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ɨɬɤɭɞɚ
ሺሻ
ሺqሻ
ࣝ
ሺqሻ
ࣝ
ఆ
ఆ
ൌ
െ݅߬ߗ߬ܦݍ
(ɦɵ ɩɪɟɧɟɛɪɟɝɥɢ ɫɥɚɝɚɟɦɵɦɢ ݅߬ߗ, ߬ܦݍ
ൌ
ଶ
ଶ
ɜ ɱɢɫɥɢɬɟɥɟ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɟɞɢɧɢɰɟɣ).
݃
െ݅߬ߗ߬ܦݍ
ǡ
ଶ
ሺ
Ǥͳ
ɗɬɨ ɢ ɟɫɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɭɩɟɪɨɧɚ. ɉɪɢɦɟɱɚɬɟɥɶɧɨ, ɱɬɨ ɭ ɧɟɝɨ ɢɦɟɟɬɫɹ ɨɫɨɛɟɧ-
ɧɨɫɬɶ ɩɪɢ ݍǡߗ՜Ͳ, ɤɨɬɨɪɚɹ ɧɚɡɵɜɚɟɬɫɹ ɞɢɮɮɭɡɧɵɦ ɩɨɥɸɫɨɦ.
Ɍɟɩɟɪɶ ɩɨɞɫɬɚɜɢɦ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ (6.3) ɢ ɜɵɱɢɫɥɢɦ ɩɨɩɪɚɜɤɭ ɤ ɩɪɨɜɨɞɢɦɨ-
ሺqሻ
ɫɬɢ. Ⱦɥɹ ɷɬɨɝɨ ɜɨ ɜɫɟɦ ɜɵɪɚɠɟɧɢɢ ɩɨɞ ɢɧɬɟɝɪɚɥɨɦ ɤɪɨɦɟ ࣝ
ఆ
ɩɨɥɨɠɢɦ
ߗൌݍൌͲ. Ɍɨɝɞɚ
ଶ
݁
ߜߪ
ሺሻ
ሺߗሻ
ൌെ
ߨ݉
ȼɵɱɢɫɥɹɟɦ ɢɧɬɟɝɪɚɥ ɩɨ ݀
ଷ
݀
p
ଶ
ோ
න
ሺʹߨሻ
ȁpȁ
Ԝ
ଷ
ԜԜሾܩ
ሺ
Ͳǡp
ɢɧɬɟɝɪɚɥ ɩɨ ߦ ɪɚɜɟɧ Ͷߨ߬
ɟɤɰɢɟɣ ɫɩɢɧɚ) ɩɨɥɭɱɢɦ ͳʹߨ݉݊
ଶ
݁
ߜߪ
ሺሻ
ሺߗሻ
ൌെ
ͳʹߨ݉݊߬
ߨ݉ଶ
ଷ
݀
q
Ԝන
ଶ
ሺʹߨሻ
ଶ
ሾ
ሿ
ሻ
ሺ
ܩ
ଷ
, ɭɱɬɟɦ ɬɚɤɠɟ
ଷ
ଷ
݀
p
ሺqሻ
න
ࣝ
ఆ
ଷ
Ͳǡp
Ԝන
ଷ
p
ሺʹߨሻ
ሻ
ሺʹߨሻ
Ͷߨ
ଶ
ሿ
ൌ
ሺʹߨሻ
ଷ
߬ଷȀ, ɩɨɞɫɬɚɜɥɹɟɦ ɜ (6.17)
ଷ
݀
q
ሺqሻ
ࣝ
ఆ
ଷ
ȁpȁ
Ԝ
ଷ
ସ
න݀ߦ
ଷ
ݒ
ൌߨଶ݊
ൌെʹቆ
ଶ
ோ
ԜԜሾܩ
െߦ
ቀ
(ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɨɞɧɨɣ ɩɪɨ-
ଶ
݁
݊߬
݉
ሺ
Ͳǡp
ቇ߬ଶන
ʹ߬
݅
ሻ
ቁଶቀ
ሿ
ଶ
ሾ
ͳ
ܩ
െߦെ
ଷ
݀
ሺʹߨሻ
ሺ
q
Ͳǡp
ଷ
ʹ߬
ࣝ
ሻ
ሿ
݅
ቁ
ሺqሻǤሺ
ఆ
ଶ
ǤሺǤͳ
ǡሺǤͳͺ
ଶ
Ǥͳͻ
ሻ
ሻ
ሻ
ሻ
ɂɦɟɹ ɜɜɢɞɭ ɮɨɪɦɭɥɭ Ⱦɪɭɞɟ ߪ
ൌ݁ଶ݊߬Ȁ݉ ɢ ɩɨɞɫɬɚɜɥɹɹ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɭ-
ɩɟɪɨɧɚ (6.16), ɩɨɥɭɱɢɦ
ɝɞɟ ݍ
௫
ൎሺݒ߬
ሺሻ
ሺߗሻ
ߜߪ
ିଵ
ሻ
, ɬɚɤ ɤɚɤ ɩɪɢ ݍݒ߬بͳ ɜɟɟɪɧɵɟ ɞɢɚɝɪɚɦɦɵ ɦɚɥɵ. ȼ ɢɧɬɟɝɪɚɥɟ
ൌെ
ߪ
߬݃
ߨ
ೌೣ
න
ଶ
ଶ
ݍ
݀ݍ
െ݅ߗܦݍ
ǡ
ଶ
ሺ
ǤʹͲ
ɨɫɨɛɟɧɧɨɫɬɟɣ ɩɪɢ ݍ՜Ͳ ɧɟɬ, ɩɨɷɬɨɦɭ ɩɨɥɨɠɢɦ ߗൌͲ, ɩɨɥɭɱɢɦ
ሺሻ
ߜߪ
ߪ
ɩɨɞɫɬɚɜɥɹɹ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ݃ ɢɡ (6.2), ɞɥɹ ܦ ɢɡ (6.11) ɢ ݍ
ሺሻ
ߜߪ
ߪ
ൌെ
ൎെቆ
߬݃ݍ
ߨଶܦ
݉ݒ
௫
ଶ
߬
ቇଶǤ
ିଵ
ሻ
, ɩɨɥɭɱɢɦ
ሺ
Ǥʹͳ
ሺ
Ǥʹʹ
ǡ
ൎሺݒ߬
௫
ɗɬɨ ɢ ɟɫɬɶ ɤɜɚɧɬɨɜɚɹ ɩɨɩɪɚɜɤɚ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɬɪɟɯɦɟɪɧɨɦ ɫɥɭɱɚɟ. ȿɟ ɤɜɚɧɬɨɜɚɹ ɩɪɢɪɨɞɚ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɷɬɨ ɟɫɬɶ ɤɜɚɞɪɚɬ ɨɬɧɨɲɟɧɢɹ ɯɚɪɚɤɬɟɪɧɨɣ
Ⱦɟ Ȼɪɨɣɥɟɜɫɤɨɣ ɞɥɢɧɵ ɜɨɥɧɵ ɷɥɟɤɬɪɨɧɚ ߣ
ɛɟɝɚ ݈ൌݒ
߬, ɢ ɨɧɚ ɨɩɢɫɵɜɚɟɬ ɜɤɥɚɞ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɵɯ ɷɮɮɟɤɬɨɜ ɜ ɩɪɨɜɨɞɢ-
ൌȀ݉ݒ
ɤ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨ-
61
ሻ
ሻ
ሻ
ɦɨɫɬɶ. Ɍɚɤ ɠɟ ɤɚɤ ɢ ɜ ɨɩɬɢɤɟ, ɤɨɝɞɚ ɩɚɪɚɦɟɬɪ ߣ
Ȁ݈ ɦɚɥ, ɷɬɢ ɷɮɮɟɤɬɵ ɦɚɥɵ. ɉɨ-
ɷɬɨɦɭ ɜ ɬɪɟɯɦɟɪɧɨɦ ɫɥɭɱɚɟ ɜ ɜɵɪɨɠɞɟɧɧɨɦ ɷɥɟɤɬɪɨɧɧɨɦ ɝɚɡɟ ɩɪɢ ɦɚɥɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɟɣ ɞɪɟɣɮ ɷɥɟɤɬɪɨɧɨɜ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɦɨɠɧɨ ɨɩɢɫɵɜɚɬɶ
ɤɥɚɫɫɢɱɟɫɤɢ.
6.2. ɉɪɨɜɨɞɢɦɨɫɬɶ ɞɜɭɦɟɪɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɞɜɭɦɟɪɧɵɣ ɜɵɪɨɠɞɟɧɧɵɣ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ. Ɏɨɪɦɭɥɵ ɞɥɹ
ɩɪɨɜɨɞɢɦɨɫɬɢ (4.65) ɢ ɞɥɹ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ (5.36), (5.37) ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɪɚɡɦɟɪɧɨɫɬɢ ɩɪɨɫɬɪɚɧɫɬɜɚ. ɂɡɦɟɧɟɧɢɹ ɛɭɞɭɬ ɤɚɫɚɬɶɫɹ ɧɟɤɨɬɨɪɵɯ ɞɟɬɚɥɟɣ, ɬɚɤ ɜ ɢɦɩɭɥɶɫɧɨɦ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɧɭɠɧɨ ɡɚɦɟɧɢɬɶ ɢɧɬɟɝɪɚɥɵ ɩɨ ɜɨɥɧɨɜɵɦ ɱɢɫɥɚɦ ɩɨ ɩɪɚɜɢɥɭ
ଷ
݀
p
න
ሺʹߨሻ
ଷ
՜න
ɫɜɹɡɶ ɮɟɪɦɢ-ɢɦɩɭɥɶɫɚ (ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ) ɫ ɞɜɭɦɟɪɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɛɭɞɟɬ ɬɚɤɨɣ
ଶ
ൌͶߨ݊ǡ
ɚ ɫɟɱɟɧɢɹ ɪɚɫɫɟɹɧɢɹ ɜ ɛɨɪɧɨɜɫɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɬɚɤɨɜɨ
ଶ
݉
ߪ
ൌ
ଶ
ȼɪɟɦɹ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ߬ ɬɨɱɧɨ ɬɚɤ ɠɟ ɫɜɹɡɚɧɨ ɫ ɫɟɱɟɧɢɟɦ ɢ ɫ ɞɜɭɦɟɪɧɨɣ
ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɩɪɢɦɟɫɟɣ ߬
ିଵ
ʹߨସ݇
ൌ݊ݒߪ
නȁݑሺ߮
ɭɫɥɨɠɧɟɧɢɣ, ɬɚɤ ɠɟ ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ, ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɩɨɬɟɧɰɢɚɥ ݑሺ߮
ɧɟ ɡɚɜɢɫɹɳɢɦ ɨɬ ɭɝɥɚ ɢ ɪɚɜɧɵɦ ݑ
, ɬɨɝɞɚ ɤɚɠɞɚɹ ɩɪɢɦɟɫɧɚɹ ɥɢɧɢɹ ɜ ɞɢɚɝɪɚɦɦɚɯ
ɩɪɢɜɧɨɫɢɬ ɦɧɨɠɢɬɟɥɶ
݊
ݑ
݃ൌ
ɉɪɨɞɟɦɨɧɫɬɪɢɪɭɟɦ, ɱɬɨ ɜ ɞɜɭɦɟɪɧɨɦ ɫɥɭɱɚɟ ɜɨɫɩɪɨɢɡɜɨɞɢɬɫɹ ɮɨɪɦɭɥɚ Ⱦɪɭɞɟ
ɜ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɞɢɚɝɪɚɦɦɚɦɢ ɫ ɩɨɩɟɪɟɱɧɵɦɢ ɩɪɢɦɟɫɧɵɦɢ ɥɢɧɢɹɦɢ
ߪ
ఈఉ
ൌߜ
ሺߗሻ
ఈఉ
ൌ
݁ଶ
Ͷߨ݉
ଶ
݁
ʹߨ݉
ଶ
ʹߨ
Ͷߨଶݒ
Ԝන
ଶ
ଶ
݀
ሺʹߨሻ
ଷ
ͳെ݅߬ߗ
p
ଶ
ʹߨ߬
ȼɵɱɢɫɥɢɦ ɬɟɩɟɪɶ ɩɨɩɪɚɜɤɭ ɤ ɞɜɭɦɟɪɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɛɭɫɥɨɜɥɟɧɧɭɸ ɤɭ-
ɩɟɪɨɧɨɦ (ɬɨ ɟɫɬɶ ɜɟɟɪɧɵɦɢ ɞɢɚɝɪɚɦɦɚɦɢ, ɢ ɬɨɠɟ ɨɛɨɡɧɚɱɢɦ ɟɟ ߜߪ
ɞɨɛɢɬɫɹ ɞɜɭɦɟɪɧɵɣ ɜɚɪɢɚɧɬ ɢɧɬɟɝɪɚɥɚ (6.4), ɨɛɨɡɧɚɱɢɜ ɟɝɨ ࣤ
ɥɵɦ, ɬɚɤ ɱɬɨ ȁp
ȁൎȁ
q െpȁൎ
)
ଶ
݀
ሺʹߨሻ
p
ǡ
ଶ
ሺ
ሺ
ଶగ
. Ⱦɥɹ ɢɡɛɟɠɚɧɢɹ ɧɟɩɪɢɧɰɢɩɢɚɥɶɧɵɯ
ଶ
ଶ
ଶ
Ԝp
ൌ
݉߬
ఈpఉԜܩோ
ൌߜ
ଶ
ሻ
ȁ
݀߮Ǥ
Ǥ
ሺ
ߗǡpሻܩ
݁ଶ݊߬݉ͳ
ఈఉ
ሺ
Ͳǡpሻൌ
ͳെ݅߬ߗ
ሺ
ሺ
Ǥ
ሺሻ
(ɫɱɢɬɚɟɦ ȁqȁ ɦɚ-
ଶ
ሺ
). ɇɚɦ ɩɨɧɚ-
Ǥʹ͵
ǤʹͶ
Ǥʹͷ
ሻ
Ǥʹ
Ǥʹ
ሻ
ሻ
ሻ
,
ሻ
ሻ
62
ൌ
ࣤ
ଶ
ሺʹߨሻ
ൌන
ଶ
න݀߮݀݇
ଶ
݀
p
ሺʹߨሻ
ቀߗെݒ
ଶ
ܩ
݇
ோ
ሺ
ߗǡpሻܩ
ሺ
Ͳǡq െpሻൌ
ͳ
݅
ቁቀെݒ݇െ߂ሺpǡqሻെ
ʹ߬
ʹ߬
ሺ
ǡ
݅
ቁ
Ǥʹͺ
ሻ
ɝɞɟ ߂ሺpǡqሻൌߦሺq െpሻെߦ
ሺpሻ
, ɚ ߮ ɭɝɨɥ, ɫɜɹɡɚɧɧɵɣ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɟɤɬɨɪɚ p,
ɢɧɬɟɝɪɢɪɭɟɦ ɩɨ ݇
ሺʹߨሻ
ଶ
ݒ
ଶగ
ʹߨ߬න ݀߮
ͳെ݅߬൫ߗ߂ሺpǡqሻ൯
ͳ
ɫɱɢɬɚɹ ߬ߗاͳ ɢ ߬߂ሺpǡqሻاͳ, ɪɚɡɥɨɠɢɦ ɡɧɚɦɟɧɚɬɟɥɶ ɜ ɪɹɞ
ଶగ
݀߮
߬න
ቀͳ݅߬൫ߗ߂ሺpǡqሻ൯െ߬ଶ߂
ʹߨ
ɢɦɟɟɦ ߂ሺpǡqሻൌݒ
ଶగ
݀߮
න
ʹߨ
ଶగ
݀߮
ଶ
ሺ
pǡqሻൌ
න
߂
ʹߨ
ଶ
ሺ
pǡqሻቁǡ
ݍ߮, ɝɞɟ ߮ ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ p ɢ q.
߂ሺpǡqሻൌͲǡ
ͳ
ݒ
ʹ
ଶ
ݍଶൌ
ͳ
߬
ܦݍଶǡ
ɩɪɢ ɦɚɥɵɯ ݍൌ
ݒ
ȁqȁ
ɝɞɟ
ଶ
߬Ȁʹ
ܦൌݒ
ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɜ ɩɥɨɫɤɨɫɬɢ. Ɍɨɝɞɚ
߬ሺͳെ݅߬ߗെ߬ܦݍ
ݒ
݉߬
ଶ
ሻ
ൌ
ሺ
ͳ݅߬ߗെ߬ܦݍ
ȼ ɢɬɨɝɟ ɞɥɹ ɜɵɱɢɫɥɹɟɦɨɝɨ ɢɧɬɟɝɪɚɥɚ ɫ ɭɱɟɬɨɦ (6.26) ɩɨɥɭɱɚɟɦ
ͳ
ሺ
ͳ݅߬ߗെ߬ܦݍ
ൌ
ࣤ
ଶ
݃
ଶ
ሻ
Ǥ
ሺ
ǡ
ଶ
ሻ
Ǥ
Ǥʹͻ
ሺ
Ǥ͵Ͳ
ሺ
Ǥ͵ͳ
ሺ
Ǥ͵ʹ
ሺ
Ǥ͵͵
ሺ
Ǥ͵Ͷ
ሺ
Ǥ͵ͷ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (6.4), ɩɨɥɭɱɢɦ
ሺሻ
ࣝ
ఆ
ሺqሻൌ݃ሺ
ͳ݅߬ߗെ߬ܦݍ
ଶ
ሻ
Ǥ
Ɋɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ (6.5) ɞɥɹ ɤɭɩɟɪɨɧɚ ɞɚɟɬ ɬɨ ɠɟ ɫɚɦɨɟ ɜɵɪɚɠɟɧɢɟ, ɱɬɨ ɢ ɜ
ɬɪɟɯɦɟɪɧɨɦ ɫɥɭɱɚɟ:
ሺqሻ
ࣝ
ൌ
ఆ
݃
െ݅߬ߗ߬ܦݍ
Ǥ
ଶ
63
ሺ
Ǥ͵
ሺ
Ǥ͵
ሻ
ሻ
ȼɵɱɢɫɥɹɟɦ ɩɨɩɪɚɜɤɭ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ
ଶ
݁
ߜߪ
ሺሻ
ሺߗሻ
ൌെ
Ͷߨ݉
ȼɵɱɢɫɥɹɟɦ ɢɧɬɟɝɪɚɥ ɩɨ ݀
ɢɧɬɟɝɪɚɥ ɩɨ ߦ ɪɚɜɟɧ Ͷߨ߬
ଶ
݁
ߜߪ
ሺሻ
ሺߗሻ
ൌെ
Ͷߨ݉
Ԝන
ଶ
ሺʹߨሻ
݀
න
ሺʹߨሻ
ʹߨ
ൌ
ሺʹߨሻ
ଷ
ଷ
ʹ
Ԝ
ଶ
ݒ
ଶ
݀
q
ሺqሻ
ࣝ
ఆ
ଶ
ଶ
p
ଶ
p
ଶ
ȁpȁ
Ԝ
ԜԜሾܩ
ଶ
ଷ
න݀ߦ
ଶ
ݒ
, ɩɨɥɭɱɢɦ ʹ
ଷ
ଶ
݀
߬
ൌെ
න
ሺʹߨሻ
ଶ
݁
Ͷߨ݉
q
ࣝ
ଶ
Ԝ
ଶ
݀
න
ሺʹߨሻ
ோ
ሺ
Ͳǡp
ቀെߦ
ଷ
߬ଷȀݒ
ሺqሻ
ఆ
ଷ
ʹ
߬
ʹߨݒ
ଶ
p
ଶ
ோ
ȁpȁ
Ԝ
ଶ
ଶ
ሻ
ሾ
ሿ
ሺ
Ͳǡp
ԜԜሾܩ
ሺ
ሻ
Ͳǡp
ሿ
ܩ
ͳ
݅
ቁଶቀെߦെ
ʹ߬
, ɩɨɞɫɬɚɜɥɹɟɦ ɜ (6.3)
݁
ൌെ
Ͷߨ݉
ଷ
ଶ
ܦ
݉߬
ʹ߬
ଷ
ଶ
ʹ
Ԝ
ଶ
ʹߨݒ
݀ݍ
න
Ǥ
ݍ
ଶ
ሻ
ሾ
ሿ
ܩ
ଶ
ൌ
ǡ
ଶ
݅
ቁ
ଷ
߬
න
݉߬
ଶ
ሺ
ሻ
ሿ
Ͳǡp
ݍ݀ݍ
െ݅߬ߗ߬ܦݍ
ɍɱɬɟɦ (6.33), ɬɨɝɞɚ
ଶ
݀ߪ
ሺሻ
ሺߗሻ
ൌെ
ͳ
ʹߨ
݀ݍ
݁
න
ଶ
Ǥ
ݍ
ɗɬɨɬ ɢɧɬɟɝɪɚɥ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢ ɪɚɫɯɨɞɢɬɫɹ. ɋɧɢɡɭ ɨɧ ɨɛɪɟɡɚɟɬɫɹ ɧɚ ɨɛɪɚɬɧɨɣ
ɞɢɮɮɭɡɢɨɧɧɨɣ ɞɥɢɧɟ ݍ
ିଵ
ሻ
ݍ
௫
ൎሺݒ߬
, ɩɪɢ ɷɬɨɦ
ൌඥߗȀܦ, ɚ ɫɜɟɪɯɭ ɤɚɤ ɢ ɜ ɬɪɟɯɦɟɪɧɨɦ ɫɥɭɱɚɟ ɧɚ
ǤሺǤ͵ͺ
ሺ
Ǥ͵ͻ
ൌ
ଶ
ሺ
ǤͶͲ
ሺ
ǤͶͳ
ሻ
ሻ
ሻ
ሻ
ݍ
ݍ
௫
ܦ
ξ
ൌ
Ԝݒ߬
ߗ
ξ
ͳ
ൌ
ξ
Ǥ
ʹߗ߬
ሺ
ǤͶʹ
ȼ ɢɬɨɝɟ (ɨɩɭɫɤɚɹ ɞɜɨɣɤɭ ɩɨɞ ɥɨɝɚɪɢɮɦɨɦ) ɩɨɥɭɱɚɟɦ ɨɤɨɧɱɚɬɟɥɶɧɵɣ ɨɬɜɟɬ
ଶ
݀ߪ
ሺሻ
ሺߗሻ
ൌെ
Ͷߨ
ͳ
ଶ
ͳ
݁
൬
൰Ǥ
ߗ߬
ሺ
ǤͶ͵
Ɉɬɦɟɬɢɦ, ɱɬɨ ɜɵɪɚɠɟɧɢɟ ɩɟɪɟɞ ɥɨɝɚɪɢɮɦɨɦ ɫɨɫɬɨɢɬ ɬɨɥɶɤɨ ɢɡ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ ɤɨɧɫɬɚɧɬ ɢ ɧɟ ɫɨɞɟɪɠɢɬ ɧɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɟɣ, ɧɢ ɤɨɧɰɟɧɬɪɚɰɢɢ
ɷɥɟɤɬɪɨɧɨɜ. ȼɵɱɢɫɥɢɦ ɨɬɧɨɲɟɧɢɟ ɷɬɨɣ ɜɟɥɢɱɢɧɵ ɤ ɨɫɧɨɜɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɞɚ-
ɜɚɟɦɨɣ ɮɨɪɦɭɥɨɣ Ⱦɪɭɞɟ, ɭɱɢɬɵɜɚɹ
ଶ
݁
Ͷߨଶ
ɷɬɨ ɤɚɤ ɪɚɡ ɦɚɥɵɣ ɩɚɪɚɦɟɬɪ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɣ ɩɪɢɦɟɧɢɦɨɫɬɶ ɤɢɧɟɬɢɱɟɫɤɨɝɨ
ɭɪɚɜɧɟɧɢɹ. Ɉɞɧɚɤɨ ɜ ɞɜɭɦɟɪɧɨɦ ɫɥɭɱɚɟ ɧɚ ɱɚɫɬɨɬɚɯ ߗا߬
ଶ
ൌͶߨ݊
݉
ൌ
ଶ
݊߬
݁
ͳ
ߨ
, ɩɨɥɭɱɢɦ
݉
ଶ
߬
ͳ
ݒ
ǡ
߬
ିଵ
ሺെݒ߬
ሺ
ǤͶͶ
ሻ
ɤɜɚɧ-
64
ሻ
ሻ
ሻ
ɬɨɜɚɹ ɩɨɩɪɚɜɤɚ ɨɬɪɢɰɚɬɟɥɶɧɚ ɢ ɫɬɚɧɨɜɢɬɫɹ ɩɨɪɹɞɤɚ ɨɫɧɨɜɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɱɬɨ
ɭɤɚɡɵɜɚɟɬ ɧɚ ɨɬɫɭɬɫɬɜɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɞɜɭɦɟɪɧɨɣ ɫɢɫɬɟɦɟ ɢ ɥɨɤɚɥɢɡɚɰɢɸ ɷɥɟɤɬɪɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ.
Ʌɢɬɟɪɚɬɭɪɚ
əɜɥɟɧɢɟ ɫɥɚɛɨɣ ɥɨɤɚɥɢɡɚɰɢɢ ɜ ɞɜɭɦɟɪɧɨɣ ɫɢɫɬɟɦɟ, ɤɨɬɨɪɨɟ ɩɪɢɜɨɞɢɬ ɤ
ɨɫɨɛɟɧɧɨɫɬɹɦ ɜ ɤɜɚɧɬɨɜɨɣ ɩɨɩɪɚɜɤɟ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɛɵɥɨ ɜɩɟɪɜɵɟ ɪɚɫɫɦɨɬɪɟɧɨ ɜ [6].
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ
1. Ʉɚɤɨɣ ɩɨɪɹɞɨɤ ɦɚɥɨɫɬɢ ɤɜɚɧɬɨɜɨɣ ɩɨɩɪɚɜɤɢ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɬɪɟɯɦɟɪɧɨɦ
ɫɥɭɱɚɟ?
2. Ʉɚɤɨɣ ɩɨɪɹɞɨɤ ɦɚɥɨɫɬɢ ɤɜɚɧɬɨɜɨɣ ɩɨɩɪɚɜɤɢ ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɞɜɭɦɟɪɧɨɦ
ɫɥɭɱɚɟ?
3. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɞɢɮɮɭɡɧɵɣ ɩɨɥɸɫ ɜ ɤɭɩɟɪɨɧɟ (6.37) ɩɪɢɜɨɞɢɬ ɤ ɥɨɝɚɪɢɮɦɢ-
ɱɟɫɤɨɣ ɨɫɨɛɟɧɧɨɫɬɢ ɜ ɤɜɚɧɬɨɜɨɣ ɩɨɩɪɚɜɤɟ, ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɞɜɭɦɟɪɧɨɦ ɫɥɭɱɚɟ.
4. ɉɨɱɟɦɭ ɞɢɚɝɪɚɦɦɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɤɥɚɞɭ, ɨɩɢɫɵɜɚɟɦɨɦɭ
ɧɚɡɵɜɚɸɬɫɹ ɜɟɟɪɧɵɦɢ?
ɤɭɩɟɪɨɧɨɦ,
65
Ƚɥɚɜɚ 7
ɉɊɈȼɈȾɂɆɈɋɌɖ ɗɅȿɄɌɊɈɇɇɈ-ȾɕɊɈɑɇɈȽɈ
ɇȿȼɕɊɈɀȾȿɇɇɈȽɈ ȽȺɁȺ ȼ ɉɈɌȿɇɐɂȺɅȿ
ɉɊɂɆȿɋȿɃ
ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɬɟɨɪɢɢ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜɵɪɨɠɞɟɧɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ, ɨɫɧɨɜɚɧɧɨɣ ɧɚ ɭɫɪɟɞɧɟɧɢɢ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ, ɦɵ ɫɭɳɟɫɬɜɟɧɧɨ ɢɫɩɨɥɶɡɨɜɚɥɢ ɧɚɥɢɱɢɟ
ɭ ɷɬɨɣ ɫɢɫɬɟɦɵ ɩɨɜɟɪɯɧɨɫɬɢ Ɏɟɪɦɢ. ɂɦɟɧɧɨ ɷɥɟɤɬɪɨɧɵ, ɧɚɯɨɞɹɳɢɟɫɹ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɮɟɪɦɢ-ɫɮɟɪɵ, ɜɧɨɫɢɥɢ ɝɥɚɜɧɵɣ ɜɤɥɚɞ ɜ ɬɪɚɧɫɩɨɪɬ ɷɥɟɤɬɪɨɧɨɜ. Ɇɚɬɟɦɚɬɢɱɟɫɤɢ ɷɬɨ ɩɪɨɹɜɥɹɥɨɫɶ ɜ ɬɨɦ, ɱɬɨ ɝɥɚɜɧɵɟ ɜɤɥɚɞɵ ɜ ɢɧɬɟɝɪɚɥɵ ɨɬ ɩɪɨɢɡɜɟɞɟɧɢɹ
ɮɭɧɤɰɢɣ
ሺ
ݒ
Ƚɪɢɧɚ ɩɨ ɢɦɩɭɥɶɫɚɦ ɨɩɪɟɞɟɥɹɥɢɫɶ ɭɡɤɨɣ ɨɛɥɚɫɬɶɸ ɲɢɪɢɧɨɣ ɩɨɪɹɞɤɚ
ିଵ
ሻ
߬
ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɩɨɜɟɪɯɧɨɫɬɢ ɫɮɟɪɵ ɪɚɞɢɭɫɚ
. ɂ, ɧɚɩɪɢɦɟɪ, ɤɨɧɰɟɧɬɪɚ-
ɰɢɹ ɷɥɟɤɬɪɨɧɨɜ ɜ ɮɨɪɦɭɥɟ Ⱦɪɭɞɟ (5.48) ɜɨɡɧɢɤɚɥɚ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɮɨɪɦɭɥɵ
ଷ
ൌߨଶ݊
.
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɛɟɡ ɫɨɦɧɟɧɢɹ, ɮɨɪɦɭɥɚ Ⱦɪɭɞɟ ɜɟɪɧɚ ɞɥɹ ɥɸɛɵɯ ɧɟɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ, ɢɦɟɸɳɢɯ ɧɟɤɨɬɨɪɵɣ ɦɟɯɚɧɢɡɦ ɪɟɥɚɤɫɚɰɢɢ ɢɦɩɭɥɶɫɚ, ɬɚɤ ɤɚɤ ɨɧɚ ɨɩɢɫɵɜɚɟɬ ɨɞɧɨɱɚɫɬɢɱɧɵɣ ɷɮɮɟɤɬ. ɂ ɟɫɥɢ ɪɚɫɫɟɹɧɢɟ ɧɨɫɢɬɟɥɟɣ ɧɚ ɩɪɢɦɟɫɹɯ ɭɩɪɭɝɨɟ, ɬɨ ɩɪɨɜɨɞɢɦɨɫɬɶ ɞɨɥɠɧɚ ɩɨɥɭɱɚɬɶɫɹ ɩɪɨɫɬɵɦ ɭɫɪɟɞɧɟɧɢɟɦ ɩɨ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɧɨɫɢɬɟɥɟɣ ɩɨ ɷɧɟɪɝɢɢ.
ɋ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ
, ɩɪɟɞɫɬɚɜɥɹɟɬ ɦɟɬɨɞɢɱɟɫɤɢɣ ɢɧɬɟɪɟɫ ɜɵɜɟɫɬɢ ɫ ɩɨɦɨɳɶɸ
ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɮɨɪɦɭɥɭ Ⱦɪɭɞɟ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ ɜ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ, ɜ ɤɨ-
ɬɨɪɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ܶ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɜɟɥɢɱɢɧɚ ɡɚɩɪɟɳɟɧɧɨɣ ɳɟɥɢ ߂.
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɧɨɫɢɬɟɥɟɣ ɩɨ ɢɦɩɭɥɶɫɚɦ ɛɭɞɟɬ ɨɩɢɫɵɜɚɬɶɫɹ ɦɚɤɫ-
ɜɟɥɥɨɜɫɤɨɣ ɮɭɧɤɰɢɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ܶ, ɢ ɧɢ ɨ ɤɚɤɨɣ ɪɟɡɤɨɣ ɝɪɚ-
ɧɢɰɟ ɜ ɢɦɩɭɥɶɫɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɧɨɫɢɬɟɥɟɣ ɭ ɷɬɨɣ ɮɭɧɤɰɢɢ ɝɨɜɨɪɢɬɶ ɧɟ ɩɪɢɯɨɞɢɬɫɹ. ɗɬɨɦɭ ɢ ɛɭɞɟɬ ɩɨɫɜɹɳɟɧɚ ɞɚɧɧɚɹ ɝɥɚɜɚ.
7.1. ɏɢɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɞɜɭɯɡɨɧɧɨɝɨ
ɩɨɥɭɩɪɨɜɨɞɧɢɤɚ
Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨɫɬɭɸ ɦɨɞɟɥɶ ɞɜɭɯɡɨɧɧɨɝɨ ɩɪɨɜɨɞɧɢɤɚ. ɉɭɫɬɶ ߥሺߝ
ɫɨɫɬɨɹɧɢɣ ɷɥɟɤɬɪɨɧɨɜ, ɨɬɧɟɫɟɧɧɚɹ ɤ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ, ɜ ɧɟɤɨɬɨɪɨɦ ɤɪɢɫɬɚɥɥɟ ɬɚɤɚɹ ɱɬɨ
ሻ
ɩɥɨɬɧɨɫɬɶ
ሺߝሻ
ߥ
ߥሺߝሻൌቐ
ሺߝሻ
ɝɞɟ ߥ
ɩɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ɜ ɜɚɥɟɧɬɧɨɣ ɡɨɧɟ, ɚ ߥ
௩
ɜ ɡɨɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ, ߝ
ǡ ɩɪɢ ߝ
௩
Ͳǡ ɩɪɢ Ͳ൏ߝ൏߂ǡ
ሺߝሻ
ǡ ɩɪɢ ߂൏ߝǡ
ߥ
ɭɪɨɜɟɧɶ ɷɧɟɪɝɢɢ ɞɧɚ ɜɚɥɟɧɬɧɨɣ ɡɨɧɵ ߝ
൏ߝ൏Ͳǡ
ሺǤͳሻ
ሺߝሻ
– ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
൏Ͳ,
߂ ɡɚɩɪɟɳɟɧɧɚɹ ɳɟɥɶ. ɉɭɫɬɶ ɩɪɢ ɷɬɨɦ ɜɚɥɟɧɬɧɚɹ ɡɨɧɚ ɫɨɞɟɪɠɢɬ ɫɬɨɥɶɤɨ ɦɟɫɬ
ɫɤɨɥɶɤɨ ɷɥɟɤɬɪɨɧɨɜ ɜ ɫɢɫɬɟɦɟ:
66
ܰ
ൌන ߥ
ܸ
ఌ
ሺߝሻ
݀ߝǤ
௩
ሺ
Ǥʹ
ɏɢɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɫɢɫɬɟɦɵ ߤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ
ɝɞɟ ݊
ܰ
ൌන ݊
ܸ
ሺߝሻ
ɮɟɪɦɢɟɜɫɤɨɟ ɱɢɫɥɨ ɡɚɩɨɥɧɟɧɢɹ (ɜ ɷɬɨɣ ɝɥɚɜɟ ɷɬɚ ɮɭɧɤɰɢɹ ɡɚɜɢɫɢɬ ɨɬ
ி
ሺ
ߝെߤሻߥ
ி
ఌ
௩
ሺߝሻ
ஶ
݀ߝන ݊
௱
ሺ
ߝെߤሻߥ
ி
ሺߝሻ
݀ߝǡ
ሺ
Ǥ͵
ɷɧɟɪɝɢɢ, ɚ ɧɟ ɱɚɫɬɨɬɵ)
ሺߝሻ
݊
ி
ͳ
ൌ
Ǥ
ఌ
்
݁
ͳ
ሺ
ǤͶ
ɉɟɪɜɵɣ ɢɧɬɟɝɪɚɥ ɜ (7.3) ɩɪɟɨɛɪɚɡɭɟɦ ɫ ɭɱɟɬɨɦ (7.2)
න݊
ఌ
ൌ
ሺ
ߝെߤሻߥ
ி
ܰ
නሺ݊
ܸ
ఌ
ሺߝሻ
௩
ሺ
ி
ɝɞɟ ɦɵ ɭɱɥɢ ɪɚɜɟɧɫɬɜɨ ݊
݀ߝሻൌන ߥ
ߝെߤሻെͳ
ி
ሺߝሻ
െͳൌെ݊
ఌ
ሺߝሻ
݀ߝනሺ݊
௩
ሻ
ሺߝሻ
݀ߝൌ
ߥ
௩
ி
ఌ
ܰ
ܸ
ሺെߝሻ
. ɉɨɞɫɬɚɜɢɦ ɷɬɨ ɜ (7.3), ɢ ɫɞɟɥɚɜ ɡɚ-
ሺ
ி
െන ݊
ఌ
ߝെߤሻെͳ
ሺ
ߤെߝሻߥ
ி
ሻ
௩
ߥ
௩
ሺߝሻ
ሺߝሻ
݀ߝൌ
݀ߝǡሺǤͷ
ɦɟɧɭ ߝ՜െߝ ɜ ɩɟɪɜɨɦ, ɚ ߝ՜ߝ߂ ɜɨ ɜɬɨɪɨɦ ɢɧɬɟɝɪɚɥɟ, ɩɨɥɭɱɢɦ
ȁ
ȁ
ఌ
න݊
ሺ
ߤߝሻߥ
ி
ሺെߝሻ
௩
݀ߝൌන ݊
ஶ
ሺ
߂െߤߝሻߥ
ி
ሺ
߂ߝሻ݀ߝǤ
ሺ
Ǥ
ɉɪɟɞɩɨɥɨɠɢɦ ɬɟɩɟɪɶ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɚ ɬɚɤɨɜɚ, ɱɬɨ ߂بܶ, ɤɚɤ ɦɵ ɭɜɢɞɢɦ
ɧɢɠɟ, ɩɪɢ ɷɬɨɦ ɨɤɚɠɟɬɫɹ, ɱɬɨ ߤبܶ ɢ ɩɪɢ ɷɬɨɦ ߂െߤߤ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɮɟɪ-
ɦɢɟɜɫɤɚɹ ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɦɚɤɫɜɟɥɥɨɜɫɤɭɸ:
ሺ
݊
ߤߝሻൎ൬െ
ி
ሺ
߂െߤߝሻൎ൬െ
݊
ி
ߤߝ
൰ǡ
ܶ
߂െߤߝ
ܶ
൰ǡ
ሺ
ሺ
Ǥ
Ǥͺ
ɩɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (7.6), ɩɨɥɭɱɢɦ
ȁ
ȁ
ఌ
ఓ
ି
்
න݁
݁
ఌ
ି
்
ሺെߝሻ
݀ߝൌ݁
ߥ
௩
ሺ
ఓି௱
்
ஶ
ሻ
න݁
ఌ
ି
்
ሺ
߂ߝሻ݀ߝǡ
ߥ
ሺ
Ǥͻ
ɨɬɤɭɞɚ
ሺ
ሻ
݁
ଶఓି௱
்
ሺܶሻ
ܫ
௩
ൌ
ሺܶሻ
ܫ
ሺ
ǤͳͲ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
67
ɢɥɢ
ߤൌ
ܶ
߂
ʹ
ʹ
Ԝቆ
ሺܶሻ
ܫ
௩
ቇǡ
ሺܶሻ
ܫ
ሺ
Ǥͳͳ
ɝɞɟ
ȁ
ȁ
ఌ
ఌ
ି
ି
ሺܶሻ
ߤൎ
௩
ఌ
்
߂
ሺܶሻ
்
ሺെߝሻ
݀ߝǡ
ߥ
௩
ሺ
߂ߝሻ݀ߝǤ
ߥ
, ɬɨ
Ǥ
ʹ
ɢ ɱɢɫɥɨ ɞɵɪɨɤ ɜ ɜɚɥɟɧɬɧɨɣ ɡɨɧɟ
௱
ି
ଶ்
ሺܶሻ
ܫ
Ԝ݁
Ǥ
ሺ
Ǥͳʹ
ሺ
Ǥͳ͵
ሺ
ǤͳͶ
ሺ
Ǥͳͷ
ሺܶሻ
ൌන ݁
ܫ
௩
ܫ
ȿɫɥɢ ɩɪɢ ɷɬɨɦ ɨɤɚɠɟɬɫɹ ܫ
ሺܶሻ
ൌන ݁
ሺܶሻ
௩
ஶ
ൎܫ
ɑɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ ɡɨɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ܰ
ɪɚɜɧɵ ɞɪɭɝ ɞɪɭɝɭ, ɢ ɩɪɢ ɷɬɨɦ
ܰ
௩
ൌܰ௩ൌඥܫ
ܰ
7.2. Ɏɭɧɤɰɢɢ Ƚɪɢɧɚ ɫɜɨɛɨɞɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ
Ɇɵ ɛɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɜɛɥɢɡɢ ɩɨɬɨɥɤɚ ɜɚɥɟɧɬɧɨɣ ɡɨɧɵ ɢ ɞɧɚ ɡɨɧɵ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɷɥɟɤɬɪɨɧɨɜ ɤɜɚɞɪɚɬɢɱɟɧ ɩɨ ɜɨɥɧɨɜɨɦɭ ɜɟɤɬɨɪɭ, ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɷɤɫɬɪɟɦɭɦɚ, ɢ ɩɨɷɬɨɦɭ ɞɥɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɫɩɟɤɬɪɚ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɧɚɩɢɫɚɬɶ
ଶ
ଶ
ൌെ
ʹ݉
ʹ݉
ȁkȁ
ଶ
௩
ȁkȁ
ǡ
ଶ
ǡ
ሺ
Ǥͳ
ሺ
Ǥͳ
ሺkሻ
ߝǁ
௩
ሺkሻ
ߝǁ
ൌ߂
ɢ ݉
ɝɞɟ ݉
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɪɢɜɢɡɧɵ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɡɨɧ ɜɛɥɢɡɢ ɷɤɫɬɪɟɦɭ-
௩
ɦɨɜ, ɤɨɬɨɪɵɟ ɩɪɟɜɪɚɬɹɬɫɹ ɜɩɨɫɥɟɞɫɬɜɢɢ ɜ ɷɮɮɟɤɬɢɜɧɵɟ ɦɚɫɫɵ ɞɵɪɨɤ ɢ ɷɥɟɤɬɪɨɧɨɜ. Ɍɨɝɞɚ, ɜɜɟɞɹ ɮɟɪɦɢɟɜɫɤɢɟ ɨɩɟɪɚɬɨɪɵ ɪɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɜ ɜɚɥɟɧɬɧɨɣ ɡɨɧɟ
ɢ ɡɨɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɡɚɩɢɲɟɦ ɝɚɦɢɥɶɬɨɧɢɚɧ ɷɥɟɤɬɪɨɧɨɜ ɜɨ ɜɬɨɪɢɱɧɨ ɤɜɚɧɬɨɜɚɧɧɨɦ ɜɢɞɟ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ᇱ
ܪ
ൌሺߝǁ
k
௩
ሺkሻ
Ԝܽො
ା
ܽො௩kߝǁ
௩k
ሺkሻ
ା
ሻ
Ԝܽො
ܽො
k
k
ɉɟɪɟɯɨɞɹ ɤ ɛɨɥɶɲɨɦɭ ɤɚɧɨɧɢɱɟɫɤɨɦɭ ɚɧɫɚɦɛɥɸ ɫ ɩɟɪɟɦɟɧɧɵɦ ɱɢɫɥɨɦ ɱɚɫɬɢɰ ɩɨ ɩɪɚɜɢɥɭ
68
ሺ
Ǥͳͺ
ሻ
ɩɨɥɭɱɢɦ
ᇱ
ᇱ
՜ܪ
ܪ
െߤܰൌܪ
ǡ
ሺ
Ǥͳͻ
ሻ
ܪ
ൌሺߝ
k
௩
ሺkሻ
ା
Ԝܽො
௩k
ܽො௩kߝ
ሺkሻ
ା
ሻ
Ԝܽො
ܽො
ǡ
k
k
ሺ
ǤʹͲ
ɝɞɟ
ଶ
ଶ
ሺkሻ
ߝ
௩
ሺkሻ
ߝ
ൌߝǁ
ൌߝǁ
ሺkሻ
௩
ሺkሻ
െߤൌെ
െߤൌ߂
ʹ݉
ʹ݉
ȁkȁ
ଶ
௩
ȁkȁ
ଶ
െߤǡ
െߤǤ
ሺ
Ǥʹͳ
ሺ
Ǥʹʹ
ɑɬɨɛɵ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɜɚɥɟɧɬɧɨɣ ɡɨɧɟ ɢɦɟɥɢ ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ, ɩɟɪɟɣɞɟɦ ɨɬ ɨɩɟɪɚɬɨɪɨɜ ɪɨɠɞɟɧɢɹ ɢ ɭɧɢɱɬɨɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɜ ɷɬɨɣ ɡɨɧɟ ɤ ɨɩɟɪɚɬɨɪɚɦ
ɞɵɪɨɤ, ɩɨ ɩɪɚɜɢɥɭ
ା
ܽො
ൌܾ
ǡԜԜԜܽො௩kൌܾ
k
௩k
ା
ǡ
k
ሺ
Ǥʹ͵
ɚ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɜ ɡɨɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɪɨɫɬɨ ɩɨɦɟɧɹɟɦ ɞɥɹ ɟɞɢɧɨɨɛɪɚɡɢɹ ɨɛɨɡɧɚɱɟɧɢɹ
ା
ା
ൌܾ
ܽො
˔k
ǡԜԜԜܽොkൌܾ
k
ǡ
k
ሺ
ǤʹͶ
ɬɨɝɞɚ ɝɚɦɢɥɶɬɨɧɢɚɧ ɩɪɢɦɟɬ ɜɢɞ
ܪ
ൌቈቆ
ൌ൫െߝ
ଶ
ȁkȁ
ʹ݉
ଶ
ߤቇԜܾ
௩
ሺkሻ
ା
k
Ԝܾ
ܾ
k
ା
k
ܾ
kߝ
ቆ
ଶ
ʹ݉
ሺkሻ
Ԝܾ
ଶ
ȁkȁ
߂െߤቇԜܾ
ା
ܾ
൯kൌ
k
k
ା
ܾ
k
k
ሺ
kǡ
Ǥʹͷ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ɝɞɟ ɦɵ ɞɥɹ ɟɞɢɧɨɨɛɪɚɡɢɹ ɩɟɪɟɨɛɨɡɧɚɱɢɥɢ ݉
՜݉ ɢ ݉՜݉
௩
ȼɜɟɞɹ ɨɛɵɱɧɵɦ ɨɛɪɚɡɨɦ (3.5) ɝɟɣɡɟɧɛɟɪɝɨɜɫɤɢɟ ɨɩɟɪɚɬɨɪɵ ܾ
ା
ܾ
ሺݐሻ
k
, ܾ
ሺݐሻ
, ɨɩɪɟɞɟɥɢɦ ɞɵɪɨɱɧɭɸ ɢ ɷɥɟɤɬɪɨɧɧɭɸ ɡɚɩɚɡɞɵɜɚɸɳɭɸ ɮɭɧɤɰɢɢ
k
Ƚɪɢɧɚ
ோ
ሺ
ݐǡkሻൌെ݅ߠሺݐሻԜൻܾ
ܩ
ோ
ሺ
ݐǡkሻൌെ݅ߠሺݐሻԜൻܾ
ܩ
k
ା
ሺݐሻ
ሺͲሻ
ܾ
k
k
ା
ሺݐሻ
ሺͲሻ
ܾ
k
ܾ
ܾ
ା
ሺͲሻ
ܾ
k
k
ା
ሺͲሻ
ܾ
k
k
ɚɧɚɥɨɝɢɱɧɨ ɞɥɹ ɨɩɟɪɟɠɚɸɳɢɯ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ
ሺ
ݐǡkሻൌ݅ߠሺെݐሻԜൻܾ
ܩ
ሺ
ݐǡkሻൌ݅ߠሺെݐሻԜൻܾ
ܩ
k
ା
ሺݐሻ
ሺͲሻ
ܾ
k
k
ା
ሺݐሻ
ሺͲሻ
ܾ
k
ܾ
ܾ
ା
ሺͲሻ
ܾ
k
k
ା
ሺͲሻ
ܾ
k
k
69
ሺݐሻ
ሺݐሻ
ሺݐሻ
ሺݐሻ
.
k
ൿ
ǡ
்
ൿ
ǡ
்
ൿ
ǡ
்
ൿ
Ǥ
்
ሺݐሻ
, ܾ
k
ሺ
ሺ
ሺ
ሺ
ା
ሺݐሻ
Ǥʹ
Ǥʹ
Ǥʹͺ
Ǥʹͻ
,
ሻ
ሻ
ሻ
ሻ
ɉɟɪɟɯɨɞɹ ɤ ɱɚɫɬɨɬɧɨɦɭ ɩɪɟɞɫɬɚɜɥɟɧɢɸ, ɨɛɵɱɧɵɦ ɨɛɪɚɡɨɦ ɩɨɥɭɱɢɦ ɝɪɢɧɨɜɫɤɢɟ ɮɭɧɤɰɢɢ ɫɜɨɛɨɞɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ
ோǡ
ሺ
߱ǡkሻൌ
ܩ
ோǡ
ሺ
߱ǡkሻൌ
ܩ
ߝെ
ߝെ
ଶ
ʹ݉
ȁkȁ
ʹ݉
ଶ
ଶ
ȁkȁ
െ߂ߤേ݅ߜ
ଶ
െߤേ݅ߜ
ǡ
ǡ
ሺ
Ǥ͵Ͳ
ሺ
Ǥ͵ͳ
ɝɞɟ ɞɥɹ ɭɞɨɛɫɬɜɚ ɜɦɟɫɬɨ ɱɚɫɬɨɬɵ ߱ ɜɜɟɞɟɧɚ ɩɟɪɟɦɟɧɧɚɹ ߝൌ߱ ɫ ɪɚɡɦɟɪɧɨɫɬɶɸ
ɷɧɟɪɝɢɢ.
7.3. ɍɫɪɟɞɧɟɧɢɟ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɷɥɟɤɬɪɨɧɨɜ
ɢ ɞɵɪɨɤ ɩɨ ɩɨɥɨɠɟɧɢɸ ɩɪɢɦɟɫɟɣ
ȼ ɫɥɭɱɚɟ ɜɵɪɨɠɞɟɧɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɝɚɡɚ ɭɫɥɨɜɢɟɦ ɩɪɢɦɟɧɢɦɨɫɬɢ ɤɢɧɟɬɢ-
ɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɛɵɥɨ ɧɟɪɚɜɟɧɫɬɜɨ
ɱɢɫɥɨ) Ɏɟɪɦɢ, ݒ
ɫɤɨɪɨɫɬɶ Ɏɟɪɦɢ, ɚ ߬ ɜɪɟɦɹ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɷɥɟɤɬɪɨɧɚ ɜ
߬بͳ, ɝɞɟ
ݒ
ɩɨɥɟ ɩɪɢɦɟɫɟɣ. ɋɮɨɪɦɭɥɢɪɭɟɦ ɚɧɚɥɨɝɢɱɧɨɟ ɭɫɥɨɜɢɟ ɜ ɫɥɭɱɚɟ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ ɜ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ, ɩɪɢ ɷɬɨɦ ɛɭɞɟɦ ɩɢɫɚɬɶ ɨɰɟɧɨɱɧɵɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɞɵɪɨɤ
ɢ ɷɥɟɤɬɪɨɧɨɜ ɨɞɧɨɜɪɟɦɟɧɧɨ, ɩɨɞɪɚɡɭɦɟɜɚɹ ɩɨɞ ݉ ɥɢɛɨ ݉
ɬɟɦɩɟɪɚɬɭɪɟ ܶ ɭ ɧɚɫ ɟɫɬɶ ɯɚɪɚɤɬɟɪɧɵɣ «ɬɟɩɥɨɜɨɣ» ɢɦɩɭɥɶɫ (ɜɨɥɧɨɜɨɟ ɱɢɫɥɨ)
ξ݉ܶȀ, ɨɛɪɚɬɧɚɹ ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɨɝɨ ɟɫɬɶ ɬɟɩɥɨɜɚɹ ɞɥɢɧɚ ɜɨɥɧɵ Ⱦɟ Ȼɪɨɣɥɹ
்
Ȁξ݉ܶ
, ɢ ɷɬɚ ɞɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɫɩɪɚɜɟɞɥɢɜɨɫɬɢ ɤɜɚɡɢɤɥɚɫɫɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ
ɞɨɥɠɧɚ ɛɵɬɶ ɧɚɦɧɨɝɨ ɦɟɧɶɲɟ ɞɥɢɧɵ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɷɥɟɤɬɪɨɧɚ ɢɥɢ ɞɵɪɤɢ
ݒ
߬ൌ߬ඥܶȀ݉, ɬɚɤɢɦ ɨɛɪɚɡɨɦ
்
ɢɦɩɭɥɶɫ (ɜɨɥɧɨɜɨɟ
, ɥɢɛɨ ݉
. Ɍɨɝɞɚ ɩɪɢ
ሻ
ሻ
ا߬
ܶ
ඨ
݉
ԜԜԜ֜ԜԜԜܶب
݉ܶ
ξ
ǡ
߬
ሺ
Ǥ͵ʹ
ɜ ɞɚɥɶɧɟɣɲɟɦ ɧɚɦ ɛɭɞɟɬ ɭɞɨɛɧɟɟ ɨɩɟɪɢɪɨɜɚɬɶ ɧɟ ɜɪɟɦɟɧɟɦ ߬, ɚ ɨɛɪɚɬɧɨɣ ɜɟɥɢɱɢɧɨɣ ߛൌͳȀ߬ – ɞɟɤɪɟɦɟɧɬɨɦ ɡɚɬɭɯɚɧɢɹ ɫɨɫɬɨɹɧɢɹ. Ɍɨɝɞɚ ɭɫɥɨɜɢɟ ɩɪɢɦɟɧɢɦɨ-
ɫɬɢ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɟɫɬɶ
ܶبԜߛǤ
ሺ
Ǥ͵͵
Ɍɟɩɟɪɶ ɩɟɪɟɣɞɟɦ ɤ ɭɫɪɟɞɧɟɧɧɵɦ ɩɨ ɛɟɫɩɨɪɹɞɤɭ ɮɭɧɤɰɢɹɦ Ƚɪɢɧɚ. Ɋɚɫɫɦɨɬɪɢɦ ɨɩɟɪɟɠɚɸɳɭɸ ɞɵɪɨɱɧɭɸ ɮɭɧɤɰɢɸ Ƚɪɢɧɚ, ɞɥɹ ɨɫɬɚɥɶɧɵɯ ɮɭɧɤɰɢɣ ɜɵɜɨɞ
ɚɧɚɥɨɝɢɱɟɧ, ɢ ɦɵ
ɩɪɢɜɟɞɟɦ ɥɢɲɶ ɪɟɡɭɥɶɬɚɬ. ȼɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ (7.33) ɩɨɡɜɨɥɹɟɬ ɩɪɟɧɟɛɪɟɱɶ ɞɢɚɝɪɚɦɦɚɦɢ ɫ ɩɟɪɟɫɟɤɚɸɳɢɦɢɫɹ ɩɪɢɦɟɫɧɵɦɢ ɥɢɧɢɹɦɢ ɩɨɞɨɛɧɨ ɜɬɨɪɨɣ ɞɢɚɝɪɚɦɦɟ ɧɚ ɪɢɫ. 5.5, ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɹ ɧɚ ɭɫɪɟɞɧɟɧɧɭɸ
ɮɭɧɤɰɢɸ Ƚɪɢɧɚ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ (ɪɢɫ. 5.6):
70
ሻ
ሻ
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