯɨɥɨɞɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɹɞɟɪ-ɦɢɲɟɧɟɣ 233U ɢ 235U (ɉ. Ⱦɠɟɣɫɢɧɝɟɪ ɢ ɞɪ.) ɛɵɥɢ ɨɛɧɚɪɭɠɟɧɵ T-ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɩɫɟɜɞɨɫɤɚɥɹɪɧɨɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɛɪɚɳɟɧɢɸ ɜɪɟɦɟɧɢ ɫɬɪɭɤɬɭɪɨɣ ɜɢɞɚ: ı >e LF , e3 @ , ɝɞɟ ı , e LF , e3 – ɟɞɢɧɢɱɧɵɟ ɜɟɤɬɨɪɵ, ɫɨɜɩɚɞɚɸɳɢɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɜɟɤɬɨɪɨɦ ɩɨɥɹɪɢɡɚɰɢɢ ɧɟɣɬɪɨɧɚ ɢ ɫ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɜɵɥɟɬɚ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ ɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ƚɟɨɦɟɬɪɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɜɵɛɢɪɚɥɚɫɶ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɟɤɬɨɪɨɜ e LF ɢ ı ɛɵɥɢ ɩɚɪɚɥɥɟɥɶɧɵ ɨɫɹɦ x ɢ y ɥ. ɫ. ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɚ ɜɟɤɬɨɪ e3 ɦɟɧɹɥɫɹ ɜ ɩɥɨɫɤɨɫɬɢ x, z . ȼ ɷɬɨɦ ɫɥɭɱɚɟ Ɍ-ɧɟɱɟɬɧɭɸ ɚɫɢɦɦɟɬɪɢɸ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ı >e LF u e3 @ ı y ª¬ e LF z u e3 x º¼ ı y e LF z cos M3 sin T3 , (53)
ɝɞɟ ɭɝɥɵ T3 ɢ M3 ɨɩɪɟɞɟɥɹɸɬ ɧɚɩɪɚɜɥɟɧɢɟ ɜɵɥɟɬɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɜ ɥ.ɫ. Ɉɬɫɸɞɚ ɜɢɞɧɨ, ɱɬɨ ɚɫɢɦɦɟɬɪɢɹ ɜɢɞɚ (53) ɢɦɟɟɬ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢ M3 0, S ; T3 S 2 ɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜɟɤɬɨɪɚ e3 ɜ ɩɥɨɫɤɨɫɬɢ x, z , ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɭɝɥɭ M3 0 , ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ T3 ɜ ɨɛɥɚɫɬɢ 60° d T3 d 120°, ɝɞɟ ɦɟɧɹɟɬɫɹ ɨɬ 0.87 ɞɨ 1. ȿɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɜɵɥɟɬɚ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ ɫ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ ɫɨɜɩɚɞɚɟɬ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ, ɬɨ ɢɡ ɮɨɪɦɭɥɵ (53) ɬɚɤɠɟ ɫɥɟɞɭɟɬ, ɱɬɨ Ɍ-ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ ɜ ɨɬɥɢɱɢɟ ɨɬ ɜɫɟɯ ɢɫɫɥɟɞɨɜɚɧɧɵɯ ɪɚɧɟɟ ɚɫɢɦɦɟɬɪɢɣ ɫɜɹɡɚɧɵ ɫ ɧɚɪɭɲɟɧɢɟɦ ɚɤɫɢɚɥɶɧɨɣ 37
ɫɢɦɦɟɬɪɢɢ ɞɟɥɟɧɢɹ, ɩɨɫɤɨɥɶɤɭ ɜ ɮɨɪɦɭɥɭ (53) ɜɯɨɞɢɬ ɚɡɢɦɭɬɚɥɶɧɵɣ ɭɝɨɥ M3 ɞɥɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ. Ʉɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɜ ɪɚɛɨɬɟ [24], ɟɞɢɧɫɬɜɟɧɧɵɦ ɢɫɬɨɱɧɢɤɨɦ ɧɚɪɭɲɟɧɢɹ ɚɤɫɢɚɥɶɧɨɣ ɫɢɦɦɟɬɪɢɢ ɜ ɩɪɨɰɟɫɫɟ ɞɟɥɟɧɢɹ ɹɜɥɹɟɬɫɹ Ʉɨɪɢɨɥɢɫɨɜɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ. ȼ ɷɤɫɩɟɪɢɦɟɧɬɟ ɨɩɪɟɞɟɥɹɥɢɫɶ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ D : V V D , (54) V V ɝɞɟ V ɢ V – ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɫɟɱɟɧɢɹ ɢɫɫɥɟɞɭɟɦɨɣ ɪɟɚɤɰɢɢ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɫɩɢɪɚɥɶɧɨɫɬɢ ɩɭɱɤɚ ɩɪɨɞɨɥɶɧɨɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɍɫɪɟɞɧɟɧɧɵɟ ɩɨ ɷɧɟɪɝɢɢ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ E3 ɤɨɷɮɮɢɰɢɟɧɬɵ ɚɫɢɦɦɟɬɪɢɢ ɨɤɚɡɚɥɢɫɶ ɞɨɫɬɚɬɨɱɧɨ ɛɥɢɡɤɢɦɢ ɞɥɹ Į-ɱɚɫɬɢɰ ɢ ɬɪɢɬɨɧɨɜ ɢ ɪɚɜɧɵɦɢ: DD 2.52 r 0.14 u 103 , Dt 1.99 r 0.63 u 103 (55) 233 ɞɥɹ ɹɞɪɚ-ɦɢɲɟɧɢ U ɢ DD 0.83 r 0.11 u 103 , Dt 0.60 r 0.41 u 10 3 (56) 235 ɞɥɹ ɹɞɪɚ-ɦɢɲɟɧɢ U. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬɵ D ɭɜɟɥɢɱɢɜɚɥɢɫɶ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ E3 ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ. ɇɚɣɞɟɧɧɵɟ ɞɥɹ ɞɜɭɯ ɬɢɩɨɜ ɬɪɟɬɶɢɯ ɱɚɫɬɢɰ ( D -ɱɚɫɬɢɰ ɢ ɬɪɢɬɨɧɨɜ) ɤɨɷɮɮɢɰɢɟɧɬɵ ɚɫɢɦɦɟɬɪɢɢ D ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɦɟɧɹɥɢɫɶ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɭɝɥɚ T3 ɜɵɥɟɬɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɜɵɥɟɬɚ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ. ɋɭɦɦɚɪɧɨɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɫɟɱɟɧɢɟ ( V V ), ɫɬɨɹɳɟɟ ɜ ɡɧɚɦɟɧɚɬɟɥɟ ɮɨɪɦɭɥɵ (54), ɫɨɜɩɚɞɚɟɬ ɫ ɭɞɜɨɟɧɧɵɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɫɟɱɟɧɢɟɦ ɪɟɚɤɰɢɢ n, f ɧɚ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɚɯ ɢ ɢɦɟɟɬ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɭɝɥɚ T3 . ɉɨɷɬɨɦɭ ɫɥɚɛɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɚɫɢɦɦɟɬɪɢɢ D ɨɬ ɭɝɥɚ T3 ɜɨɡɦɨɠɧɚ ɥɢɲɶ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɱɢɫɥɢɬɟɥɶ ɮɨɪɦɭɥɵ (53), ɨɩɪɟɞɟɥɹɟɦɵɣ ɪɚɡɧɨɫɬɶɸ ɫɟɱɟɧɢɣ ( V V ), ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɭɝɥɚ T3 , ɛɥɢɡɤɭɸ ɤ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɷɬɨɝɨ ɭɝɥɚ ɫɭɦɦɵ ɫɟɱɟɧɢɣ ( V V ). Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɫɟɱɟɧɢɣ V ɢ V ɨɬ ɭɝɥɚ T3 ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧɧɨɣ ɜɵɲɟ ɫɥɚɛɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɝɥɚ T3 Ɍ-ɧɟɱɟɬɧɨɣ ɤɨɪɪɟɥɹɰɢɢ (53). ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɟɱɟɧɢɹ V ɢ V ɜɯɨɞɢɬ ɛɨɥɟɟ ɫɥɨɠɧɚɹ ɩɨ ɫɬɪɭɤɬɭɪɟ Ɍ-ɧɟɱɟɬɧɚɹ ɤɨɪɪɟɥɹɰɢɹ, ɧɟɠɟɥɢ ɤɨɪɪɟɥɹɰɢɹ (53). ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɤɨɪɪɟɥɹɰɢɹ (53) ɩɪɚɜɢɥɶɧɨ ɨɬɪɚɠɚɟɬ ɫɜɨɣɫɬɜɚ ɫɟɱɟɧɢɣ V ɢ V ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɦɭ ɨɬɪɚɠɟɧɢɸ ɜɟɤɬɨɪɨɜ ı , e LF , e3 ɢ ɤ ɢɯ ɢɡɦɟɧɟɧɢɸ ɩɪɢ ɜɪɟɦɟɧɧɨɣ ɢɧɜɟɪɫɢɢ. ɂɫɫɥɟɞɭɟɦɚɹ ɤɨɪɪɟɥɹɰɢɹ (53) ɹɜɥɹɟɬɫɹ Ɍ-ɧɟɱɟɬɧɨɣ, ɩɨɫɤɨɥɶɤɭ ɨɧɚ ɦɟɧɹɟɬ ɡɧɚɤ ɩɪɢ ɨɬɪɚɠɟɧɢɢ ɜɪɟɦɟɧɢ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɨɧɚ ɹɜɥɹɟɬɫɹ Ɋ-ɱɟɬɧɨɣ, 38
ɩɨɫɤɨɥɶɤɭ ɧɟ ɦɟɧɹɟɬ ɡɧɚɤɚ ɩɪɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɦ ɨɬɪɚɠɟɧɢɢ ɜɟɤɬɨɪɨɜ e3 ɢ e LF (ɢɦɩɭɥɶɫɨɜ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɢ ɥɟɝɤɨɝɨ ɮɪɚɝɦɟɧɬɚ), ɫɜɹɡɚɧɧɵɯ ɫɨ ɫɜɨɣɫɬɜɚɦɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ȼ ɧɟɟ ɧɟ ɜɯɨɞɢɬ ɟɞɢɧɢɱɧɵɣ ɜɟɤɬɨɪ en , ɧɚɩɪɚɜɥɟɧɧɵɣ ɩɨ ɢɦɩɭɥɶɫɭ ɧɚɥɟɬɚɸɳɟɝɨ ɧɟɣɬɪɨɧɚ. ɗɬɢɦ ɨɧɚ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɜɵɡɵɜɚɸɳɢɯ ɩɪɚɜɨ-ɥɟɜɭɸ ɚɫɢɦɦɟɬɪɢɸ Ɍ-ɧɟɱɟɬɧɵɯ ɢ P-ɱɟɬɧɵɯ ɤɨɪɪɟɥɹɰɢɣ ı >en u e LF @ ɢ ı >en u e3 @ , ɢɫɫɥɟɞɨɜɚɧɧɵɯ ɪɚɧɟɟ ɜ ɞɟɥɟɧɢɢ ɹɞɟɪ ɩɨɩɟɪɟɱɧɨ-ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ ɢ ɜɨɡɧɢɤɚɸɳɢɯ ɢɡ-ɡɚ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɞɟɥɢɬɟɥɶɧɵɯ ɚɦɩɥɢɬɭɞ s- ɢ ɪ-ɧɟɣɬɪɨɧɧɵɯ ɪɟɡɨɧɚɧɫɨɜ ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɨɹɜɥɟɧɢɟ ɤɨɪɪɟɥɹɰɢɣ (53) ɫɜɹɡɚɧɨ ɫ ɚɧɚɥɨɝɢɱɧɨɣ ɢɧɬɟɪɮɟɪɟɧɰɢɟɣ ɞɟɥɢɬɟɥɶɧɵɯ ɚɦɩɥɢɬɭɞ ɧɟɣɬɪɨɧɧɵɯ ɪɟɡɨɧɚɧɫɨɜ ɨɞɧɨɣ ɱɟɬɧɨɫɬɢ. ɉɨɫɤɨɥɶɤɭ s-ɧɟɣɬɪɨɧɧɵɟ ɪɟɡɨɧɚɧɫɵ ɜɨɡɛɭɠɞɚɸɬɫɹ ɯɨɥɨɞɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ ɫ ɧɚɢɛɨɥɶɲɢɦɢ ɜɟɪɨɹɬɧɨɫɬɹɦɢ, ɬɨ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɤɨɪɪɟɥɹɰɢɢ (53) ɦɨɠɧɨ ɨɝɪɚɧɢɱɢɬɶɫɹ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɬɨɥɶɤɨ s-ɧɟɣɬɪɨɧɧɵɯ ɪɟɡɨɧɚɧɫɨɜ. ȼ ɪɚɛɨɬɟ [24] ɛɵɥɚ ɢɫɫɥɟɞɨɜɚɧɚ ɪɟɚɤɰɢɹ n, f ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɫ ɜɵɥɟɬɨɦ D -ɱɚɫɬɢɰ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɹɞɪɚ-ɦɢɲɟɧɢ ɫɨ ɫɩɢɧɨɦ I , ɟɝɨ ɩɪɨɟɤɰɢɟɣ M I ɧɚ ɨɫɶ Z ɥ. ɫ. ɢ ɱɟɬɧɨɫɬɶɸ S ɩɪɨɞɨɥɶɧɨ-ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɯɨɥɨɞɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ. ɗɬɚ ɪɟɚɤɰɢɹ ɩɪɨɬɟɤɚɟɬ ɱɟɪɟɡ ɮɨɪɦɢɪɨɜɚɧɢɟ s -ɧɟɣɬɪɨɧɧɵɯ ɪɟɡɨɧɚɧɫɨɜ ɫɨɫɬɚɜɧɨɝɨ ɹɞɪɚ, ɤɨɬɨɪɵɟ ɨɩɢɫɵɜɚɸɬɫɹ ɜɨɥɧɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ < sJ sS M (8). ȼ ɪɚɛɨɬɟ [24] ɛɵɥɚ ɜɜɟɞɟɧɚ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ AmI S M I , ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɭɩɟɪɩɨɡɢɰɢɟɣ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ s
ɧɟɣɬɪɨɧɧɵɯ ɪɟɡɨɧɚɧɫɨɜ, ɜɨɡɛɭɠɞɚɟɦɵɯ ɜ ɢɫɫɥɟɞɭɟɦɨɣ ɪɟɚɤɰɢɢ n, f :
AmI S M I s
¦ hsJ s CIJ1s MM I ms < sJ sS M , sJ s
(57)
2
ɝɞɟ hsJ s ɩɪɢɱɟɦ
Js * sn
E EsJ s i* sJ s 2
(58)
,
Js * sn – ɚɦɩɥɢɬɭɞɚ ɧɟɣɬɪɨɧɧɨɣ ɲɢɪɢɧɵ ɪɚɫɩɚɞɚ s -ɧɟɣɬɪɨɧɧɨɝɨ
ɪɟɡɨɧɚɧɫɚ, E – ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɞɟɥɹɳɟɣɫɹ ɫɢɫɬɟɦɵ ɜ ɫ. ɰ. ɦ., EsJ s ɢ * sJ s – ɷɧɟɪɝɢɹ ɢ ɩɨɥɧɚɹ ɲɢɪɢɧɚ ɪɚɫɩɚɞɚ s -ɧɟɣɬɪɨɧɧɨɝɨ ɪɟɡɨɧɚɧɫɚ. Ⱥɫɢɦɩɬɨɬɢɤɚ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɧɟɣɬɪɨɧɧɨɝɨ ɪɟɡɨɧɚɧɫɚ < sJ sS M ɜ ɤɥɚɫɬɟɪɧɨɣ ɨɛɥɚɫɬɢ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɤɚɤ (49) ɫ ɤɚɧɚɥɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ UDJ sS M , ɢɦɟɸɳɢɦɢ J S M ɫɬɪɭɤɬɭɪɭ (48), ɝɞɟ ɜɧɭɬɪɟɧɧɹɹ ɮɭɧɤɰɢɹ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ
ɡɚɦɟɧɹɟɬɫɹ ɧɚ ɜɧɭɬɪɟɧɧɸɸ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ < 3 [3 ɞɥɹ D -ɱɚɫɬɢɰɵ ɫɨ
39
ɫɩɢɧɨɦ J 3
0 . Ⱥɦɩɥɢɬɭɞɚ ɩɚɪɰɢɚɥɶɧɨɣ ɲɢɪɢɧɵ
J SM
* qKs D s
ɬɪɨɣɧɨɝɨ
ɞɟɥɟɧɢɹ ɜ ɤɚɧɚɥ D ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ, ɚɧɚɥɨɝɢɱɧɨɣ (50). ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɤɚɧɚɥɨɜɨɣ ɮɭɧɤɰɢɢ UDJ sS M , ɩɪɟɨɛɪɚɡɨɜɚɧɧɨɣ ɜ ɜ. ɫ., ɮɨɪɦɭɥɵ (50), ɩɪɢ ɭɱɟɬɟ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ
<
J sS M qK s as
ɦɨɞɵ ɞɟɥɟɧɢɹ q
ɩɪɢɧɢɦɚɟɬ ɜɢɞ [24], ɚɧɚɥɨɝɢɱɧɵɣ (51). ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ (51) ɫ ɭɱɟɬɨɦ (8) ɜ ɮɨɪɦɭɥɭ (57) ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɟ ɩɨɜɟɞɟɧɢɟ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ AmI S M I . ȼɜɨɞɹ ɦɧɨɝɨɦɟɪɧɵɣ ɨɩɟɪɚɬɨɪ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɱɚɫɬɢɰ s
jU ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ ȡ ɢ ɩɪɨɜɨɞɹ ɟɝɨ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɜɧɭɬɪɟɧɧɢɦ ɤɨɨɪɞɢɧɚɬɚɦ [1 , [ 2 , [3 ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɢ ɭɝɥɚɦ
ɗɣɥɟɪɚ Z , ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɟɥɢɱɢɧɭ B 0 : R , :r , H , ɫɜɹɡɚɧɧɭɸ ɫ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɫɟɱɟɧɢɟɦ d 3V d : R d :r d H ɪɟɚɤɰɢɢ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ ɧɚɥɟɬɚɸɳɟɝɨ ɧɟɣɬɪɨɧɚ kn ɫɨɨɬɧɨɲɟɧɢɟɦ d 3V d : R d :r d H
4S kn2
n, f
B 0 : R , :r , H
ɞɥɹ
(59)
ɢ ɨɩɪɟɞɟɥɹɟɦɭɸ ɤɚɤ B 0 : R , :r , H
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(60)
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s
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uP l ', l ', O ', H cos
sJ s ' J f qKs s ' s
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(62)
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(61)
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hsJ s hs 's ' u
Js Js' *J s Js' ¦ U MM ' ^ DMK s Z DM ' K s Z
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ɚ ɮɚɡɚ G sJ s s ' J s ' ɨɩɪɟɞɟɥɟɧɚ ɤɚɤ
40
(63)
Js * Js ' s s'
h h
J Js'
ȼ ɮɨɪɦɭɥɭ ɞɥɹ FK s s
J
G sJ s s ' J s '
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.
(64) J J
s s' , ɜɯɨɞɢɬ ɫɩɢɧɨɜɚɹ ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ U MM '
ɭɱɢɬɵɜɚɸɳɚɹ ɢɧɬɟɪɮɟɪɟɧɰɢɸ ɫɨɫɬɨɹɧɢɣ ɪɚɡɥɢɱɧɵɯ s -ɧɟɣɬɪɨɧɧɵɯ ɪɟɡɨɧɚɧɫɨɜ, ɢɦɟɸɳɢɯ, ɜ ɩɪɢɧɰɢɩɟ, ɪɚɡɥɢɱɧɵɟ ɫɩɢɧɵ [24]. ɉɨɞɨɛɧɚɹ ɢɧɬɟɪɮɟɪɟɧɰɢɹ ɹɜɥɹɟɬɫɹ ɭɧɢɤɚɥɶɧɵɦ ɫɜɨɣɫɬɜɨɦ ɹɜɥɟɧɢɹ ɞɟɥɟɧɢɹ ɹɞɟɪ. ɗɬɚ ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ ɞɥɹ ɫɥɭɱɚɹ ɡɚɯɜɚɬɚ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɦ ɹɞɪɨɦ-ɦɢɲɟɧɶɸ ɫɨ ɫɩɢɧɨɦ I ɢɦɟɟɬ ɫɬɪɭɤɬɭɪɭ: Js Js ' U MM '
ɝɞɟ ɮɭɧɤɰɢɹ U
1 2 M I M I' mm ' I
1 I JsM JsM C 1 C 1 U 2 ' , I M I m I M I m M I M I mm ' ' M I M I mm ' 2 2
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(65)
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ
ɩɥɨɬɧɨɫɬɢ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɹɞɪɚ-ɦɢɲɟɧɢ ɧɚ ɫɩɢɧɨɜɭɸ ɦɚɬɪɢɰɭ ɩɥɨɬɧɨɫɬɢ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ ɫ ɜɟɤɬɨɪɨɦ ɩɨɥɹɪɢɡɚɰɢɢ p n , ɧɚɩɪɚɜɥɟɧɧɵɦ ɩɨ ɨɫɢ y : 1 2 M I M I' mm ' I
1 ª º. (66) G ' G m, m ' pn V y m, m ' »¼ 2 2 I 1 M I , M I «¬ ɋɩɢɧɨɜɭɸ ɦɚɬɪɢɰɭ ɩɥɨɬɧɨɫɬɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ (65) ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɤ ɜɢɞɭ:
U
Js Js' U MM '
ipn 1 J M' J M' G J , J G M ,M ' A J s , J s ' ªC J s1' M 1 C J s1' M 1 º , (67) s ¬ s ¼ 2 2 I 1 s s ' 2 2 I 1 § · Js J 1 A J s , J s ' G Js , Js ' ¨ G J s , J s G J s , J! ¸ ¨ 2 J s 1 ¸ 2Js © ¹
(68)
2Js 1 2J s 1 G J s , J s ' 1 G J , J 1, 2J s 2 J s 1 s s ' ɝɞɟ J ! I 1/ 2 , J I 1/ 2 . ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ ɮɨɪɦɭɥɵ (61) ɜ ɮɨɪɦɭɥɭ (59) ɢ ɩɪɨɜɟɞɟɧɢɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ dZ ɫ ɭɱɟɬɨɦ ɫɜɨɣɫɬɜ ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ [2] ɱɥɟɧ, ɫɬɨɹɳɢɣ ɜ ɮɢɝɭɪɧɵɯ ɫɤɨɛɤɚɯ ɮɨɪɦɭɥɵ (62), ɩɪɢɜɨɞɢɬɫɹ ɤ ɞɢɚɝɨɧɚɥɶɧɨɦɭ ɩɨ ɢɧɞɟɤɫɚɦ M , M ' ɜɢɞɭ. ɇɨ ɬɨɝɞɚ ɡɚɜɢɫɹɳɚɹ ɨɬ ɩɨɥɹɪɢɡɚɰɢɢ ɧɟɣɬɪɨɧɚ J J
s s ' (67), ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɬɨɥɶɤɨ ɫɩɢɧɨɜɚɹ ɱɚɫɬɶ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ U MM ' ɧɟɞɢɚɝɨɧɚɥɶɧɵɟ ɩɨ ɢɧɞɟɤɫɚɦ M , M ' ɤɨɦɩɨɧɟɧɬɵ, ɧɟ ɞɚɫɬ ɜɤɥɚɞɚ ɜ ɜɟɥɢɱɢɧɭ (62) ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɫɟɱɟɧɢɟ ɪɟɚɤɰɢɢ n, f . ɍɤɚɡɚɧɧɨɟ ɫɟɱɟɧɢɟ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɟɪɜɵɦ ɱɥɟɧɨɦ
41
ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ, ɫɨɜɩɚɞɚɸɳɢɦ ɫɨ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ ɞɥɹ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ, ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ [14]: d 3V 4S 0 B : R , :r , H { d : R d :r d H kn2 {
1
¦
J
kn2 ss ' J s J s 'qK s
J S
J
J S
J
Js s b s' s' aKs aKs ' bsqK s ' qK hs hs ' s
s
s
s
2 J s 1 ¦ * qK s c fqKsJ ss s ' J s ' TrR , H , 2 2 I 1 c
(69) Ɇɟɬɨɞɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɞɚɥɢ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ ɩɪɢɪɨɞɭ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ ɩɪɢ ɭɱɟɬɟ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨ ɫɩɢɧɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. l Cor ɞɥɹ ɫɥɭɱɚɹ D Ƚɚɦɢɥɶɬɨɧɢɚɧ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ H ɱɚɫɬɢɰɵ ɢɦɟɟɬ ɜɢɞ: =2 Hˆ Cor (70) J l J l , 2 J0 ɝɞɟ ɨɩɟɪɚɬɨɪɵ J r ɢ lr ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ J r J x ' r iJ y ' , lr l x ' r il y ' , (71) ɩɪɢɱɟɦ J x ' , J y ' – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɫɩɢɧɚ J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɨɫɢ x ' ɢ y ' ɜ. ɫ., ɚ ɢ l x ' , l y ' – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɬɪɟɬɶɟɣ J ɱɚɫɬɢɰɵ ɨɫɢ x ' ɢ y ' ɜ. ɫ. Ⱦɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɨɜ (71) ɧɚ ɮɭɧɤɰɢɸ DMK Z ɢ
ɲɚɪɨɜɭɸ ɮɭɧɤɰɢɸ YlKl :r' ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɚɦɢ 12
J J r DMK Z ª¬ J r K J B K 1 º¼
J DMK B1 Z ;
lrYlKl :r'
(72)
12
ª¬ l B Kl l r Kl 1 º¼ Yl K r1 :r' . (73) l J SM ɉɨɷɬɨɦɭ ɞɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɚ Hˆ Cor ɧɚ (70) ɧɚ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ < qKs s
ɦɨɞɵ ɞɟɥɟɧɢɹ q ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬ ɫɬɪɭɤɬɭɪɭ ɷɬɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ. ȼ ɧɟɣ ɢɫɱɟɡɚɟɬ ɜɟɞɭɳɢɣ ɱɥɟɧ ɫ l 0 , ɚ ɨɫɧɨɜɧɭɸ ɪɨɥɶ ɧɚɱɢɧɚɸɬ ɢɝɪɚɬɶ ɱɥɟɧɵ ɫ l z 0 . Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ Cor
J S ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ Ʉɨɪɢɨɥɢɫɨɜɚ ɝɚɦɢɥɶɬɨɧɢɚɧɚ (70) ɲɢɪɢɧɵ §¨ * qKs D ·¸ s ¹ © ɜɦɟɫɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ H A ɜ ɮɨɪɦɭɥɟ (50) ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ UDJ sS M (48)
ɧɟɨɛɯɨɞɢɦɨ
ɡɚɦɟɧɢɬɶ
ɧɚ
ɧɨɜɵɟ
ɤɚɧɚɥɨɜɵɟ
ɮɭɧɤɰɢɢ
J SM
UD s ( D { D m, m r1 ), ɭɱɢɬɵɜɚɸɳɢɟ ɯɚɪɚɤɬɟɪ ɞɟɣɫɬɜɢɹ ɝɚɦɢɥɶɬɨɧɢɚɧɚ Hˆ Cor ɧɚ
ɜɨɥɧɨɜɭɸ
ɮɭɧɤɰɢɸ
J SM
< qKs
s
.
ɗɬɨ 42
ɩɪɢɜɟɞɟɬ
ɤ
ɡɚɦɟɧɟ
ɮɭɧɤɰɢɣ
J DM r K Z Yl 0 TrR
ɜ
J DM r K m
Z
ɤɚɧɚɥɨɜɨɣ
l Ylm : 'r D00
Z .
ɮɭɧɤɰɢɢ
UDJ sS M
ɧɚ
ɮɭɧɤɰɢɢ
ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ ɩɨɥɭɱɟɧɧɨɣ ɚɦɩɥɢɬɭɞɵ Cor
J S J SM ɩɚɪɰɢɚɥɶɧɨɣ ɲɢɪɢɧɵ §¨ * qKs D ·¸ ɢ ɤɚɧɚɥɨɜɨɣ ɮɭɧɤɰɢɢ UD s ɜ s ¹ © ɮɨɪɦɭɥɭ (49) ɢ ɩɪɨɜɨɞɹ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ ɢɧɞɟɤɫɚɦ E , m ɚɫɢɦɬɨɬɢɤɭ J S M Cor
ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ < qKs
<
3
J
DMs ( K F S1
V1K1
s 1)
[1 FVS22K2 [ 2
Z Yl 1 :r' b1
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J
s 1)
Z Yl 1 :r' b1
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Z Yl1 :r' b1
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DMs( K
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
1 1K1
3
2J s 1 =2 ¦ G K , K K *qK s c D00l Z l l 1 FLm :'R u 16S 2 2 J 0 clLO s 1 2
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s
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Js M ( K s 1)
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Z Yl1 :r' b1
l, l, O,H
eikc U sinH cosH U
5
, 2
(74)
J s B K s J s r K s 1 . Ⱦɨɛɚɜɥɹɹ ɚɫɢɦɩɬɨɬɢɱɟɫɤɭɸ ɮɭɧɤɰɢɸ
ɝɞɟ br1
<
J sS M Cor qK s
J SM
(74) ɤ ɧɟɜɨɡɦɭɳɟɧɧɨɣ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɮɭɧɤɰɢɢ < qKs
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Ⱥɧɚɥɢɡ ɩɨɥɧɨɝɨ ɫɟɱɟɧɢɹ ɪɟɚɤɰɢɢ n, f ɫ ɭɱɟɬɨɦ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨ ɫɩɢɧɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɩɨɡɜɨɥɢɥ ɨɛɴɹɫɧɢɬɶ ɧɚɛɥɸɞɚɟɦɵɟ ɫɜɨɣɫɬɜɚ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ ɫ ɜɵɥɟɬɨɦ D -ɱɚɫɬɢɰ. ɅɂɌȿɊȺɌɍɊȺ 1. ɏɚɥɩɟɪɧ ɂ. Ⱦɟɥɟɧɢɟ ɹɞɟɪ / ɂ. ɏɚɥɩɟɪɧ. – Ɇ. : Ɏɢɡɦɚɬɝɢɡ, 1962. – 156 ɫ. 2. Bohr A. Nu clear Structure / A. Bohr, B. Mottelson. – N.Y. : Benjamin, 1974. – Vol. 1. – 456 p.; Vol. 2. – 664 p. Ɉɫɬɚɩɟɧɤɨ ɘ.Ȼ. Ɏɨɬɨɞɟɥɟɧɢɟ ɩɪɢ ɩɨɞɛɚɪɶɟɪɧɵɯ ɜɨɡɛɭɠɞɟɧɢɹɯ 3. ɹɞɟɪ / ɘ.Ȼ. Ɉɫɬɚɩɟɧɤɨ [ɢ ɞɪ.] // Ɏɢɡɢɤɚ ɷɥɟɦɟɧɬɚɪɧɵɯ ɱɚɫɬɢɰ ɢ ɚɬɨɦɧɨɝɨ ɹɞɪɚ. – 1981. – Ɍ. 12, ɜɵɩ. 6. – ɋ. 1364–1431. 4. Fong P. Dynamical interpretation of the statistical theory of fission / P. Fong // Phys. Rev. C. – 1979. – V. 19. – P. 868–870. 5. Winhold E.J. The Angular Distribution of Fission Fragments in the Photofission of Thorium / E.J. Winhold, P.T. Demos, I. Halpern // Phys. Rev. – 1952. – V. 87. – P. 1139–1140. 6. Ⱦɚɧɢɥɹɧ Ƚ.ȼ. P-ɧɟɱɟɬɧɚɹ ɚɫɢɦɦɟɬɪɢɹ ɩɪɢ ɞɟɥɟɧɢɢ 233U ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɬɟɩɥɨɜɵɦɢ ɧɟɣɬɪɨɧɚɦɢ / Ƚ.ȼ. Ⱦɚɧɢɥɹɧ [ɢ ɞɪ.] // ɉɢɫɶɦɚ ɜ ɀɗɌɎ. – 1977. – Ɍ. 26. – ɋ. 68–74. 7. Aleksandrovich Ⱥ.Ɋ. New observation of space-parity violation in neutron-induced fission of 229Th, 241Pu and 241Am / A.P. Aleksandrovich [et al.] / Nucl. Phys. A. – 1994. – V. 567. – P. 541–552. 44
8. ɉɟɬɭɯɨɜ Ⱥ.Ʉ. Ⱥɫɢɦɦɟɬɪɢɹ ɪɚɡɥɟɬɚ ɨɫɤɨɥɤɨɜ ɞɟɥɟɧɢɹ 233U ɢ 239Ɋu ɦɟɞɥɟɧɧɵɦɢ ɩɨɥɹɪɢɡɨɜɚɧɧɵɦɢ ɧɟɣɬɪɨɧɚɦɢ / Ⱥ.Ʉ. ɉɟɬɭɯɨɜ [ɢ ɞɪ.] // ɉɢɫɶɦɚ ɜ ɀɗɌɎ. – 1980. – Ɍ. 30. – ɋ. 324–331. 9. ȼɟɫɧɚ ȼ.Ⱥ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɭɝɥɨɜɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɜɵɥɟɬɚ ɨɫɤɨɥɤɨɜ ɞɟɥɟɧɢɹ 233U ɢ 235U ɩɪɢ ɡɚɯɜɚɬɟ ɬɟɩɥɨɜɨɝɨ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɧɟɣɬɪɨɧɚ / ȼ.Ⱥ. ȼɟɫɧɚ [ɢ ɞɪ.] // ɉɢɫɶɦɚ ɜ ɀɗɌɎ. – 1980. – Ɍ. 31. – P. 704–709. 10. ɋɭɲɤɨɜ Ɉ.ɉ. ɇɚɪɭɲɟɧɢɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɱɟɬɧɨɫɬɢ ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɧɟɣɬɪɨɧɨɜ ɫ ɬɹɠɟɥɵɦɢ ɹɞɪɚɦɢ / Ɉ.ɉ. ɋɭɲɤɨɜ, ȼ. ȼ. Ɏɥɚɦɛɚɭɦ // ɍɎɇ. – 1982. – Ɍ. 136. – ɋ. 3–24. 11. Bunakov V.E. Parity violation and related effects in neutron-induced reactions / V.E. Bunakov, V.P. Gudkov // Nucl. Phys. A. – 1983. – V. 401. – P. 93–116. 12. Bunakov V.E. Enhancement of T-noninvariant effects in neutroninduced nuclear reactions / V.E. Bunakov, V.P. Gudkov // Z. Phys. A. – 1985. – V. 308. – P. 363–364. 13. Barabanov A. Formal theory of neutron induced fission / A. Barabanov, W. Furman // Z. Phys. A. – 1997. – V. 357. – P. 414–418. Lanɟ A.M. R-Matrix Theory of Nuclear Reactions // A.M. Lane, 14. R.G. Thomas // Rev. Mod. Phys. – 1958. – V. 30. – P. 257–353. 15. Ƚɨɥɶɞɛɟɪɝɟɪ Ɇ. Ɍɟɨɪɢɹ ɫɬɨɥɤɧɨɜɟɧɢɣ / M. Ƚɨɥɶɞɛɟɪɝɟɪ, K. ȼɚɬɫɨɧ. – Ɇ. : Ɇɢɪ, 1967. – 823 ɫ. 16. Ʉɚɞɦɟɧɫɤɢɣ ɋ.Ƚ. Ɍɟɨɪɢɹ ɨɬɤɪɵɬɵɯ Ɏɟɪɦɢ-ɫɢɫɬɟɦ ɞɥɹ ɨɩɢɫɚɧɢɹ ɚɬɨɦɧɵɯ ɹɞɟɪ ɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ / ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 1999. – Ɍ. 62. – ɋ. 1054–1059. Ʉɚɞɦɟɧɫɤɢɣ ɋ.Ƚ. Ɋɚɫɩɚɞ ɢ ɞɟɥɟɧɢɟ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɯ ɹɞɟɪ / 17. ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 2002. – Ɍ. 65, ʋ 8. – ɋ. 1424–1437. 18. Ʉɚɞɦɟɧɫɤɢɣ ɋ.Ƚ. Ʉɜɚɧɬɨɜɵɟ ɢ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɢɧɞɭɰɢɪɨɜɚɧɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ / ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 2005. – Ɍ. 68, ʋ 12. – ɋ. 2030–2041. 19. Ʉɚɞɦɟɧɫɤɢɣ ɋ.Ƚ. ɒɢɪɢɧɵ ɢ ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ ɪɚɫɩɚɞɧɵɯ ɹɞɟɪɧɵɯ ɫɨɫɬɨɹɧɢɣ ɫ ɭɱɟɬɨɦ ɫɜɹɡɢ ɤɚɧɚɥɨɜ / ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 2004. – Ɍ. 68, ʋ 12. – ɋ. 1257–1261. 20. ȼɢɥɶɞɟɪɦɭɬ K. ȿɞɢɧɚɹ ɬɟɨɪɢɹ ɹɞɪɚ / K. ȼɢɥɶɞɟɪɦɭɬ, ə. Ɍɚɧ. – Ɇ. : Ɇɢɪ, 1980. – 502 ɫ. 21. Ʉɚɞɦɟɧɫɤɢɣ ɋ.Ƚ. Ɇɟɯɚɧɢɡɦɵ ɞɜɨɣɧɨɝɨ ɢ ɬɪɨɣɧɨɝɨ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ ɫ ɭɱɟɬɨɦ ɷɮɮɟɤɬɨɜ ɧɟɫɮɟɪɢɱɧɨɫɬɢ / ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 2004. – Ɍ. 67, ʋ 1. – ɋ. 167–179. Mutterer M. Nuclear Decay Modes / M. Mutterer and J. P. Theobald. – 22. Bristol: IOP Publ. – 1996. – Ch. 12. – 38 ɪ. 23. Ʉɚɞɦɟɧɫɤɢɣ ɋ.Ƚ. Ɍɪɨɣɧɨɟ ɞɟɥɟɧɢɟ ɹɞɟɪ ɜ ɚɞɢɚɛɚɬɢɱɟɫɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ / ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 2002. – Ɍ. 65, ʋ 10. – ɋ. 1833– 1842. 45
24. Ȼɭɧɚɤɨɜ ȼ.ȿ. Ɍ-ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ ɜ ɭɝɥɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹɯ ɩɪɨɞɭɤɬɨɜ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ / ȼ.ȿ. Ȼɭɧɚɤɨɜ, ɋ.Ƚ. Ʉɚɞɦɟɧɫɤɢɣ // əɎ. – 2003. – T. 66, ʋ 10. – C. 1894–1908. 25. Tamimura O. Dynamical model for alpha-particle emission during fission / O. Tamimura, T. Fliesssbach // Z. Phys. A. – 1987. – V. 328. – P. 475. ɋɈȾȿɊɀȺɇɂȿ ȼɜɟɞɟɧɢɟ............................................................................................................. 3 1. Ɉɛɳɢɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɫɩɨɧɬɚɧɧɨɦ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɢɧɞɭɰɢɪɨɜɚɧɧɨɦ ɞɜɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ.................3 2. Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ...................................................................................... 13 Ɉɛɳɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ..... 13 Ɇɟɯɚɧɢɡɦ ɝɟɧɟɪɚɰɢɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ ɫɩɢɧɨɜ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɜɨɣɧɨɝɨ ɞɟɥɟɧɢɹ................................21 ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɨ «ɯɨɥɨɞɧɨɫɬɢ» ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ............................... 24 3. Ɉɛɳɢɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ............... 26 4. Ʉɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɫɩɨɧɬɚɧɧɨɝɨ ɢ ɧɢɡɤɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɜɵɧɭɠɞɟɧɧɨɝɨ ɬɪɨɣɧɨɝɨ ɞɟɥɟɧɢɹ ɹɞɟɪ...................................................................................... 29 5. Ɍ-ɧɟɱɟɬɧɵɟ ɚɫɢɦɦɟɬɪɢɢ ɜ ɬɪɨɣɧɨɦ ɞɟɥɟɧɢɢ ɹɞɟɪ ..................................... 37 Ʌɢɬɟɪɚɬɭɪɚ ......................................................................................................... 44 ɋɨɞɟɪɠɚɧɢɟ ........................................................................................................ 46
46
ɍɱɟɛɧɨɟ ɢɡɞɚɧɢɟ
ɄȼȺɇɌɈȼȺə ɌȿɈɊɂə ȾȼɈɃɇɈȽɈ ɂ ɌɊɈɃɇɈȽɈ ȾȿɅȿɇɂə ȺɌɈɆɇɕɏ əȾȿɊ ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ
ɋɨɫɬɚɜɢɬɟɥɢ: Ʉɚɞɦɟɧɫɤɢɣ ɋɬɚɧɢɫɥɚɜ Ƚɟɨɪɝɢɟɜɢɱ, Ɍɢɬɨɜɚ Ʌɚɪɢɫɚ ȼɢɬɚɥɶɟɜɧɚ Ɋɟɞɚɤɬɨɪ Ⱥ.ɉ. ȼɨɪɨɧɢɧɚ
ɉɨɞɩɢɫɚɧɨ ɜ ɩɟɱɚɬɶ 13.06.07. Ɏɨɪɦɚɬ 60×84/16. ɍɫɥ. ɩɟɱ. ɥ. 2,8. Ɍɢɪɚɠ 50 ɷɤɡ. Ɂɚɤɚɡ 954. ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 394000, ɝ. ȼɨɪɨɧɟɠ, ɩɥ. ɢɦ. Ʌɟɧɢɧɚ, 10. Ɍɟɥ. 208-298, 598-026 (ɮɚɤɫ) http://www.ppc.vsu.ru; e-mail:
[email protected] Ɉɬɩɟɱɚɬɚɧɨ ɜ ɬɢɩɨɝɪɚɮɢɢ ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɨɝɨ ɰɟɧɬɪɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 394000, ɝ. ȼɨɪɨɧɟɠ, ɭɥ. ɉɭɲɤɢɧɫɤɚɹ, 3. Ɍɟɥ. 204-133. 47
