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Файл:Функции Грина и проводимость. Учебное пособие
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Ƚɥɚɜɚ 10
ɉɊɈȼɈȾɂɆɈɋɌɖ ɈȾɇɈɆȿɊɇɈȽɈ ɆȿɌȺɅɅȺ
ȼ ɉȿɊȿɆȿɇɇɈɆ ɉɈɅȿ
10.1. Ʉɚɱɟɫɬɜɟɧɧɚɹ ɨɰɟɧɤɚ Ɇɨɬɬɚ ɞɥɹ ࣌ሺࢹ
ሻ
Ɋɚɜɟɧɫɬɜɨ ɧɭɥɸ ɫɬɚɬɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɞɧɨɦɟɪɧɨɝɨ ɦɟɬɚɥɥɚ ɫɬɚɜɢɬ ɜɨ-
߂ࣟൌ
ߥሺ߳ሻൌ
ͳ
ሺ
݁ܧ
Ͷ
ሻ
ɩɪɢ ɨɬɥɢɱɧɨɣ ɨɬ ɧɭɥɹ ɱɚɫɬɨɬɟ ɩɪɢɥɨɠɟɧ-
ɜ ɩɟɪɟɦɟɧɧɨɦ ɩɨɥɟ ɧɟ ɦɨɠɟɬ
ͳ
ʹ
݀
݀߳
ଶ
ሻ
ߪሺߗሻܧ
ൌ
ߨ
ȁ
߳
െ߳
ȁ
ȁ
ݖ
ଶ
ǡ
ͳ
ǡ
ߨݒ
ɢ ߳
, ɧɚɯɨɞɹɳɢɟɫɹ ɧɚ ɪɚɫɫɬɨɹ-
ȁ൏ȁ
߳
െ߳
ଶ
ሻ
ǡ
ߥሺ߳
ሻ
, ɱɬɨ ɟɫɬɶ ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ
ȁ
, ɜɟɪɨɹɬɧɨɫɬɶ ɩɟɪɟ-
ሺ
ͳͲǤͳ
ሺ
ͳͲǤʹ
, ɧɚɯɨɞɹɳɟɣɫɹ
ሺ
ͳͲǤ͵
ɩɪɨɫ ɨ ɜɟɥɢɱɢɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ߪሺߗ
ɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. Ʉɚɱɟɫɬɜɟɧɧɵɣ ɨɬɜɟɬ ɧɚ ɷɬɨɬ ɜɨɩɪɨɫ ɛɵɥ ɞɚɧ Ɇɨɬɬɨɦ
[11]. ɂɡ-ɡɚ ɜɚɠɧɨɝɨ ɡɧɚɱɟɧɢɹ ɷɬɨɝɨ ɪɟɡɭɥɶɬɚɬɚ ɜɨɫɩɪɨɢɡɜɟɞɟɦ ɢɧɬɭɢɬɢɜɧɵɣ ɜɵ-
ɜɨɞ Ɇɨɬɬɚ, ɚɞɚɩɬɢɪɨɜɚɧɧɵɣ ɤ ɨɞɧɨɦɟɪɧɨɦɭ ɫɥɭɱɚɸ.
ɉɪɨɜɨɞɢɦɨɫɬɶ ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ
ɛɵɬɶ ɫɥɟɞɫɬɜɢɟɦ ɩɪɨɰɟɫɫɚ ɞɢɮɮɭɡɢɢ ɡɚɪɹɞɚ, ɚ ɩɨɥɧɨɫɬɶɸ ɨɛɭɫɥɨɜɥɟɧɚ ɩɪɨɰɟɫɫɚɦɢ ɩɟɪɟɫɤɨɤɚ ɦɟɠɞɭ ɥɨɤɚɥɢɡɨɜɚɧɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ. Ȼɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɬ
ɮɚɤɬ, ɱɬɨ ɷɧɟɪɝɢɹ, ɩɨɝɥɨɳɚɟɦɚɹ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɧɚ ɟɞɢɧɢɰɟ ɞɥɢɧɵ ɨɛɪɚɡɰɚ,
ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧɚ ɤɚɤ
ɝɞɟ ܧ
– ɚɦɩɥɢɬɭɞɚ ɩɟɪɟɦɟɧɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ܧሺݐሻൌܧߗݐ.
ɋɨɫɬɨɹɧɢɹ ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɧɚɛɨɪ ɞɢɫɤɪɟɬɧɵɯ ɭɪɨɜɧɟɣ ɜ ɯɚɨɬɢɱɟɫɤɢ ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɹɦɚɯ ɫ ɩɥɨɬɧɨɫɬɶɸ ɫɨɫɬɨɹɧɢɣ
– ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ.
ɝɞɟ ݒ
ɉɭɫɬɶ ɢɦɟɸɬɫɹ ɞɜɟ ɹɦɵ ɫ ɭɪɨɜɧɹɦɢ ɷɧɟɪɝɢɢ ߳
ɧɢɢ ݖ ɞɪɭɝ ɨɬ ɞɪɭɝɚ. ɉɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɞɥɹ ɥɸɛɨɣ ɹɦɵ ɫ ɷɧɟɪɝɢɟɣ ߳
ɦɟɠɞɭ ɞɜɭɦɹ ɜɵɞɟɥɟɧɧɵɦɢ, ɢɦɟɟɬ ɦɟɫɬɨ
ɯɨɞɚ ɢɡ ɫɨɫɬɨɹɧɢɹ ܽ ɜ ɫɨɫɬɨɹɧɢɟ ܾ ɩɨɞ ɜɥɢɹɧɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɟɫɬɶ
ʹߨ
ɡɞɟɫɶ ɦɵ ɭɱɥɢ, ɱɬɨ ɷɧɟɪɝɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɷɥɟɤɬɪɨɧɚ ɫ ɩɨɥɟɦ ɟɫɬɶ ݁ܧሺݐሻݖ.
ɉɨɫɤɨɥɶɤɭ ɧɚɫ ɢɧɬɟɪɟɫɭɟɬ ɩɨɥɧɚɹ ɩɨɝɥɨɳɟɧɧɚɹ ɷɧɟɪɝɢɹ, ɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɧɹɬɶ ɜɨ ɜɧɢɦɚɧɢɟ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɹɦɚɦɢ, ɞɥɹ ɷɬɨɝɨ ɧɭɠɧɨ
(10.3) ɭɦɧɨɠɢɬɶ ɧɚ ݀ݖ ɢ ɩɪɨɢɧɬɟɝɪɢɪɨɜɚɬɶ, ɚ ɡɚɬɟɦ ɭɦɧɨɠɢɬɶ ɧɚ ɱɢɫɥɨ ɷɥɟɤɬɪɨ-
ɧɨɜ, ɭɱɚɫɬɜɭɸɳɢɯ ɜ
ɩɨɝɥɨɳɟɧɢɢ, ɬɨ ɟɫɬɶ ɧɚ ߗߥሺ߳
ɢɧɬɟɪɜɚɥɟ ɷɧɟɪɝɢɣ ߗ. Ɂɚɬɟɦ ɟɳɟ ɧɭɠɧɨ ɭɦɧɨɠɢɬɶ ɪɟɡɭɥɶɬɚɬ ɧɚ ɷɧɟɪɝɢɸ, ɩɨɝɥɨɳɚɟɦɭɸ ɜ ɨɞɧɨɦ ɚɤɬɟ ɩɟɪɟɯɨɞɚ, ɬɨ ɟɫɬɶ ɧɚ ߗ. ɉɨɞɟɥɢɜ ɡɚɬɟɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚ-
ଶ
ɠɟɧɢɟ ɧɚ ܧ
Ȁʹ, ɜ ɢɬɨɝɟ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɨɥɭɱɢɦ
ሻ
ሻ
ሻ
101
ߪሺߗሻ݁
ଶߥଶ
ଶ
ሺ
ሻ
߳
ߗ
ி
නȁݖ
ଶ
ȁ
݀ݖǤ
ሺ
ͳͲǤͶ
ሻ
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɫɥɭɱɚɣ ɦɚɥɵɯ ɱɚɫɬɨɬ ߗ߬
ɥɵɟ ɷɧɟɪɝɢɢ ɩɟɪɟɯɨɞɚ ߗൌ߳
, ɧɨ ɬɨɝɞɚ ɜɚɠɧɨ ɬɨ, ɱɬɨ ɛɥɚɝɨɞɚɪɹ ɜɟɪɨɹɬɧɨɫɬɢ
െ߳
اͳ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɚɠɧɵ ɦɚ-
ଶ
ɬɭɧɧɟɥɢɪɨɜɚɧɢɹ ɢɡ ɹɦɵ ܽ ɜ ɹɦɭ ܾ ɫɭɳɟɫɬɜɭɟɬ ɪɟɡɨɧɚɧɫɧɨɟ ɪɚɫɳɟɩɥɟɧɢɟ ɭɪɨɜɧɹ
ɩɨɪɹɞɤɚ ܫ
ɮɭɧɤɰɢɣ, ݈ൌݒ
ሺെݖȀʹԜ݈ሻ, ɮɚɤɬɨɪ ʹ ɜ ɷɤɫɩɨɧɟɧɬɟ ɨɬɜɟɱɚɟɬ ɩɟɪɟɤɪɵɬɢɸ ɜɨɥɧɨɜɵɯ
– ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɹɦɚɦɢ, ɚ ܫͳȀ߬
߬ଶ
ɟɫɬɶ ɟɞɢɧɫɬɜɟɧɧɵɣ
ଶ
ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɦɚɫɲɬɚɛ ɞɥɹ ɪɚɫɳɟɩɥɟɧɢɹ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɪɨɢɡɨɲɥɨ ɩɨɝɥɨɳɟ-
ɧɢɟ, ɷɬɨ ɪɚɫɳɟɩɥɟɧɢɟ ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ ߗ, ɬɨ ɟɫɬɶ
௭
ͳ
ି
ଶ௩
ߗ
బఛమ
݁
߬
ଶ
ǡ
ሺ
ͳͲǤͷ
ɨɬɤɭɞɚ ɩɨɥɭɱɚɟɦ ɭɫɥɨɜɢɟ ɧɚ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɹɦɚɦɢ
ݖݖ
ൌʹݒ߬ଶ൬
ߗ߬
ͳ
൰Ǥ
ଶ
ሺ
ͳͲǤ
ɗɬɨ ɨɩɪɟɞɟɥɹɟɬ ɧɢɠɧɢɣ ɩɪɟɞɟɥ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜ (10.4), ɩɪɢ ɬɚɤɢɯ ɡɧɚɱɟɧɢɹɯ
ݖ ɞɥɹ ɦɚɬɪɢɱɧɨɝɨ ɷɥɟɦɟɧɬɚ ɤɨɨɪɞɢɧɚɬɵ ɢɦɟɟɦ ݖ
ɨɧ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɧɚ ɦɚɫɲɬɚɛɟ ݒ
ݖ, ɚ ɩɪɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ
, ɱɬɨ ɞɚɟɬ ɨɰɟɧɤɭ ɞɥɹ ɢɧɬɟ-
߬ଶ
ɝɪɚɥɚ ɜ (10.4)
ଷଶ
ሺ
ݒ
߬ଶ
ሻ
ߗ߬ଶǤ
ሺ
ͳͲǤ
ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (10.4) ɢ ɭɱɢɬɵɜɚɹ (10.2), ɩɨɥɭɱɢɦ
ߪሺߗሻ݁
ଶ
ሺ
ݒ
߬ଶ
ሻሺ
ߗ߬
ଶ
ଶଶ
ሻ
ߗ߬ଶǤ
ሺ
ͳͲǤͺ
ɗɬɨ ɢ ɟɫɬɶ ɪɟɡɭɥɶɬɚɬ Ɇɨɬɬɚ.
10.2. ɍɫɪɟɞɧɟɧɢɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɨ ɛɟɫɩɨɪɹɞɤɭ ɩɪɢ ࢹ്
ȼɟɪɧɟɦɫɹ ɤ ɨɛɳɢɦ ɮɨɪɦɭɥɚɦ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ (8.79), (8.80), (8.81) ɢ ɩɟɪɟ-
ɩɢɲɟɦ ɢɯ ɜ ɧɟɫɤɨɥɶɤɨ ɢɧɨɣ ɮɨɪɦɟ. ɉɭɫɬɶ ݐ
ଵݐଶݐଷݐସ
ɷɬɢɯ ɩɟɪɟɦɟɧɧɵɯ
ሺସሻ
ܣ
ఆ
ሺ
ݐ
ଵǡݐଶǡݐଷǡݐସ
െܵ
መ
ఆԜଵଶ
ሺ
ሻ
ݐ
ଷǡݐସ
ൌൣܵ
ሻ
መ
ఆԜଶଶ
ൣܵ
መ
ܵ
መ
ఆԜଶଶ
Ԝଶଵ
ݐ
ሺ
ଵǡݐଶ
ሺ
ݐ
ݐ
ଷǡݐସ
ሻ
ଷǡݐସ
ܵ
ሻ
መ
Ԝଵଵ
ሻ
൧Ԝൣܵ
ܵ
መ
ሺ
Ԝଵଵ
መ
ఆԜଶଶ
ݐ
ଵǡݐଶ
ሺ
ሺ
ݐ
ଷǡݐସ
ሺ
ݐ
ሻ
ଵǡݐସ
െܵ
ሻ
ሻ
መ
െ
ܵ
ఆԜଶଵ
መ
Ԝଵଵ
ɬɨɝɞɚ ɮɨɪɦɭɥɭ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ (8.79) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
ߪሺߗሻൌ
௧
ଶ
݁
ݒ
ʹߨ
ቊ
න݀
ିஶ
ݐଵԜܣ
ሺସሻ
ఆ
ሺ
λǡݐǡݐ
ǡെλሻන݀
ଵ
ஶ
ݐଵԜܣ
௧
ఆ
, ɜɜɟɞɟɦ ɮɭɧɤɰɢɸ
ݐ
ଵǡݐଶ
ݐ
ଵǡݐସ
ሺ
λǡݐ
መ
ሻ
ܵ
Ԝଵଶ
ିଵ
ሻ
൧
ǡݐǡെλ
ଵ
ሺ
ሺ
ሺସሻ
ǡ
ሺ
ݐ
ଵǡݐଶ
ሻ
ቋ
ǤሺͳͲǤͳͲ
ሻ
൧
ሺ
ͳͲǤͻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
102
Ʉ ɫɨɠɚɥɟɧɢɸ, ɧɚɩɪɹɦɭɸ ɩɪɢɦɟɧɢɬɶ ɬɟɨɪɢɸ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɧɚ ɩɥɨɫ-
ሺସሻ
ሺ
ɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ ɞɥɹ ɭɫɪɟɞɧɟɧɢɹ ɜɟɥɢɱɢɧɵ ܣ
ȼɨɡɧɢɤɚɸɬ ɫɥɟɞɭɸɳɢɟ ɩɪɟɩɹɬɫɬɜɢɹ. ȿɫɥɢ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫɪɟɞɧɟɝɨ ɨɬ
ሺ
ݐ
ଵǡݐସ
መ
ሻ
ሺ
ܵ
Ԝଵଵ
ൣܵ
መ
Ԝଶଶ
ݐ
ଵǡݐସ
ିଵ
ሻ
൧
ɜ ɜɵɪɚɠɟɧɢɢ (9.2) ɩɨɬɪɟɛɨɜɚɥɨɫɶ ɪɚɫɫɦɨɬɪɟɬɶ ɨɞɧɭ
ఆ
ݐ
ଵǡݐଶǡݐଷǡݐସ
ɬɪɚɟɤɬɨɪɢɸ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɧɚ ɢɧɬɟɪɜɚɥɟ «ɜɪɟɦɟɧɢ»
ሻ
ɧɟ ɭɞɚɟɬɫɹ.
ሻ
ሺ
ɢ ɩɨɫɬɪɨɢɬɶ
ݐ
ସǡݐଵ
ɮɭɧɤɰɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɟɝɨ ɤɨɧɟɱɧɨɣ ɬɨɱɤɢ, ɬɨ ɞɥɹ ɭɫɪɟɞɧɟɧɢɹ
ሺସሻ
ሺ
ܣ
ݐ
ଵǡݐଶǡݐଷǡݐସ
ఆ
Ⱦɜɚ ɧɚ ɢɧɬɟɪɜɚɥɟ «ɜɪɟɦɟɧɢ»
ɫ ߱ൌߗ ɢ ɟɳɟ ɞɜɚ ɧɚ ɢɧɬɟɪɜɚɥɟ ሺݐ
ɡɚɬɪɭɞɧɟɧɢɹɦ ɫ ɜɜɟɞɟɧɢɟɦ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɚ ɧɚɥɢɱɢɟ ɞɜɭɯ ɦɚɬɪɢɰ ܮ
ሻ
ɩɪɢɞɟɬɫɹ ɪɚɫɫɦɨɬɪɟɬɶ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ 4 ɫɥɭɱɚɣɧɵɯ ɩɪɨɰɟɫɫɚ.
ሺ
ሻ
ݐ
ɨɞɢɧ ɫ ߱ൌͲ ɜ ɦɚɬɪɢɰɟ ܮ
ସǡݐଷ
ሻ
. ɇɚɥɢɱɢɟ ɩɚɪɵ ɢɧɬɟɪɜɚɥɨɜ ɩɪɢɜɨɞɹɬ ɤ
ଶǡݐଵ
(8.40), ɚ ɞɪɭɝɨɣ
ɩɪɢɜɨɞɢɬ ɤ ɩɪɨɛɥɟɦɚɦ ɜ ɫɨɫɬɚɜɥɟɧɢɢ ɭɪɚɜɧɟɧɢɹ, ɚɧɚɥɨɝɢɱɧɨɝɨ ɭɪɚɜɧɟɧɢɸ ɞɢɮɮɭɡɢɢ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɜɨɡɧɢɤɲɟɣ ɩɪɨɛɥɟɦɵ ɦɵ ɩɪɢɦɟɧɢɦ ɦɟɬɨɞ ɩɪɹɦɨɝɨ ɭɫɪɟɞɧɟɧɢɹ
ɨɩɪɟɞɟɥɟɧɧɵɯ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ ɩɨ ɩɨɥɹɦ ߞ, ɢɫɩɨɥɶɡɭɹ ɝɚɭɫɫɨɜɨɫɬɶ ɷɬɢɯ ɩɨɥɟɣ
ɢ ɨɬɫɭɬɫɬɜɢɟ ɤɨɪɪɟɥɹɰɢɣ ɜ ɪɚɡɧɵɟ
ɦɨɦɟɧɬɵ «ɜɪɟɦɟɧɢ». Ɍɚɤɨɟ ɭɫɪɟɞɧɟɧɢɟ ɩɨɡɜɨɥɢɬ ɩɨɥɭɱɢɬɶ ɪɟɤɭɪɪɟɧɬɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɫɥɭɱɚɣɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ. ɗɬɢ
ɪɟɤɭɪɪɟɧɬɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɦɵ ɩɨɩɵɬɚɟɦɫɹ ɪɚɡɪɟɲɢɬɶ ɫ ɩɨɦɨɳɶɸ ɜɜɟɞɟɧɢɹ ɩɪɨɢɡɜɨɞɹɳɢɯ ɮɭɧɤɰɢɣ, ɧɚ ɤɨɬɨɪɵɟ ɩɨɥɭɱɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜ ɱɚɫɬɧɵɯ ɩɪɨɢɡɜɨɞɧɵɯ. Ɋɟɲɟɧɢɟ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ ɩɨɡɜɨɥɢɬ ɜɵɱɢɫɥɢɬɶ ɜɟɥɢɱɢɧɭ
ሺସሻ
ሺ
ܣ
λǡݐǡݐ
ఆ
ሻ
ǡെλ
ɢ ɧɚɣɬɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ.
ଵ
Ⱦɥɹ ɪɟɚɥɢɡɚɰɢɢ ɷɬɨɣ ɩɪɨɝɪɚɦɦɵ ɜɜɟɞɟɦ ɟɳɟ ɞɜɟ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ɮɭɧɤɰɢɢ
መ
ൌൣܵ
ఆԜଶଶ
ܣ
ൌൣܵ
መ
ఆԜଶଶ
ɩɪɢ ɷɬɨɦ ɮɭɧɤɰɢɹ ܣ
ܣ
ሺ
ሺଶሻ
ఆ
ሺଷሻ
ఆ
ሺ
ݐ
ݐ
ଷǡݐସ
ଷǡݐସ
ሺ
ݐ
ሺ
ݐ
ൈԜൣܵ
ሺଶሻ
ఆ
ൈൣܵ
ଷǡݐସ
ሻ
ଶǡݐଷǡݐସ
ሻ
ሺ
ሻ
ܵ
ൌ
መ
ሺ
ܵ
ݐ
Ԝଵଵ
ଷǡݐସ
መ
ሺ
ݐ
ఆԜଶଶ
ଶǡݐସ
ሻ
ݐ
ൌ
ଷǡݐସ
መ
ሺ
ݐ
Ԝଵଵ
ଷǡݐସ
መ
ሺ
ݐ
ఆԜଶଶ
ሻ
ɨɛɥɚɞɚɟɬ ɨɱɟɜɢɞɧɵɦ ɫɜɨɣɫɬɜɨɦ
ܣ
௧య՜௧
ర
௧భ՜௧
௧మ՜௧
ሻ
ଷǡݐସ
ሺଶሻ
ఆ
ሻ
ሻ
െܵ
ሺ
ܣ
మ
െܵ
መ
ܵ
Ԝଵଵ
య
መ
መ
ሻ
ܵ
ݐ
ଷǡݐସ
ሺସሻ
ఆ
መ
ఆԜଵଶ
ܣ
ఆԜଵଶ
Ԝଵଵ
ሺଷሻ
ఆ
ሺ
ݐ
ଵǡݐଶǡݐଷǡݐସ
ሺ
ݐ
ଷǡݐସ
ሺ
ݐ
ଶǡݐସ
ሺ
ݐ
ଶǡݐଷǡݐସ
ሺ
ݐ
ଷǡݐସ
ሺ
ݐ
ଷǡݐସ
ሻ
ൌͳǤ
ሻ
ൌ
መ
ሻ
ሺ
ܵ
Ԝଶଵ
ିଵ
ሻ
൧
Ǣ
ሻ
ൌ
መ
ሻ
ܵ
Ԝଶଵ
ିଵ
ሻ
൧
ሻ
ݐ
൧ൈ
ଷǡݐସ
ሺ
ሻ
ݐ
൧Ԝൈ
ଷǡݐସ
ሺ
ͳͲǤͳͳ
ሺ
ͳͲǤͳʹ
ሺ
ͳͲǤͳ͵
Ɇɵ ɢɫɩɨɥɶɡɭɟɦ ɷɬɢ ɫɨɨɬɧɨɲɟɧɢɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɇɵ ɩɨɥɭɱɢɦ ɞɢɮɮɟ-
ሺଶሻ
ሺ
ɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ܣ
ఆ
ሻ
ݐ
ɤɚɤ ɮɭɧɤɰɢɢ ݐ
ଷǡݐସ
, ɪɟɲɢɜ ɟɝɨ, ɦɵ
ଷെݐସ
ɧɚɣɞɟɦ ɷɬɭ ɮɭɧɤɰɢɸ. ɉɨɫɥɟ ɷɬɨɝɨ ɦɵ ɩɨɥɭɱɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ
,
ሻ
ሻ
ሻ
103
ሺଷሻ
ሺ
ݐ
ܣ
ఆ
ଶǡݐଷǡݐସ
ሻ
ɩɨ ɩɟɪɟɦɟɧɧɨɣ ݐ
ɭɫɥɨɜɢɟ. ɇɚɤɨɧɟɰ, ɦɵ ɧɚɣɞɟɦ ܣ
ɢ ɩɪɢ ɷɬɨɦ ɢɫɩɨɥɶɡɭɟɦ ܣ
ଷ
ሺସሻ
ሺ
ఆ
ݐ
ଵǡݐଶǡݐଷǡݐସ
ሻ
ɚɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ.
ఆ
ሺଶሻ
ሺ
ݐ
ଷǡݐସ
ሻ
ɤɚɤ ɝɪɚɧɢɱɧɨɟ
ɗɬɨ ɨɛɳɚɹ ɢɞɟɹ. Ɉɞɧɚɤɨ ɟɟ ɧɟɜɨɡɦɨɠɧɨ ɪɟɚɥɢɡɨɜɚɬɶ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ, ɩɨ-
ሺଶሻ
ሺ
ɬɨɦɭ ɱɬɨ ɬɨɥɶɤɨ ɜ ɮɭɧɤɰɢɢ ܣ
ఆ
ሻ
ݐ
ɜɨɡɧɢɤɚɸɬ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ܵ
ଷǡݐସ
ɫ ɨɞɧɢɦ ɧɚɛɨɪɨɦ ɚɪɝɭɦɟɧɬɨɜ, ɧɚɩɪɢɦɟɪ, ݐ
ሺସሻ
ܣ
ఆ
ሺ
ݐ
ଵǡݐଶǡݐଷǡݐସ
ሻ
ɷɬɨ ɧɟ ɬɚɤ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɛɨɣɬɢ ɷɬɨ ɡɚɬɪɭɞɧɟɧɢɟ, ɧɚɩɢɲɟɦ,
. ȼ ɮɭɧɤɰɢɹɯ ܣ
ଷǡݐସ
ሺଷሻ
ఆ
ሺ
ݐ
መ
ǡݐଷǡݐ
ଶ
ɩɨɥɶɡɭɹɫɶ ɩɨɥɭɝɪɭɩɩɵɜɵɦ ɫɜɨɣɫɬɜɨɦ ܵ-ɦɚɬɪɢɰɵ (8.45):
ൣܵ
መ
ሺ
ሻ
ఆԜଶଶ
መ
Ԝଵଵ
ஶ
ሺ
ݐ
ଵǡݐଶ
ݐ
ଵǡݐଶ
ஶ
ሻ
ܵ
ൌൣܵ
ൈൣܵ
ൌ ሺെͳ
ୀ
భୀ
మ
ൈ
ൣܵ
ܵ
መ
ఆԜଶଶ
መ
ఆԜଶଶ
መ
Ԝଵଵ
ൣܵ
መ
భା
ሻ
መ
Ԝଵଶ
Ԝଵଵ
ሺ
ሺ
ሺ
ݐ
ݐ
ݐ
ሺ
ଵǡݐସ
ଶǡݐସ
ଶǡݐସ
మ
ሺ
ݐ
ݐ
ଵǡݐଶ
ൣܵ
መ
ൣܵ
ଵǡݐଶ
ሻ
ܵ
ሻ
ሻ
መ
ఆԜଶଵ
ఆԜଶଶ
ሻ
መ
Ԝଵଵ
ܵ
ܵ
መ
ሻ
ܵ
መ
ܵ
Ԝଵଵ
መ
ఆԜଶଵ
መ
Ԝଵଶ
ሺ
ሺ
ݐ
Ԝଶଵ
ሺ
ݐ
ଵǡݐଶ
ݐ
ଵǡݐସ
ଵǡݐଶ
ሺ
ሺ
ݐ
ሺ
ݐ
ሺ
ݐ
ሻ
ݐ
ଶǡݐସ
ଶǡݐସ
ሻ
ଵǡݐଶ
ଵǡݐଶ
ሻ
ܵ
መ
ܵ
ఆԜଶଶ
ሻ
൧
መ
ఆԜଵଶ
൧
ିଵ
ሻ
ሻ
ሻ
൧
మାଵ
ܵ
ܵ
መ
ሺ
ൌ
መ
ఆԜଵଶ
Ԝଶଵ
ሺ
ݐ
ݐ
ଶǡݐସ
మ
ሺ
ሺ
ଶǡݐସ
Ǥ
ݐ
ݐ
ሻ
ଶǡݐସ
ଶǡݐସ
ሻ
൧
భାଵ
൧
ିଵ
ሻ
൧
ൈ
ିଵ
ሻ
൧
ൌ
భ
ൈ
ఓఔ
ሺ
ሺ
ݐ
ǡݐ
ሻ
ସ
ͳͲǤͳͶ
ɢ
ሻ
ሻ
Ɉɛɪɚɬɢɦ ɬɟɩɟɪɶ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɜ ɩɟɪɜɨɦ ɦɧɨɠɢɬɟɥɟ ɩɨɞ ɡɧɚɤɨɦ ɫɭɦɦɵ
ɨɛɹɡɚɬɟɥɶɧɨ ɜɫɬɪɟɱɚɸɬɫɹ ݊
ɧɟ ɩɚɪɧɵɯ ɦɧɨɠɢɬɟɥɟɣ ߞ
ଵ
כ
ɧɚ ɢɧɬɟɪɜɚɥɟ
ሺ
ݖଶǡݖ
ሻ
ଵ
. ɗɬɨ
ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɫɨɯɪɚɧɢɬɫɹ ɢ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɦɵ ɭɱɬɟɦ ɢ ɩɟɪɜɵɣ ɦɧɨɠɢɬɟɥɶ
ɜ ɮɨɪɦɭɥɟ (10.11), ɨɬɧɟɫɟɧɧɵɣ ɤ ɬɨɦɭ ɠɟ ɢɧɬɟɪɜɚɥɭ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɬɢ ɧɟ ɩɚɪ-
כ
ɧɵɟ ߞ
ɩɪɢ ɭɫɪɟɞɧɟɧɢɢ ɦɨɝɭɬ ɛɵɬɶ ɤɨɦɩɟɧɫɢɪɨɜɚɧɵ ɬɨɥɶɤɨ ߞ ɜ ɬɟɯ ɠɟ ɬɨɱɤɚɯ ɢɡ
ɜɬɨɪɨɝɨ ɦɧɨɠɢɬɟɥɹ ɜ ɫɭɦɦɟ (10.14), ɬɨ ɟɫɬɶ ɩɨɫɥɟ ɭɫɪɟɞɧɟɧɢɹ ɨɫɬɚɧɭɬɫɹ ɬɨɥɶɤɨ
ɫɥɚɝɚɟɦɵɟ ɜ ɫɭɦɦɟ ɫ ݊
. ɋɝɪɭɩɩɢɪɨɜɚɜ ɫɨɦɧɨɠɢɬɟɥɢ ɭɞɨɛɧɵɦ ɞɥɹ ɞɚɥɶɧɟɣ-
ଵൌ݊ଶ
ɲɟɝɨ ɫɩɨɫɨɛɨɦ, ɩɨɥɭɱɢɦ
ൣܵ
መ
ఆԜଶଶ
ሺ
ݐ
ଵǡݐସ
ൈ
ஶ
መ
ሺ
ൣܵ
ఆԜଶଵ
መ
ሺ
ݐ
ൣܵ
ఆԜଶଶ
ୀ
መ
ሻ
ሺ
ܵ
ݐ
Ԝଶଵ
ଶǡݐସ
መ
ሻ
ሺ
ݐ
ଶǡݐସ
ሻ
ܵ
Ԝଵଵ
ൣܵ
ݐ
ଵǡݐସ
ൣܵ
መ
መ
ఆԜଵଶ
ఆԜଶଶ
ିଵ
ሻ
൧
՜
ሺ
ݐ
ଶǡݐସ
ሺ
ݐ
ଶǡݐସ
መ
ሻ
ሺ
ܵ
Ԝଵଵ
ݐ
ଵǡݐଶ
ଵǡݐଶ
ሻ
൧
ାଵ
൧
መ
ሻ
ሺ
ܵ
Ԝଵଶ
መ
ሻ
ሺ
ܵ
ݐ
Ԝଵଵ
Ǥ
ݐ
ଵǡݐଶ
ଵǡݐଶ
ሻ
൧
ൈ
ାଵ
ሻ
൧
ሺ
ͳͲǤͳͷ
ȼɜɟɞɟɦ ɬɟɩɟɪɶ ɜɟɥɢɱɢɧɵ
ܤ
ܤ᪄Ԣ
᪄
ሺ
ሺ
ݐ
ଵെݐଶ
ݐ
ଷെݐସ
ሻ
ሻ
ൌۦܤԢ
ൌۦܤ
ݐ
ݐ
ሺ
ሺ
ଵǡݐଶ
ଵǡݐଶ
ݐ
ଷǡݐସ
ݐ
ଷǡݐସ
መ
ሻ
ሺ
ܵ
Ԝଵଶ
መ
ሻ
ሺ
ܵ
Ԝଵଵ
መ
ሻ
ܵ
Ԝଶଵ
መ
ሻ
ܵ
Ԝଵଵ
መ
ሺ
ൣܵ
ሺ
ሻ
ۧ
ݐ
ଵǡݐଶ
ሺ
ሻ
ۧ
ݐ
ଷǡݐସ
ൌൽ
ൌൽ
ൣܵ
ൣܵ
ൣܵ
ఆԜଶଵ
መ
ఆԜଶଶ
መ
ఆԜଵଶ
መ
ఆԜଶଶ
ሺ
ݐ
ݐ
ሺ
ሺ
ଵǡݐଶ
ଵǡݐଶ
ݐ
ଷǡݐସ
ݐ
ଷǡݐସ
ሻ
൧
ඁǡሺͳͲǤͳ
ሻ
൧
ሻ
൧
ඁǡሺͳͲǤͳ
ሻ
൧
104
ሻ
ሻ
ሻ
᪄
ൌൽ
ൣܵ
ൣܵ
መ
ఆԜଶଶ
መ
ఆԜଵଶ
ሺ
ݐ
ܥ
ଶെݐଷǡݐଷെݐସ
ሺ
ݐ
ଶǡݐସ
ሺ
ሻ
ݐ
ܵ
ଶǡݐସ
െܵ
ሻ
ܵ
መ
መ
ఆԜଵଶ
መ
Ԝଶଵ
Ԝଵଵ
ሻ
ሺ
ሻ
ݐ
ଶǡݐସ
ሺ
ሻ
ݐ
൧
ଶǡݐସ
ሺ
ሻ
ݐ
ܵ
ଷǡݐସ
ൌۦܥ
൧
ାଵ
መ
Ԝଶଵ
ൣܵ
ሺ
መ
ݐ
ሺ
ఆԜଶଶ
ଷǡݐସ
ݐ
ଶǡݐଷǡݐସ
ሺ
ݐ
ሻ
൧ൿ
ଷǡݐସ
ሻ
ۧ
ൌ
መ
ሻ
ሺ
ݐ
ଷǡݐସ
ሻ
െ
ሺ
ͳͲǤͳͺ
ܵ
Ԝଵଵ
Ǥ
ɋ ɩɨɦɨɳɶɸ (10.15), (10.16, 10.17) ɢ (10.18) ɫɪɟɞɧɟɟ ɨɬ ɮɭɧɤɰɢɢ (10.9) ɦɨɠɧɨ
ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
ሺସሻ
᪄
ሺ
ܣ
ൌሾܤ
ݐ
ଵെݐଶǡݐଶെݐଷǡݐଷെݐସ
ఆ
ஶ
᪄
ሺ
ݐ
ଵെݐଶ
ୀ
ሻ
െܤ
᪄
ାଵ
ሺ
ݐ
ɝɞɟ ɛɵɥɨ ɭɱɬɟɧɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɱɬɨ ɜɟɥɢɱɢɧɵ ܤ
ሻ
ൌർܣ
ଵെݐଶ
ሺସሻ
ሺ
ఆ
᪄
ሻ
ሿ
Ԝܥ
ሺ
ݐ
ݐ
ଵǡݐଶǡݐଷǡݐସ
ሺ
ݐ
ଶെݐଷǡݐଷെݐସ
ሻ
ɢ ܥ
ଵǡݐଶ
ሻ
ሺ
ݐ
ଶǡݐଷǡݐସ
ൌ
ሻ
ǡ
ሺ
ͳͲǤͳͻ
ሻ
ɭɫɪɟɞɧɹɸɬɫɹ ɧɟɡɚɜɢɫɢɦɨ, ɬɚɤ ɤɚɤ ɢɧɬɟɪɜɚɥɵ, ɧɚ ɤɨɬɨɪɵɯ ɨɧɢ ɨɩɪɟɞɟɥɟɧɵ, ɧɟ ɩɟɪɟɫɟɤɚɸɬɫɹ. ɗɬɢ ɜɟɥɢɱɢɧɵ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɫɥɟɞɭɸɳɢɦ «ɝɪɚɧɢɱɧɵɦ» ɭɫɥɨɜɢɹɦ
᪄
ሺͲሻ
ܤ
᪄
ሺ
Ͳǡݐ
ܥ
ሺସሻ
᪄
ሺ
ܣ
ఆ
ሻ
ଷെݐସ
Ͳǡݐ
ଶെݐଷǡݐଷെݐସ
ൌܤԢ
ൌܤ᪄Ԣ
ሺ
ݐ
ሺͲሻ
ଷെݐସ
ሻ
ൌܥ
ൌߜ
ǡ
ሻ
െܤԢ
ାଵ
ሺ
ݐ
ଶെݐଷǡݐଷെݐସ
ሺ
ݐ
ଷെݐସ
ሺ
ͳͲǤʹͲ
ሻ
ǡ
ሻ
Ǥ
ሺ
ͳͲǤʹͳ
ሺ
ͳͲǤʹ͵
ሻ
ሻ
ሻ
ሻ
ሻ
ȼɵɪɚɡɢɦ ɬɟɩɟɪɶ ɭɫɪɟɞɧɟɧɧɭɸ ɩɪɨɜɨɞɢɦɨɫɬɶ ɐሺߗ
ሻ
ɱɟɪɟɡ ɷɬɢ ɜɟɥɢɱɢɧɵ. ɂɡ
ɮɨɪɦɭɥɵ (10.10) ɩɨɫɥɟ ɭɫɪɟɞɧɟɧɢɹ, ɢɫɩɨɥɶɡɭɹ ɩɟɪɜɭɸ ɱɚɫɬɶ ɮɨɪɦɭɥɵ (10.19),
ɩɨɥɭɱɚɟɦ
ɐሺߗሻൌ
௧
ଶ
ݒ
݁
ʹߨ
ቊ
න݀
ିஶ
ݐଵԜܣ
ൌ
ሺସሻ
᪄
ఆ
݁
ሺ
λǡݐെݐ
ଶ
ݒ
ߨ
ஶ
න݀
ǡλሻන݀
ଵ
᪄
ݐଵԜܣ
ሺସሻ
ఆ
ሺ
λǡݐ
௧
ஶ
ǡλሻǡ
ଵ
ݐଵԜܣ
ሺସሻ
᪄
ሺ
λǡݐ
ఆ
ଵ
െݐǡλ
ሻ
ቋ
ൌ
ሺ
ͳͲǤʹͶ
ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ݐ, ɤɚɤ ɢ ɨɠɢɞɚɥɨɫɶ, ɢɫɱɟɡɥɚ. ɂɫɩɨɥɶɡɭɹ ɜɬɨɪɭɸ ɱɚɫɬɶ ɮɨɪɦɭɥɵ
(10.19), ɩɨɥɭɱɢɦ
ஶ
ஶ
ଶ
ݒ
݁
ɐሺߗሻൌ
ߨ
න݀
ݐሾܤ
ୀ
᪄
ሺλሻ
െܤ
᪄
ାଵ
ȼɜɟɞɟɦ ɬɟɩɟɪɶ ɩɪɨɢɡɜɨɞɹɳɢɟ ɮɭɧɤɰɢɢ ɞɥɹ ɜɟɥɢɱɢɧ ܤ
ஶ
ିଵ
᪄
ሺݐሻ
ܤሺݔǡݐሻൌܤ
ୀଵ
ݔ
ሺλሻ
ǡ
᪄
ሺ
ሿ
ݐǡλሻǤ
Ԝܥ
᪄
᪄
ሺݐሻ
ɢ ܥ
ሺݐሻ
ؠܥ
ሺ
ͳͲǤʹͷ
᪄
ሺ
ሺ
ͳͲǤʹ
ݐǡλ
105
ሻ
ሻ
ሻ
ሻ
ஶ
᪄
ሺݐሻ
ݔ
ܥሺݔǡݐሻൌܥ
ୀ
ǡ
ɬɨɝɞɚ ɫɭɦɦɭ ɜ (10.25) ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɷɬɢ ɮɭɧɤɰɢɢ, ɩɨɥɨɠɢɜ ݔ
ିఝ
ൌ݁
ݔ
ଶ
ɢ ɭɱɢɬɵɜɚɹ
ଶగ
݀߮
Ԝݔ
ݔ
න
ʹߨ
ൌߜǤ
ଵ
ଶ
Ɋɟɡɭɥɶɬɚɬ ɛɭɞɟɬ ɬɚɤɨɜ
ஶ
ɐሺߗሻൌ
ଶ
ݒ
݁
න݀
ߨ
ݐන
ଶగ
݀߮
ሾ
ͳെሺͳെݔ
ʹߨ
ଵ
ሻܤሺ
ሻ
ሿ
ݔ
ǡλ
ܥሺݔଶǡݐሻǤ
ଵ
10.3. Ɋɟɤɭɪɪɟɧɬɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɫɪɟɞɧɢɯ ɜɟɥɢɱɢɧ
᪄
ሺ࢚ሻ
10.3.1. Ɋɟɤɭɪɪɟɧɬɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ
ɋɨɫɬɚɜɥɟɧɢɟ ɭɪɚɜɧɟɧɢɣ ɧɚ ɷɬɢ ɜɟɥɢɱɢɧɵ ɧɚɱɧɟɦ ɫ ܤ
᪄
ɦɟɬɢɦ, ɱɬɨ ܤ᪄Ԣ
ሺݐሻ
ɬɟɥɶɧɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ߞߞ
ɜɚɧɢɢ (8.61) ɫ ߱
ଵ
ሺݐሻ
ൌܤ
. ɗɬɨ ɜɵɬɟɤɚɟɬ ɢɡ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɫɪɟɞɧɟɝɨ ɨɬɧɨɫɢ-
כ
ɢ ɬɨɝɨ ɮɚɤɬɚ, ɱɬɨ ɩɪɢ ɤɚɥɢɛɪɨɜɨɱɧɨɦ ɩɪɟɨɛɪɚɡɨ-
ൌߗ ɜ ɜɵɪɚɠɟɧɢɹɯ ɬɢɩɚ (10.16) ɢ (10.17) ɦɧɨɠɢɬɟɥɢ ɬɢɩɚ ݁
ɫɨɤɪɚɳɚɸɬɫɹ ɢ ɩɪɢ ɷɬɨɦ
ܵ
ܵ
ܵ
መ
መ
Ԝଵଶ
Ԝଵଵ
መ
ܵ
ఆԜଶଵ
መ
ఆԜଶଶ
ሺ
ሺ
ሼ
ሼߞǡߞ
ߞǡߞ
ሺ
ሼߞǡߞ
ሺ
ሼ
ߞǡߞ
כ
ሽሻ՜ܵ
כ
ሻ
ሽ
՜ܵ
כ
ሽሻ՜ܵ
כ
ሻ
ሽ
መ
መ
ିఆԜଵଵ
՜ܵ
ିఆԜଵଶ
መ
Ԝଶଵ
መ
Ԝଶଶ
൫ሼߞ
൫൛ߞ
൫ሼߞ
൫൛ߞ
כ
ሚ
ሚ
ǡߞ
ఆ
ఆ
כ
ሚ
ሚ
ǡߞ
ఆ
ఆ
כ
ሚ
ሚ
ǡߞ
ఆ
ఆ
כ
ሚ
ሚ
ǡߞ
ൟ൯ൌܵ
ఆ
ఆ
ሽ൯ൌܵ
ൟ൯ൌܵ
ሽ൯ൌܵ
መ
መ
መ
כ
መ
ఆԜଵଶ
כ
ఆԜଵଵ
כ
Ԝଶଵ
כ
Ԝଶଶ
൫ሼߞ
൫൛ߞ
൫ሼߞ
൫൛ߞ
כ
ሚ
ሚ
ǡߞ
ఆ
ఆ
כ
ሚ
ሚ
ǡߞ
ఆ
ఆ
כ
ሚ
ሚ
ǡߞ
ఆ
ఆ
כ
ሚ
ሚ
ǡߞ
ൟ൯ൌܵ
ఆ
ఆ
ɝɞɟ ɦɵ ɭɱɥɢ ɫɜɨɣɫɬɜɨ (8.56).
ɉɨ ɫɨɨɛɪɚɠɟɧɢɹɦ ɭɞɨɛɫɬɜɚ ɦɵ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ܤ
ɞɥɹ ܤԢ
ሺ
ݐǡͲሻ. ɂɫɩɨɥɶɡɭɹ ɤɚɥɢɛɪɨɜɨɱɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ (8.61) ɞɥɹ ܵ
ɩɨɥɭɱɢɦ
ܤԢ
ൌ݁
ሺ
ݐǡͲሻൌ
ଶఆ௧
ൣܵ
ൣܵ
መ
መ
Ԝଵଶ
Ԝଶଶ
መ
ൣܵ
ఆԜଵଶ
መ
ൣܵ
ఆԜଶଶ
൫ݐǡͲǡ൛ߞ
൫ݐǡͲǡ൛ߞ
ሺ
ݐǡͲሻܵ
ሺ
ݐǡͲሻܵ
ሚ
ఆ
ሚ
ఆ
ǡߞ
ǡߞ
መ
ሺ
ݐǡͲሻ൧
Ԝଶଵ
መ
ሺ
ݐǡͲሻ൧
Ԝଵଵ
כ
ሚ
መ
ሺ
ൟ൯ܵ
Ԝଶଵ
ఆ
כ
ሚ
መ
ሺ
ൟ൯ܵ
Ԝଵଵ
ఆ
ሽ൯ൌܵ
ൟ൯ൌܵ
ሽ൯ൌܵ
ݐǡͲሻ൧
ݐǡͲሻ൧
᪄
ሺݐሻ
, ɩɪɢ ɷɬɨɦ ɫɪɚɡɭ ɨɬ-
כ
ሚ
൫ሼߞ
ఆԜଶଵ
ఆ
כ
ሚ
൫൛ߞ
ఆ
כ
ሚ
൫ሼߞ
ǡߞ
ఆ
כ
ሚ
൫൛ߞ
ǡߞ
ఆ
᪄
ሺݐሻ
ɢɡ ɜɵɪɚɠɟɧɢɹ
ǡߞ
ǡߞ
ሚ
ሚ
ሚ
ఆ
ఆ
መ
መ
መ
Ԝଵଵ
መ
ఆԜଶଶ
Ԝଵଶ
ൌ
ǡ
ሚ
ఆ
ఆ
ሺ
ͳͲǤʹ
ఝ
ൌ݁
ଵ
ሺ
ͳͲǤʹͺ
ሺ
ͳͲǤʹͻ
ఠభ௧
ሽ൯ǡ
ൟ൯ǡ
ሽ൯ǡ
ൟ൯ǡሺͳͲǤ͵Ͳ
መ
ሺ
ݐǡͲ
ఆ
ሺ
ͳͲǤ͵ͳ
ɢ
ሻ
ሻ
ሻ
ሻ
ሻ
,
ሻ
ɞɚɥɟɟ ɜɵɪɚɠɚɟɦ ܤԢ
መ
ܵ
ሺ
ݐߜǡͲሻൌ݁
ఠ
ሺ
ݐߜǡͲሻ ɱɟɪɟɡ ܤԢ
ഘಿశభ
መ
ሺ
ܵ
ఠ
ሺ
ሻ
ݐǡͲ
ɫ ɩɨɦɨɳɶɸ ɫɨɨɬɧɨɲɟɧɢɹ
ݐǡͲሻǡ᩷ܮ
ఠேାଵ
ൌߞ
ሚ
ఠ
106
Ԝߪොାߞ
כ
ሚ
Ԝߪොିǡ
ఠ
ሺ
ͳͲǤ͵ʹ
ሻ
ɩɨɥɭɱɚɟɦ
መ
Ԝଵଶ
Ԝଶଶ
መ
ܵ
መ
ܵ
መ
Ԝଵଵ
Ԝଶଵ
ଶ
Ԝଵଶ
Ԝଶଶ
᪄
.
መ
ܵ
መ
ܵ
ൈ
൯൧
ൌ
൯൧
Ԝଶଵ
ቇǤሺͳͲǤ͵͵
Ԝଵଵ
መ
ܵ
Ԝଶଵ
ቇǤሺͳͲǤ͵Ͷ
መ
ܵ
Ԝଵଵ
ሺݐሻ൯ǡሺ
ͳͲǤ͵ͷ
ሺ
ͳͲǤ͵
ሺ
ͳͲǤ͵
ൣ൫ܵ
ሺ
ݐߜǡͲሻൌ݁
ܤԢ
ଶఆሺ௧ାఋ
ሻ
ൌሺͳʹ݅݊ߗߜሻԜܤԢ
መ
መ
ܵ
ܵ
Ԝଶଶ
Ԝൈቆͳ݊
ൈቆെʹܤԢ
ଶ
ሚ
ߞ
ఆ
ሺ
ݐߜǡͲሻെܤԢ
ܤԢ
ሺ
ݐǡͲሻܤԢ
ߞ
כ
መ
ܵ
ሺ
Ԝଵଶ
ݐǡͲሻ݁
Ԝଵଵ
െ݊ଶߞ
መ
ܵ
Ԝଶଵ
ሺ
ݐǡͲሻൌʹ݅݊ߗߜܤԢ
ିଶఆ௧
ɍɫɪɟɞɧɹɟɦ, ɭɱɢɬɵɜɚɹ ɩɪɢ ɷɬɨɦ
߬
݀ݐ
ൌʹ݅݊ߗ߬ଶܤ
ଶ
᪄
ሺݐሻ
᪄
ሺݐሻ
݀ܤ
ɜɜɟɞɟɦ ɜɪɟɦɹ ɢ ɱɚɫɬɨɬɭ ɜ ɟɞɢɧɢɰɚɯ ߬
ݏൌݐȀ߬
᪄
ɬɨɝɞɚ ɭɪɚɜɧɟɧɢɹ ɧɚ ܤ
ɩɪɢ ɷɬɨɦ ܤ
݀ܤ
ؠͳ, ɚ ɧɚɱɚɥɶɧɨɟ ɭɫɥɨɜɢɟ ɞɥɹ ɜɟɥɢɱɢɧ ܤ
ɩɪɢɦɭɬ ɨɤɨɧɱɚɬɟɥɶɧɵɣ ɜɢɞ
᪄
݀ݏ
ൌ݅݊ߚܤ
ଶ
݊
᪄
ሺ
ܤ
᪄
መ
ߞ
Ԝଵଶ
መ
ൣ൫ܵ
ߞ
Ԝଶଶ
כ
ሚ
ሚ
ߞ
ఆ
ఆ
መ
መ
ܵ
ܵ
Ԝଶଶ
Ԝଵଵ
መ
መ
ܵ
ܵ
Ԝଵଶ
Ԝଶଵ
ଶ
ۧ
ۦȁߞȁ
ଶ
᪄
݊
൫ܤ
ଶ
ǡ᩷ߚൌʹߗ߬ଶǡ
ଶ
ܤ
ାଵ
ሚ
መ
መ
ܵ
൯൫ܵ
ఆ
Ԝଶଶ
Ԝଶଵ
כ
ሚ
መ
መ
ܵ
൯൫ܵ
Ԝଵଶ
ఆ
ሺ
ݐǡͲሻൈ
Ԝଵଵ
െ݊ଶߞכߞ݊ଶߞ
ሺ
ݐǡͲሻ݊
ሺ
ݐǡͲሻ݁
ܤԢ
ൌߜȀ߬
, ɩɨɥɭɱɚɟɦ
ଶ
᪄
ሺݐሻ
ܤ
ାଵ
᪄
ିଵ
െʹܤ
᪄
᪄
ିଵ
ሻ
ሺͲሻ
ߞכܵ
ߞܵ
መ
ܵ
כ
ሚ
ߞ
ఆ
መ
ܵ
ଶ
ȁߞȁ
ଶఆ௧
ሺݐሻ
െʹܤ
ǡ᩷݊ൌͳǡʹǡǥ
ൌߜ
ɂɧɬɟɪɟɫɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɥɭɱɚɟ ߗൌͲ ɭɪɚɜɧɟɧɢɹ (10.37) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ
ɢɡ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɥɹ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɧɚ ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ (9.56):
߬
ଶ
μሺݐǡݑ
μݐ
ሻ
μ
ଶ
ሺ
ൌ
μݑ
ሻ
ݑ
െͳ
μሺݐǡݑ
μݑ
ሻ
Ǥ
ሺ
ͳͲǤ͵ͺ
Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɜ ɫɥɭɱɚɟ ߗൌͲ ɜɟɥɢɱɢɧɚ
ܤ
ሺ
ݐǡͲሻൌ
ൣܵ
ൣܵ
መ
Ԝଶଵ
መ
Ԝଶଶ
ሺ
ݐǡͲሻܵ
ሺ
ݐǡͲሻܵ
መ
Ԝଵଶ
መ
Ԝଵଵ
ሺ
ݐǡͲሻ൧
ሺ
ݐǡͲሻ൧
ሺ
ͳͲǤ͵ͻ
ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɤɨɨɪɞɢɧɚɬɭ ߠ ɤɨɧɟɱɧɨɣ ɬɨɱɤɢ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ܤ
ሺ
ݐǡͲሻൌ
ଶ
ሺ
ߠሺݐሻȀʹሻൌቆ
ɝɞɟ ɦɵ ɜɜɟɥɢ ɩɟɪɟɦɟɧɧɭɸ ݑൌሺߠሻ.
ሺߠሺݐሻሻെͳ
ሺߠሺݐሻሻͳ
107
ቇൌ൬
ݑሺݐሻെͳ
ݑሺݐሻͳ
൰ǡሺͳͲǤͶͲ
ሻ
Ɍɨɝɞɚ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ
ݑെͳ
ݑͳ
ଶ
ሺ
ݑ
൰
൰
െͳ
ሺݐǡݑሻǡ
Ԝ߬ଶԜ
μሺݐǡݑ
ሻ
μሺݐǡݑ
μݐ
μݑ
ሻ
ሻ
ൌ
ሻ
Ǥ
᪄
ሺݐሻ
ܤ
ஶ
ൌන ൬
ଵ
ɞɢɮɮɟɪɟɧɰɢɪɭɟɦ ɩɨ ݐ ɢ ɩɪɢɦɟɧɹɟɦ ɭɪɚɜɧɟɧɢɟ ɧɚ ሺݐǡݑ
ൌන ൬
ݑെͳ
ݑͳ
ଵ
ஶ
൰
μݑ
ݑെͳ
ݑͳ
μ
᪄
݀ܤ
߬
ଶ
݀ݐ
ൌන ൬
ଵ
ሺݐሻ
ஶ
ɂɧɬɟɝɪɢɪɭɹ ɞɜɚ ɪɚɡɚ ɩɨ ɱɚɫɬɹɦ, ɩɨɥɭɱɢɦ
߬
᪄
ሺݐሻ
݀ܤ
ଶ
ൌെʹ݊න ൬
݀ݐ
ஶ
ଵ
ݑെͳ
ݑͳ
൰
μሺݐǡݑ
μݑ
ሻ
ൌͶ݊ଶන
ଵ
ஶ
ሺ
ݑെͳ
ሺ
ݑͳ
ିଵ
ሻ
ǤԜሺݐǡݑሻǤሺͳͲǤͶ͵
ାଵ
ሻ
ɉɪɨɫɬɵɦ ɜɵɱɢɫɥɟɧɢɟɦ ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ
Ͷ
ሺ
ݑെͳ
ሺ
ݑͳ
ሻ
ሻ
ିଵ
ାଵ
ൌ൬
ݑെͳ
ݑͳ
൰
ାଵ
൬
ݑെͳ
ݑͳ
൰
ିଵ
െʹ൬
ݑെͳ
ݑͳ
൰ǡ
ɩɨɷɬɨɦɭ
᪄
ሺݐሻ
݀ܤ
߬
ଶ
݀ݐ
ൌ݊
ଶ
᪄
ሺ
ܤ
ାଵ
ܤ
᪄
ିଵ
െʹܤ
᪄
ሻ
ǡ
ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɵ ɩɨɥɭɱɢɥɢ ɭɪɚɜɧɟɧɢɹ (10.37) ɫ ߚൌͲ.
᪄
10.3.2. Ɋɟɤɭɪɪɟɧɬɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ
ሺ࢚ሻ
᪄
ሺ
Ɋɟɤɭɪɪɟɧɬɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɜɟɥɢɱɢɧ ܥ
᪄
ɨɛɪɚɡɨɦ, ɜɵɪɚɡɢɜ ܥ
ɨɬɪɟɡɤɟ
ሾ
ݐǡݐߜ
ሿ
. ɇɨ ɦɵ ɩɨɫɬɭɩɢɦ ɩɨ-ɞɪɭɝɨɦɭ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɬɟɦ, ɱɬɨ ɩɪɢ
ሺ
ݐ
ଵ
ߜǡݐ
ሻ
ɱɟɪɟɡ ܥ
ଶ
᪄
ሺ
ሻ
ݐǡݐ
ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɚɧɚɥɨɝɢɱɧɵɦ
ଵ
ݐǡλሻ ɢ ɱɟɪɟɡ ɫɥɭɱɚɣɧɵɟ ɩɨɥɹ ߞ, ߞ
ߗൌͲ ɷɬɚ ɜɟɥɢɱɢɧɚ ɩɪɢɦɟɬ ɜɢɞ
መ
ሺ
ൣܵ
᪄
ሺ
ሻ
ݐǡݐ
ܥ
ଵ
ൌൽ
ൣܵ
መ
Ԝଶଶ
Ԝଵଶ
ሺ
ݐǡെݐ
ݐǡെݐ
መ
ሻ
ሺ
ܵ
ܵ
መ
Ԝଵଵ
Ԝଶଵ
ሺ
ݐǡെݐ
ݐǡെݐ
ଵ
ሻ
ଵ
ሻ
൧
ଵ
ାଵ
ሻ
൧
ଵ
ඁൌܤ
᪄
ሺ
ݐݐ
᪄
ሻ
ଵ
െܤ
ାଵ
ሺ
ݐݐ
ଵ
ሻǤሺ
ɉɨɷɬɨɦɭ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɭɪɚɜɧɟɧɢɹɦɢ (10.45), ɢ ɩɪɢ ɜɵɜɨɞɟ ɨɩɭɫɬɢɦ ɚɪɝɭ-
ɦɟɧɬɵ
ൌ݊
ଶ
ሺ
ൌ݊
᪄
ܤ
ାଵ
ൌ݊
ଶ
ܥ
ܤ
ଶ
᪄
ିଵ
ሺ
ܥ
᪄
݀ܥ
߬
Ԝ
ଶ
݀ݐ
᪄
െʹܤ
ିଵ
᪄
െܥ
ିଵ
ሺ݊ͳ
ൌ߬ଶԜ
᪄
᪄
ሻെሺ
ሻെሺ
ଶ
ሻ
᪄
݀ܤ
݀ݐ
݊ͳ
᪄
ܥ
ାଵ
݀ܤ
െ߬ଶԜ
ሻଶሺ
݊ͳ
᪄
ሻଶሺ
ܥ
െሺʹ݊ଶʹ݊ͳሻܥ
᪄
ାଵ
݀ݐ
᪄
ܤ
െܥ
ାଶ
᪄
ܤ
ାଵ
᪄
ሻ
െʹܤ
ൌ
᪄
᪄
ሻ
ൌ
ାଵ
ǡ
ሺ
ͳͲǤͶͳ
ሺ
ͳͲǤͶʹ
ሺ
ͳͲǤͶͶ
ሺ
ͳͲǤͶͷ
ͳͲǤͶ
ሺ
ͳͲǤͶ
ఆ
ɧɚ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
108
ɢɫɩɨɥɶɡɭɹ ɨɛɨɡɧɚɱɟɧɢɟ ܥ
᪄
ሺݐሻ
݀ܥ
߬
Ԝ
ଶ
݀ݐ
ൌ݊ଶܥ
᪄
ିଵ
᪄
ሺݐሻ
ؠܥ
ሺݐሻሺ
᪄
ሺ
ݐǡλሻ, ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɩɪɢ ߗൌͲ
݊ͳ
ଶ
᪄
ሻ
ሺݐሻെሺ
ܥ
ାଵ
ଶ
ʹ݊
ʹ݊ͳሻܥ
᪄
ሺݐሻ
ɋɥɚɝɚɟɦɨɟ ɫ ߗ ɥɟɝɤɨ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɤɚɥɢɛɪɨɜɨɱɧɨɝɨ ɩɪɟɨɛɪɚɡɨ-
መ
ሺ
ɜɚɧɢɟ (8.61) ɞɥɹ ܵ
ሻ
ݐǡݐ
. ɗɬɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɞɚɟɬ ɦɧɨɠɢɬɟɥɶ ሺ݅ߗሺʹ݊ͳሻݐ
ఆ
ଵ
ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɫɥɚɝɚɟɦɨɦɭ ɜ ɭɪɚɜɧɟɧɢɹɯ (10.48)
݅߬
ߗሺʹ݊ͳሻܥ
ଶ
ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɪɚɜɧɟɧɢɟ ɧɚ ܥ
᪄
ሺݏሻ
݀ܥ
ሺ݊ͳ
ൌ݅ߚሺ݊ͳȀʹሻܥ
݀ݏ
ଶ
ሻ
ܥ
᪄
᪄
ାଵ
ሺݏሻ
᪄
ሺݐሻ
ൌ݅ߚሺ݊ͳȀʹሻܥ
ɢɦɟɟɬ ɜɢɞ
᪄
ሺݏሻെሺ
ʹ݊
ሺݏሻ
݊
ଶ
ʹ݊ͳሻܥ
᪄
ሺݐሻ
ǡ
ଶ
᪄
ሺݏሻ
ିଵ
᪄
ሺݏሻ
Ǥ
ܥ
10.4. ɉɪɨɢɡɜɨɞɹɳɢɟ ɮɭɧɤɰɢɢ ɢ ɜɵɱɢɫɥɟɧɢɟ
ɩɪɨɜɨɞɢɦɨɫɬɢ ોሺࢹ
ሻ
10.4.1. ɉɨɥɭɱɟɧɢɟ ɭɪɚɜɧɟɧɢɣ ɧɚ ɩɪɨɢɡɜɨɞɹɳɢɟ ɮɭɧɤɰɢɢ
ஶ
ିଵ
ሻ
, ɢɦɟɟɦ (ɛɭɞɟɦ
᪄
ܤ
െʹܤ
ିଵ
ିଵ
᪄
ሿ
ܤ
ିଵ
᪄
Ԝݔ
ܤ
᪄
ሿ
ܤ
ǡ
ǡሺͳͲǤͷͳ
ǡሺͳͲǤͷʹ
ɉɨɥɭɱɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɧɚ ɮɭɧɤɰɢɸ ܤሺݔǡݐ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɟɪɟɦɟɧɧɭɸ ݏൌݐȀ߬
ஶ
μݏ
ሻ
ൌ
ୀଵ
ஶ
μܤሺݔǡݏ
ൌͳሾ݅ߚ݊ݔ
ୀଵ
μܤ
μ݈
ሺݏሻ
ିଵ
ିଵ
ݔ
ሺ݊െͳ
)
ଶ
ஶ
ൌݔ
ୀଵ
ଶݔିଶ
ሻ
ିଵ
ሾ
ሺ݊ͳ
݅݊ߚܤ
ଶ
᪄
ሺ
ܤ
݊
ଶݔ
ሻ
െʹ݊ଶݔ
ɭɱɢɬɵɜɚɹ
ஶ
μܤሺݔǡݏ
μݔ
ሻ
ൌሺ݊െͳ
ୀଶ
μ൫ݔ
ሻ
ݔ
ଶ
ܤሺݔǡݏሻ൯
μݔ
ିଶ
μ൫ݔܤሺݔǡݏሻ൯
᪄
Ԝܤ
ǡ᩷
ஶ
ൌሺ݊ͳ
ୀଶ
μݔ
ሻ
Ԝݔܤ
ൌ݊
᪄
ɦɨɠɧɨ ɧɚɩɢɫɚɬɶ
μ
ஶ
ൌ
ୀଵ
ሺ
ሾ
݊െͳ
μݔ
ሻ
μ
ݔԜ
μݔ
ଶݔିଶ
ሺ
ሾ
ሺ݊ͳ
ͳെݔ
ଶ
ሻ
ሻ
ܤሺݔǡݐ
ଶݔ
ሻ
ሿ
ൌ
െʹ݊ଶݔ
109
᪄
ାଵ
ୀଵ
ǡ
ǤሺͳͲǤͶͺሻ
ሺ
ͳͲǤͶͻ
ሺ
ͳͲǤͷͲ
᪄
ሻ
ሿ
ൌ
ሺ
ͳͲǤͷ͵
ሺ
ͳͲǤͷͶ
ሻ
,
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ɬɨɝɞɚ ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ
μܤሺݔǡݏ
μݏ
ሻ
ൌͳ݅ߚ
μ
൫ݔܤሺݔǡݏሻ൯
μݔ
μ
μݔ
μ
ሺ
ሾ
ݔԜ
μݔ
ͳെݔ
ଶ
ሻ
ܤሺݔǡݏ
ሻ
ሿ
ǤሺͳͲǤͷͷ
Ⱥɧɚɥɨɝɢɱɧɵɟ, ɧɨ ɧɟɫɤɨɥɶɤɨ ɛɨɥɟɟ ɝɪɨɦɨɡɞɤɢɟ ɜɵɱɢɫɥɟɧɢɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɭɪɚɜɧɟɧɢɣ (10.51) ɞɚɸɬ ɫɥɟɞɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ ɧɚ ɩɪɨɢɡɜɨɞɹɳɭɸ ɮɭɧɤɰɢɸ ܥሺݔǡݏ
ሻ
μܥሺݔǡݏ
μݏ
ሺݔെͳሻܥሺݔǡݏሻ
݅ߚ
ൌ
ܥሺݔǡݏሻ݅ߚݔ
ʹ
μ
ݔሺݔെͳ
μݔ
ɩɪɢ ɷɬɨɦ ɝɪɚɧɢɱɧɨɟ ɭɫɥɨɜɢɟ ɞɥɹ ɮɭɧɤɰɢɢ ܥሺݔǡݏ
ܥሺݔǡͲሻൌͳെሺͳെݔሻܤሺݔǡλሻǤ
ሻ
ሻ
ሻ
μܥሺݔǡݏ
ଶ
Ԝ
μݔ
μ
μݔ
ܥሺݔǡݏሻǡ
ሺ
ͳͲǤͷ
ɫɥɟɞɭɟɬ ɢɡ (10.21) ɢ ɢɦɟɟɬ ɜɢɞ
ሺ
ͳͲǤͷ
ɉɟɪɟɣɞɟɦ ɜ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɹɯ ɤ ɧɨɜɨɣ ɧɟɡɚɜɢɫɢɦɨɣ ɩɟɪɟɦɟɧɧɨɣ
ݒൌݔȀሺͳെݔ
ሻ
, ɩɪɢ ɷɬɨɦ
ݔൌ
ͳݒ
ݒ
ǡ᩷ͳെݔൌ
ͳ
ݒͳ
ǡ᩷
μ
ൌሺݒͳ
μݔ
μ
ଶ
ሻ
μݒ
ሺ
ͳͲǤͷͺ
ɢ ɜɜɟɞɟɦ ɧɨɜɵɟ ɢɫɤɨɦɵɟ ɮɭɧɤɰɢɢ ɨɬ ɩɟɪɟɦɟɧɧɨɣ ݒ
ܤሺݔǡݏሻൌሺݒͳ
ଶ
ሻ
ܴሺݒǡݏሻǡ᩷ܥሺݒǡݏሻൌሺݒͳሻߔሺݒǡݏሻǤ
ሺ
ͳͲǤͷͻ
ȼ ɧɨɜɵɯ ɩɟɪɟɦɟɧɧɵɯ ɭɪɚɜɧɟɧɢɹ (10.55) ɢ (10.56) ɩɪɢɦɭɬ ɜɢɞ
μܴሺݒǡݏ
μߔሺݒǡݏ
μ݈
ሻ
μݏ
ሻ
ൌ݅ߚඥݒሺݒͳ
ൌ
ሺ
ݒͳ
ͳ
ଶ
ሻ
݅ߚ
μ
ሻ
μݒ
μ
ݒሺݒͳሻܴሺݒǡݏሻ
μݒ
ඥ
ݒሺݒͳ
ሻ
ߔሺݒǡݏሻ
μ
μݒ
μ
ݒሺݒͳ
μݒ
ݒሺݒͳ
μ
ሻ
ܴሺݒǡݏሻǡሺͳͲǤͲ
μݒ
μ
ሻ
ߔሺݒǡݏሻǤሺͳͲǤͳ
μݒ
ɉɪɟɠɞɟ ɱɟɦ ɪɟɲɚɬɶ ɷɬɢ ɭɪɚɜɧɟɧɢɹ, ɜɵɪɚɡɢɦ ɩɪɨɜɨɞɢɦɨɫɬɶ ɜ ɮɨɪɦɭɥɟ (10.29)
ሾ
ͳെሺݒ
ሻ
ͳሻܴሺݒଵǡλ
ଵ
ሻሿሺ
ݒͳሻන݀
ஶ
ݏߔሺݒǡݏሻǡሺͳͲǤʹ
ɱɟɪɟɡ ɮɭɧɤɰɢɢ ܴሺݒǡݏሻ ɢ ߔሺݒǡݏ
ɐሺߗሻൌ
ଶ
݁
ݒ߬
ߨ
ଶగ
݀߮
ଶ
න
ʹߨ
ɩɪɢ ɷɬɨɦ
ȼɵɪɚɡɢɦ ݒ
ͳ
ൌ
ݒ
ଵ
ିఝ
݁
ɱɟɪɟɡ ݒ ɢ ɩɟɪɟɣɞɟɦ ɤ ɢɧɬɟɝɪɢɪɨɜɚɧɢɸ ɨɬ ߮ ɤ ݒ
ଵ
ݒ
ൌെሺͳݒሻǡ᩷݀߮ൌ݅
ଵ
െͳ
ǡ᩷ݒൌ
ͳ
ఝ
݁
െͳ
݀ݒ
ݒሺͳݒ
Ǥ
ǡ
ሻ
ሺ
ͳͲǤ͵
ሺ
ͳͲǤͶ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
110
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