Кутыркин Сферическме сплайны (Раздаточные материалы), страница 2
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Файл "Кутыркин Сферическме сплайны" внутри архива находится в папке "Раздаточные материалы". PDF-файл из архива "Раздаточные материалы", который расположен в категории "". Всё это находится в предмете "геометрия" из 3 семестр, которые можно найти в файловом архиве МГТУ им. Н.Э.Баумана. Не смотря на прямую связь этого архива с МГТУ им. Н.Э.Баумана, его также можно найти и в других разделах. Архив можно найти в разделе "остальное", в предмете "геометрическое моделирование" в общих файлах.
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Ɍɚɤɨɟ ɩɨɞɪɚɡɞɟɥɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɭɤɥɚɞɤɨɣ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɉ. Ɉɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɧɚɛɨɪɨɦ ɬɨɱɟɤ-ɭɡɥɨɜɩɪɹɦɨɭɝɨɥɶɧɢɤɚ (ɜɟɪɲɢɧɚɦɢ ɩɪɹɦɨɭɝɨɥɶɧɢɤɨɜ ɭɤɥɚɞɤɢ). ɗɬɨɬ ɧɚɛɨɪɭɡɥɨɜ ɞɥɹ ɧɨɫɢɬɟɥɹ ɤɚɠɞɨɝɨ ɛɚɡɢɫɧɨɝɨ ɥɨɤɚɥɶɧɨɝɨ (ɫɮɟɪɢɱɟɫɤɨɝɨ)ɫɩɥɚɣɧɚ ɢɧɞɭɰɢɪɭɟɬ ɫɜɨɸ ɥɨɤɚɥɶɧɭɸ ɫɟɬɤɭ; ɞɚɥɟɟ ɨɧ ɧɚɡɵɜɚɟɬɫɹɩɫɟɜɞɨɫɟɬɤɨɣ, ɩɨɫɤɨɥɶɤɭ ɬɚɤɨɣ ɧɚɛɨɪ ɫɨɞɟɪɠɢɬ ɧɟ ɜɫɟ ɭɡɥɵ ɷɬɢɯ ɥɨɤɚɥɶɧɵɯ ɫɟɬɨɤ, ɧɨ ɩɨɡɜɨɥɹɟɬ ɢɯ ɜɨɫɫɬɚɧɨɜɢɬɶ ɢɡ ɭɡɥɨɜ ɭɤɚɡɚɧɧɨɣɩɫɟɜɞɨɫɟɬɤɢ.ɇɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ 3 ɬɚɤɚɹ ɩɫɟɜɞɨɫɟɬɤɚ ɢɦɟɟɬ ɜɢɞC^(W i , W ik ) : 0 d i d N 1,`0dk dn ,(11)ɝɞɟ A1 (S W 0 , W1, ..., W N 1) — ɱɚɫɬɶ ɫɟɬɤɢ A (S W 0 , W1,..., W N 1,WNS ), ɜɜɟɞɟɧɧɨɣ ɜ (1) ɜɦɟɫɬɟ ɫ ɫɟɬɤɨɣ A0 , ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɣɭɫɥɨɜɢɹɦ (3).Ʉɪɨɦɟ ɬɨɝɨ, ɟɫɥɢ 0 d i d N 1, ɬɨ A iɫɟɬɤɚ,ɚɧɚɥɨɝɢɱɧɚɹɫɟɬɤɟȺɢɡ( S 2 W 0i , W1i , ..., W niW i 3, W i2 , W i1, W 0i , W1i , ..., W ni , W ni1, W ni2 , W ni3 ɤɨɬɨɪɨɟ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɹɦ W 0iɥɨɝɢɱɧɵɦ ɜɜɟɞɟɧɧɵɦ ɜ (6).178ɫ(1)S 2) —ɪɚɫɲɢɪɟɧɢɟɦA 0iɜɧɟ ɨɬɪɟɡɤɚ [ S 2; S 2],W i 1 W1i2, W niW ni 1 W ni 12, ɚɧɚ-ISSN 1812-3368.
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012Ʉɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɨɞɪɚɡɞɟɥɟ, ɞɥɹ ɭɤɚɡɚɧɧɨɣ ɜɵɲɟ ɫɟɬɤɢ A 1ɧɚ ɨɬɪɟɡɤɟ [ S ; S ] ɜɜɨɞɹɬɫɹ ɛɚɡɢɫɧɵɟ ɫɩɥɚɣɧɵ H1 , …, H N 1 , ɨɩɪɟɞɟɥɟɧɧɵɟ ɜ (8). ȿɫɥɢ 0 d i d n, ɬɨ ɞɥɹ ɭɤɚɡɚɧɧɨɣ ɜɵɲɟ ɫɟɬɤɢ Ai ɫɪɚɫɲɢɪɟɧɢɟɦ Ai0 , ɧɚ ɨɬɪɟɡɤɟ [ S 2; S 2] ɜɜɨɞɹɬɫɹ ɛɚɡɢɫɧɵɟ ɫɩɥɚɣɧɵh i1 , …, h iN 1 , ɮɚɤɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɟɧɧɵɟ ɜ (9) (ɫɦ. ɬɚɤɠɟ ɜɵɪɚɠɟɧɢɹ(6) ɢ (7)).
ɗɬɢ ɨɞɧɨɦɟɪɧɵɟ ɛɚɡɢɫɧɵɟ ɫɩɥɚɣɧɵ ɩɨɡɜɨɥɹɸɬ ɜɜɟɫɬɢ ɧɚɩɪɹɦɨɭɝɨɥɶɧɢɤɟ [ S ; S ] u [ S 2 ; S 2] 3 ɞɜɭɦɟɪɧɵɟ ɫɮɟɪɢɱɟɫɤɢɟɛɚɡɢɫɧɵɟ ɫɩɥɚɣɧɵ ɜɢɞɚS x (M , T )° 1°° x°S2 (M , T )°°S i (M , T )° k®°°°S x (M , T )° n°°S x (M , T )°̄ n1N 1i¦ Hi (M )h1 (T ), M [S ; S ], T [S 2; S 2];i 1N 1i¦ Hi (M )h2 (T ), M [S ; S ], T [S 2; S 2];i 1Hi (M )hki (T ), M [S ; S ], T [S 2; S 2],(12)1 d i d N 1, 2 d k d n;N 1i¦ Hi (M )hn (T ), M [S ; S ], T [S 2; S 2];i 1N 1i¦ Hi (M )hn1 (T ), M [S ; S ], T [S 2; S 2].i 1ɍɠɟ ɭɤɚɡɵɜɚɥɨɫɶ, ɱɬɨ ɞɥɹ i 1, ..., N 1 ɫɩɥɚɣɧ H i ɢɡ (8) ɜ ɤɨɧɰɚɯɨɬɪɟɡɤɚ [ S ; S ] ɢɦɟɟɬ ɨɞɢɧɚɤɨɜɵɟ ɡɧɚɱɟɧɢɹ ɢ ɪɚɜɧɵɟ ɨɞɧɨɫɬɨɪɨɧɧɢɟɩɪɨɢɡɜɨɞɧɵɟ. Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ k 1, ..., n 1 ɫɩɥɚɣɧ hki , ɚɧɚɥɨɝɢɱɧɵɣɫɩɥɚɣɧɭ hk ɢɡ (9), ɢɦɟɟɬ ɜ ɤɨɧɰɚɯ ɨɬɪɟɡɤɚ [ S 2; S 2] ɧɭɥɟɜɵɟ ɩɪɨɢɡɜɨɞɧɵɟ.
ȼɫɥɟɞɫɬɜɢɟ ɬɚɤɢɯ ɫɜɨɣɫɬɜ ɞɥɹ m <, 1, ..., N 1 ɢk 1, ..., n 1 ɜ ɝɪɚɧɢɱɧɵɯ ɬɨɱɤɚɯ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ [ S ; S ] uu [ S 2; S 2] 3 ɫɩɥɚɣɧ S km ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɹɦ° S km ( S ; T ) S km (S ; T ), T [ S 2 ; S 2];°°° wS m ( S ; T ) wS m (S ; T )kk, T [ S 2 ; S 2];®MwwM°° mm° wS k (M ; S 2) wS k (M ; S 2) 0, M [ S ; S ].wTwT¯°ISSN 1812-3368.
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012(13)179ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɥɸɛɨɣ ɫɩɥɚɣɧ S ɢɡ ɥɢɧɟɣɧɨɣ ɨɛɨɥɨɱɤɢ ɫɩɥɚɣɧɨɜɜɢɞɚ (11) ɜ ɬɨɱɤɚɯ ɛɨɤɨɜɵɯ ɝɪɚɧɢɰ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ [ S ; S ] uu [ S 2; S 2] 3 ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɹɦ «ɩɟɪɢɨɞɢɱɧɨɫɬɢ»: S ( S ; T ) S (S ; T ), T [ S 2; S 2];°°® wS ( S ; T ) wS (S ; T )°, T [ S 2; S 2].wMwM°̄(14)Ʉɪɨɦɟ ɬɨɝɨ, ɜɫɥɟɞɫɬɜɢɟ ɜɢɞɚ ɛɚɡɢɫɧɵɯ ɫɩɥɚɣɧɨɜ (11) (ɫɦ. ɬɚɤɠɟ ɜɵɪɚɠɟɧɢɹ (3), (6), (7), (8) ɢ (13)) ɢ ɬɨɠɞɟɫɬɜ (10) ɞɥɹ ɥɸɛɨɝɨ ɜ ɬɨɱɤɚɯ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɝɪɚɧɢɰ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ [S ; S ] uu [ S 2; S 2] 3 ɫɩɪɚɜɟɞɥɢɜɵ ɫɨɨɬɧɨɲɟɧɢɹ° S (M ; S 2) S ( S ; S 2) S (S ; S 2), M [ S ; S ];°°® S (M ; S 2) S ( S ; S 2) S (S ; S 2), M [ S ; S ];°° wS (M ; S 2) wS (M ; S 2)°0, M [ S ; S ].wTwT¯Ɋɢɫ.
1. ɉɪɟɞɫɬɚɜɥɟɧɢɟɫɮɟɪɵ ɫ ɩɨɦɨɳɶɸ ɫɩɟɰɢɚɥɶɧɨɝɨ ɫɮɟɪɢɱɟɫɤɨɝɨ ɫɩɥɚɣɧɚ(15)ɋɜɨɣɫɬɜɚ (14) ɢ (15) ɫɩɥɚɣɧɚ S ɩɨɡɜɨɥɹɸɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɟɝɨ ɤɚɤ ɝɥɚɞɤɭɸ ɮɭɧɤɰɢɸ, ɡɚɞɚɧɧɭɸ ɧɚ ɫɮɟɪɟ ɟɞɢɧɢɱɧɨɝɨ ɪɚɞɢɭɫɚ,ɬ. ɟ. ɤɚɤ ɫɮɟɪɢɱɟɫɤɢɣ ɫɩɥɚɣɧ, ɫɨɝɥɚɫɧɨ ɜɜɟɞɟɧɧɨɣ ɜɵɲɟ ɬɟɪɦɢɧɨɥɨɝɢɢ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ,ɷɬɨɬ ɫɮɟɪɢɱɟɫɤɢɣ ɫɩɥɚɣɧ ɨɩɢɫɵɜɚɟɬ ɝɥɚɞɤɭɸɩɨɜɟɪɯɧɨɫɬɶ, ɨɝɪɚɧɢɱɢɜɚɸɳɭɸ ɧɟɤɨɬɨɪɭɸɡɜɟɡɞɧɭɸ ɨɛɥɚɫɬɶ ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ.ȼ ɱɚɫɬɧɨɫɬɢ, ɟɫɥɢ ɷɬɨɬ ɫɩɥɚɣɧ ɢɦɟɟɬ ɜɢɞN 1 n 1S S1x S2x ¦ ¦ S ki Snx Snx1 ,(16)i 1 k 3ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ [ S ; S ] u [ S 2; S 2] 3 ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɠɞɟɫɬɜɨS { 1.(17)Ɍɚɤɨɣ ɫɩɥɚɣɧ ɨɩɢɫɵɜɚɟɬ ɫɮɟɪɭ ɟɞɢɧɢɱɧɨɝɨ ɪɚɞɢɭɫɚ, ɩɨɤɚɡɚɧɧɭɸ ɧɚɪɢɫ.
1, ɝɞɟ N n 5.180ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012Ɇɟɬɨɞɵ ɩɨɫɬɪɨɟɧɢɹ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɩɨɜɟɪɯɧɨɫɬɢ ɫɮɟɪɢɱɟɫɤɢɦ ɫɩɥɚɣɧɨɦ. ȼ ɜɵɛɪɚɧɧɨɣ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ( R, T , M ) ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ ɝɥɚɞɤɚɹ ɩɨɜɟɪɯɧɨɫɬɶ, ɨɝɪɚɧɢɱɢɜɚɸɳɚɹ ɡɜɟɡɞɧɭɸ ɨɛɥɚɫɬɶ ɬɪɟɯɦɟɪɧɨɝɨ ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɡɚɞɚɧɚɭɪɚɜɧɟɧɢɟɦf (T , M ),RS d T d Sɢ S 2 dM d S 2 ,(18)ɝɞɟ f (T , M ) ! 0 — ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɝɥɚɞɤɚɹ ɮɭɧɤɰɢɹ ɫɜɨɢɯ ɩɟɪɟɦɟɧɧɵɯ (ɭɝɥɨɜ) ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ [ S ; S ] u [ S 2; S 2] Ȇ.ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɵɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ. Ɂɚɞɚɧɵ ɟɟ ɜɧɭɬɪɟɧɧɢɣ «ɰɟɧɬɪ», ɪɚɫɩɨɥɨɠɟɧɧɵɣ ɜɧɚɱɚɥɟ ɤɨɨɪɞɢɧɚɬ, ɢ ɬɨɱɤɢ ɩɨɜɟɪɯɧɨɫɬɢP1 f (T1 , M 1 ) H 1 , T1 , M 1 , ..., Pm f (T m , M m ) H m , T m , M m ,(19)ɝɞɟ H 1, …, H m — ɧɟɡɚɜɢɫɢɦɵɟ ɫɥɭɱɚɣɧɵɟ ɜɟɥɢɱɢɧɵ (ɩɨɝɪɟɲɧɨɫɬɢ),ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɩɨ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɧɭɥɟɜɵɦ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɨɠɢɞɚɧɢɟɦ ɢ ɨɞɢɧɚɤɨɜɨɣ ɞɢɫɩɟɪɫɢɟɣ.Ⱦɚɥɟɟ ɞɥɹ ɬɨɱɟɤ P1, …, Pm ɢɡ (17) ɩɪɢɧɹɬɵ ɨɛɨɡɧɚɱɟɧɢɹf (T1 , M 1 ) H1 , ..., RmR1f (T m , M m ) H m.(20)ɑɢɫɥɨ R ɜɢɞɚR1 m¦ Rjmj1(21)ɧɚɡɵɜɚɟɬɫɹ ɫɪɟɞɧɟɜɵɛɨɪɨɱɧɵɦ ɪɚɞɢɭɫɨɦ ɬɨɱɟɤ (19) ɞɥɹ ɩɨɜɟɪɯɧɨɫɬɢ (18).Ʉɚɤ ɛɵɥɨ ɨɩɢɫɚɧɨ, ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ ɉ ɫɨɡɞɚɸɬɫɹ ɩɫɟɜɞɨɫɟɬɤɚɜɢɞɚ (10)C^(W i , Wik):0 d i`d N 1, 0 d k d nɢ ɛɚɡɢɫ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ S <1, S <2, S ki1 d i d N 1,(22)3 d k d n 1 ,S nx , S nx1 , ɨɩɪɟɞɟɥɟɧɧɵɣ ɜ (12).Ɋɚɧɟɟ ɨɩɪɟɞɟɥɹɥɨɫɶ, ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɩɫɟɜɞɨɫɟɬɤɚ (22) ɢɧɞɭɰɢɪɭɟɬɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ ɉ ɭɤɥɚɞɤɭ, ɹɜɥɹɸɳɭɸɫɹ ɟɝɨ ɩɨɞɪɚɡɞɟɥɟɧɢɟɦ ɧɚɛɨɥɟɟ ɦɟɥɤɢɟ ɩɪɹɦɨɭɝɨɥɶɧɢɤɢ.
Ɂɞɟɫɶ ɫɟɬɤɚ (22) ɜɵɛɢɪɚɟɬɫɹ ɬɚɤɢɦɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɜ ɤɚɠɞɵɣ ɩɪɹɦɨɭɝɨɥɶɧɢɤ ɷɬɨɣ ɭɤɥɚɞɤɢ ɩɨɩɚɥɨ ɨɞɢISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012181ɧɚɤɨɜɨɟ ɱɢɫɥɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɢɡ ɧɚɛɨɪɚ (19). Ɍɨɝɞɚ ɞɥɹɨɩɪɟɞɟɥɟɧɢɹ ɫɮɟɪɢɱɟɫɤɨɝɨ ɫɩɥɚɣɧɚ S ɜɢɞɚN 1 n 1Sx1x S1x x2x S2x ¦ ¦ xki Ski xnx Snx xnx1 Snx1,(23)i 1k 3ɝɞɟ x1x , x2x , x ki1 d i d N 1,3 d k d n 1 , xnx , xnx1 — ɧɟɢɡɜɟɫɬɧɵɟɤɨɷɮɮɢɰɢɟɧɬɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɧɚɛɨɪɨɦ ɬɨɱɟɤ (19), ɨɛɨɡɧɚɱɟɧɢɹɦɢ(20) ɢ ɜɢɞɨɦ (23) ɫɩɥɚɣɧɚ S ɫɨɡɞɚɟɬɫɹ ɫɢɫɬɟɦɚ ɥɢɧɟɣɧɵɯ ɚɥɝɟɛɪɚɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ (ɋɅȺɍ)S (T j , M j )Rj , 1 d j d m .(24)ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɫɥɭɱɚɹɯ ɋɅȺɍ (24) ɩɟɪɟɨɩɪɟɞɟɥɟɧɚ. ɉɨɷɬɨɦɭɞɥɹ ɟɟ ɪɟɲɟɧɢɹ ɩɪɢɦɟɧɹɟɬɫɹ ɦɟɬɨɞ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ, ɫɨɝɥɚɫɧɨɤɨɬɨɪɨɦɭ ɫɨɡɞɚɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɧɨɪɦɚɥɶɧɚɹ ɋɅȺɍ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɧɨɪɦɚɥɶɧɨɣ ɋɅȺɍ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɟɬɨɞ ɫɨɩɪɹɠɟɧɧɵɯ ɝɪɚɞɢɟɧɬɨɜ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɧɚɣɞɟɧɧɵɟ ɧɟɢɡɜɟɫɬɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɮɟɪɢɱɟɫɤɨɝɨ ɫɩɥɚɣɧɚ S ɢɡ (23) ɩɪɟɞɫɬɚɜɥɹɸɬ ɚɩɩɪɨɤɫɢɦɚɰɢɸ ɢɫɤɨɦɨɣ ɩɨɜɟɪɯɧɨɫɬɢ.ɇɚ ɪɢɫ. 2, ɚ ɩɨɤɚɡɚɧɚ ɩɨɜɟɪɯɧɨɫɬɶ, ɞɥɹ ɤɨɬɨɪɨɣ ɩɪɢɜɟɞɟɧɧɵɦɜɵɲɟ ɦɟɬɨɞɨɦ ɩɨɫɬɪɨɟɧɚ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ m 103ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɜɢɞɚ (20), ɫ 3%-ɧɨɣ ɚɛɫɨɥɸɬɧɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɜɵɛɨɪɨɱɧɨɝɨ ɪɚɞɢɭɫɚ (21) ɢ ɫɟɬɤɢ (22), ɞɥɹɤɨɬɨɪɨɣ N 5 ɢ n 15. Ɍɚɤɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 2, ɛ.ɚɛɊɢɫ. 2. ɂɫɯɨɞɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ (ɚ) ɢ ɟɟ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɫɮɟɪɢɱɟɫɤɢɦ ɫɩɥɚɣɧɨɦ (ɛ)Ⱦɥɹ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɧɚɛɨɪɚ (20) ɢ ɩɟɪɜɢɱɧɨɣ ɩɫɟɜɞɨɫɟɬɤɢ ɋ ɢɡ (22) ɜ ɤɚɠɞɨɦ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟɭɤɥɚɞɤɢ, ɢɧɞɭɰɢɪɨɜɚɧɧɨɣ ɩɫɟɜɞɨɫɟɬɤɨɣ ɋ, ɩɪɨɢɡɜɨɞɢɬɫɹ ɭɫɪɟɞɧɟɧɢɟɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ, ɩɨɩɚɜɲɢɯ ɜ ɷɬɨɬ ɩɪɹɦɨɭɝɨɥɶɧɢɤ.
ȼ ɪɟ182ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012ɡɭɥɶɬɚɬɟ ɫɨɡɞɚɟɬɫɹ ɧɨɜɵɣ ɧɚɛɨɪ, ɫɨɞɟɪɠɚɳɢɣ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟɟɱɢɫɥɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɷɬɢɦ ɧɚɛɨɪɨɦ ɫɨɡɞɚɟɬɫɹ ɜɬɨɪɢɱɧɚɹ ɩɫɟɜɞɨɫɟɬɤɚ ɜɢɞɚ (22) ɫ ɦɟɧɶɲɢɦ ɱɢɫɥɨɦ ɭɡɥɨɜ.Ɂɚɬɟɦ, ɫɨɝɥɚɫɧɨ ɢɡɥɨɠɟɧɧɨɦɭ ɜɵɲɟ ɦɟɬɨɞɭ, ɫ ɩɨɦɨɳɶɸ ɷɬɨɝɨ ɧɨɜɨɝɨ ɧɚɛɨɪɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɢ ɫɨɤɪɚɳɟɧɧɨɣ ɩɫɟɜɞɨɫɟɬɤɢ ɫɨɡɞɚɟɬɫɹ ɫɮɟɪɢɱɟɫɤɢɣ ɫɩɥɚɣɧ, ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɣ ɩɨɜɟɪɯɧɨɫɬɶ (18).Ɍɚɤɚɹ ɩɪɨɰɟɞɭɪɚ ɩɨɫɬɪɨɟɧɢɹ ɩɪɢɛɥɢɠɟɧɢɹ ɤ ɩɨɜɟɪɯɧɨɫɬɢ (18) ɧɚɡɵɜɚɟɬɫɹ ɪɟɞɭɰɢɪɨɜɚɧɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɟɣ.
ɇɚ ɪɢɫ. 3, ɚ ɩɨɤɚɡɚɧɚ ɩɨɜɟɪɯɧɨɫɬɶ, ɞɥɹ ɤɨɬɨɪɨɣ ɛɵɥɚ ɨɫɭɳɟɫɬɜɥɟɧɚ ɪɟɞɭɰɢɪɨɜɚɧɧɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ, ɫɬɚɪɬɨɜɚɜɲɚɹ ɫ m 104 ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɜ ɧɚɛɨɪɟ(20), ɫ 5%-ɧɨɣ ɚɛɫɨɥɸɬɧɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɜɵɛɨɪɨɱɧɨɝɨ ɪɚɞɢɭɫɚ (21) ɢ ɩɟɪɜɢɱɧɨɣ ɩɫɟɜɞɨɫɟɬɤɨɣ, ɞɥɹ ɤɨɬɨɪɨɣ N 10ɢ n 100. ɉɪɢ ɪɟɞɭɰɢɪɨɜɚɧɢɢ ɜɬɨɪɢɱɧɚɹ ɩɫɟɜɞɨɫɟɬɤɚ ɢɦɟɥɚ ɩɚɪɚɦɟɬɪɵ N 5 ɢ n 30 .
Ɋɟɡɭɥɶɬɚɬ ɬɚɤɨɣ ɪɟɞɭɰɢɪɨɜɚɧɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫ. 3, ɛ.ɚɛɊɢɫ. 3. ɂɫɯɨɞɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ (ɚ) ɢ ɟɟ ɪɟɞɭɰɢɪɨɜɚɧɧɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɫɮɟɪɢɱɟɫɤɢɦ ɫɩɥɚɣɧɨɦ (ɛ).ȼɨɡɦɨɠɧɚ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɞɥɹ ɝɥɚɞɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɝɪɚɧɢɱɢɜɚɸɳɟɣ ɡɜɟɡɞɧɭɸ ɨɛɥɚɫɬɶ ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɭɤɚɡɚɧ ɧɚɛɨɪ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɜ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɧɨ ɧɟɢɡɜɟɫɬɟɧ ɰɟɧɬɪ ɷɬɨɣ ɡɜɟɡɞɧɨɣ ɨɛɥɚɫɬɢ.
Ɍɨɝɞɚ ɜ ɤɚɱɟɫɬɜɟ ɬɚɤɨɝɨ ɢɫɤɭɫɫɬɜɟɧɧɨɝɨ ɰɟɧɬɪɚ ɦɨɠɧɨ ɜɵɛɢɪɚɬɶ ɬɨɱɤɭ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɩɨɥɭɱɟɧɧɭɸɭɫɪɟɞɧɟɧɢɟɦ ɡɚɞɚɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ.ɉɨɫɥɟ ɩɨɫɬɪɨɟɧɢɹ ɷɬɨɝɨ ɰɟɧɬɪɚ ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɫɮɟɪɢɱɟɫɤɨɣɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɫ ɧɚɱɚɥɨɦ ɜ ɷɬɨɦ ɰɟɧɬɪɟ ɢ ɫɨɡɞɚɬɶ ɫɮɟɪɢɱɟɫɤɢɣɫɩɥɚɣɧ, ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɣ ɩɨɜɟɪɯɧɨɫɬɶ, ɪɚɡɪɚɛɨɬɚɧɧɵɦ ɜɵɲɟ ɦɟɬɨɞɨɦ.Ɍɚɤɭɸ ɚɩɩɪɨɤɫɢɦɚɰɢɸ ɩɨɜɟɪɯɧɨɫɬɢ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɧɟɰɟɧɬɪɢɪɨɜɚɧɧɨɣ.
ɗɤɫɩɟɪɢɦɟɧɬɵ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɧɟɰɟɧɬɪɢɪɨɜɚɧISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012183ɚɛɊɢɫ. 4. ɐɟɧɬɪɢɪɨɜɚɧɧɚɹ (ɚ) ɢ ɧɟɰɟɧɬɪɢɪɨɜɚɧɧɚɹ (ɛ) ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɫɮɟɪɵ ɫɩɨɦɨɳɶɸ ɫɮɟɪɢɱɟɫɤɨɝɨ ɫɩɥɚɣɧɚɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɧɟɫɤɨɥɶɤɨ ɧɢɠɟ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɰɟɧɬɪɢɪɨɜɚɧɧɨɣ,ɤɨɝɞɚ ɢɡɜɟɫɬɟɧ ɜɧɭɬɪɟɧɧɢɣ ɰɟɧɬɪ ɡɜɟɡɞɧɨɣ ɨɛɥɚɫɬɢ, ɨɝɪɚɧɢɱɟɧɧɨɣɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɧɟɰɟɧɬɪɢɪɨɜɚɧɧɨɣɚɩɩɪɨɤɫɢɦɚɰɢɢ ɦɨɠɧɨ ɩɨɜɵɫɢɬɶ ɫ ɩɨɦɨɳɶɸ ɞɪɭɝɨɣ ɩɪɨɰɟɞɭɪɵ ɩɨɫɬɪɨɟɧɢɹ ɢɫɤɭɫɫɬɜɟɧɧɨɝɨ ɰɟɧɬɪɚ ɩɨɜɟɪɯɧɨɫɬɢ.ɇɚ ɪɢɫ. 4, ɚ ɩɪɢɜɟɞɟɧɚ ɰɟɧɬɪɢɪɨɜɚɧɧɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɫɮɟɪɵ ɢ ɞɥɹ ɫɪɚɜɧɟɧɢɹ ɧɚ ɪɢɫ. 4, ɛ — ɧɟɰɟɧɬɪɢɪɨɜɚɧɧɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɬɨɣ ɠɟ ɫɮɟɪɵ.
ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɩɚɪɚɦɟɬɪɵɚɩɩɪɨɤɫɢɦɚɰɢɢ: m 50, N n 5 ɢ 5%-ɧɚɹ ɚɛɫɨɥɸɬɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɜɵɛɨɪɨɱɧɨɝɨ ɪɚɞɢɭɫɚ (21). ɋɧɢɠɟɧɢɟ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɧɟɰɟɧɬɪɢɪɨɜɚɧɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɫɜɹɡɚɧɨ ɫɨ ɫɥɭɱɚɣɧɵɦ ɫɦɟɳɟɧɢɟɦ ɫɪɟɞɧɟɜɵɛɨɪɨɱɧɨɝɨ ɰɟɧɬɪɚ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚ ɚɩɩɪɨɤɫɢɦɢɪɭɟɦɨɣ ɫɮɟɪɵ.Ɂɚɤɥɸɱɟɧɢɟ.
