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ܩ
ఠԜଵଵ
ሺݖሻ
ൌ
݅
ߠሺെݖሻ݁
ݒ
ఠ௭
௩
బ
ǡ᩷᩷ܩ
ఠԜଶଶ
ሺݖሻ
݅
ൌ
ݒ
ߠሺݖሻ݁
ఠ௭
ି
௩
బ
ሺ
Ǥ
ͺǤʹͺ
ɗɬɢ ɮɨɪɦɭɥɵ, ɧɟɫɤɨɥɶɤɨ ɫɢɦɜɨɥɢɱɧɨ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɦɚɬɪɢɱɧɨɦ ɜɢɞɟ
ܩ
ఠ௭ఙ
ൌെ
݅
ߠሺߪଷݖሻ݁
ݒ
ோ
ሺݖሻ
ఠ
௩
బ
య
ǡ᩷᩷ܩ
ሺݖሻ
݅
ൌ
ݒ
ߠሺെߪଷݖሻ݁
ఠ
ఠ௭ఙ
௩
య
బ
ǤሺͺǤʹͻ
ȼɵɪɚɠɟɧɢɹ ɞɥɹ «ɧɭɥɟɜɵɯ» ɮɭɧɤɰɢɣ Ƚɪɢɧɚ (8.29) ɩɨɡɜɨɥɹɸɬ ɭɫɬɚɧɨɜɢɬɶ ɝɪɚ-
ɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɪɟɲɟɧɢɣ ɭɪɚɜɧɟɧɢɹ (8.25). Ɉɛɨɡɧɚɱɢɦ ɞɥɹ ɩɪɨɫɬɨɬɵ ɜɵɪɚɠɟ-
ɧɢɣ ɫɥɭɱɚɣɧɵɣ ɦɚɬɪɢɱɧɵɣ ɩɨɬɟɧɰɢɚɥ ɤɚɤ ߮ොሺݖሻൌߟሺݖሻߞሺݖሻԜߪො
ሺାሻ
ߞ
כ
ሺݖሻ
ሺିሻ
Ԝߪො
ɦɵ ɦɨɠɟɦ ɩɪɟɞɫɬɚɜɢɬɶ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɜ ɜɢɞɟ ɪɹɞɚ ɚɧɚɥɨɝɢɱɧɨɦɭ (5.10):
ܩ
ᇱ
ሻ
ൌܩ
ோ
ఠ
ሺ
ݖെݖ
ᇱ
ሻ
݀ݖ
ோ
ሺ
ݖǡݖ
ఠ
ோ
ሺ
ሻ߮ොሺ
ݖെݖ
ܩ
ଵ
ఠ
ଵ
ோ
ሻ
ݖ
ܩ
ଵ
ఠ
ᇱ
ሺ
ሻ
ݖ
ଵ
െݖ
ڮሺͺǤ͵Ͳ
Ɋɚɫɫɦɨɬɪɢɦ ݇-ɣ ɱɥɟɧ ɷɬɨɝɨ ɪɹɞɚ ɞɥɹ ɮɭɧɤɰɢɢ ɫ ɥɟɜɵɦ ɢɧɞɟɤɫɨɦ, ɪɚɜɧɵɦ ͳ
݀ݖ
ɢɦɟɟɦ ܩ
ோ
ఠଵଵ
ଵ݀ݖଶ
ǥ݀ݖԜܩ
ሺ
ݖെݖ
ோ
ሺ
ݖെݖ
ఠଵଵ
ൈܩ
ሻ
ൌͲ ɩɪɢ ݖ൏ݖ
ଵ
ሻ
߮ො
ଵ
ଵఔ
ோ
ఠఔ
ೖశభ
ଵ
ோ
ሺ
ሻ
ݖ
ܩ
ଵ
మ
ሺ
ݖ
ǡఓ
ఠఔమఔ
െݖ
య
ᇱ
ሻ
ሺ
ݖ
ଵെݖଶ
ǡ
ሻ
ǥ߮ො
ఔೖఔ
ೖశభ
ሺ
ሻ
ݖ
ൈ
ሺ
ͺǤ͵ͳ
ɜ ɫɨɝɥɚɫɢɢ ɫ (8.27), ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɪɢ
ݖ՜െλ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ. ɋɨɜɟɪɲɟɧɧɨ ɚɧɚɥɨɝɢɱɧɵɟ ɪɚɫɫɭɠɞɟ-
ɧɢɹ ɩɨɡɜɨɥɹɸɬ ɭɫɬɚɧɨɜɢɬɶ ɫɥɟɞɭɸɳɢɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɥɸɛɨɝɨ ߥ
ܩ
ܩ
ܩ
ܩ
ఠԜԜଵఔ
ோ
ఠԜԜଵఔ
ோ
ఠԜԜఔଵ
ఠԜԜఔଵ
ሺ
ሺ
ሺ
ሺ
ݖǡݖ
ݖǡݖ
ݖǡݖ
ݖǡݖ
ᇱ
ሻ
՜Ͳǡ ܩ
ᇱ
ሻ
՜Ͳǡ ܩ
ᇱ
ሻ
՜Ͳǡ ܩ
ᇱ
ሻ
՜Ͳǡ ܩ
ோ
ఠԜԜଶఔ
ఠԜԜଶఔ
ఠԜԜఔଶ
ோ
ఠԜԜఔଶ
ᇱ
ሺ
ሻ
ݖǡݖ
՜Ͳ ɩɪɢ ݖ՜λǡ
ᇱ
ሺ
ሻ
ݖǡݖ
՜Ͳ ɩɪɢ ݖ՜െλǡ
ᇱ
ሺ
ሻ
ݖǡݖ
՜Ͳ ɩɪɢ ݖ
ᇱ
ሺ
ሻ
ݖǡݖ
՜Ͳ ɩɪɢ ݖ
ᇱ
՜λǡ
ᇱ
՜െλǤ
ሺ
ͺǤ͵ʹ
8.2. S-ɦɚɬɪɢɰɚ
Ɉɩɪɟɞɟɥɟɧɢɟ S-ɦɚɬɪɢɰɵ
ሻ
ሻ
ǡ
ሻ
ሻ
ሻ
ɉɟɪɟɣɞɟɦ ɬɟɩɟɪɶ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ܵ-ɦɚɬɪɢɰɵ, ɝɥɚɜɧɨɝɨ ɨɛɴɟɤɬɚ ɢɡɥɚɝɚɟɦɨɝɨ
ɩɨɞɯɨɞɚ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɩɟɪɟɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ ɧɚ ɮɭɧɤɰɢɸ Ƚɪɢɧɚ (8.25) ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
μݖ
μ
ሺ
ݖǡݖ
ܩ
ఠ
ͳ
ᇱ
ሻ
ൌ
ൣ݅߱ߪොଷെ݅ߟሺݖሻߪොଷെ݅ߞሺݖሻԜߪො
ݒ
݅
ߪොଷߜሺݖെݖ
െ
ݒ
ሺାሻ
݅ߞ
ᇱ
ሻ
Ǥ
כ
ሺݖሻ
ሺିሻ
Ԝߪො
൧ܩ
ᇱ
ሺ
ሻ
ݖǡݖ
ఠ
െ
ሺ
ͺǤ͵͵
Ⱦɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɫɞɟɥɚɟɦ ɧɟɫɤɨɥɶɤɨ ɭɞɨɛɧɵɯ ɨɛɨɡɧɚɱɟɧɢɣ. ȼɦɟɫɬɨ ɤɨɨɪɞɢ-
ɧɚɬɵ ɨɞɧɨɦɟɪɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ݖ ɜɜɟɞɟɦ ɭɫɥɨɜɧɨɟ «ɜɪɟɦɹ» ݐൌݖȀݒ
, ɬɨɝɞɚ ɭɪɚɜ-
ɧɟɧɢɟ ɩɪɢɦɟɬ ɜɢɞ
81
ሻ
μ
μݐ
ᇱ
ሺ
ሻ
ݐǡݐ
ܩ
ఠ
ൌൣ݅߱ߪො
െ݅ߟሺݐሻߪොଷെ݅ߞሺݐሻԜߪො
ଷ
െ
Ⱦɚɥɟɟ ɜɜɟɞɟɦ ɮɭɧɤɰɢɢ Ƚɪɢɧɚ ݃ො
ɭɩɪɨɳɟɧɢɹ ɮɨɪɦɭɥ ɜ ɞɚɥɶɧɟɣɲɟɦ
ሺ
ݐǡݐ
ܩ
ఠ
ɬɨɝɞɚ
μ
μݐ
ᇱ
ሺ
ሻ
ݐǡݐ
݃ො
ఠ
ൌൣ݅߱ߪො
െ݅ߟሺݐሻߪොଷߞሺݐሻԜߪො
ଷ
ߜሺݐെݐ
ɝɞɟ ɦɵ ɩɟɪɟɨɛɨɡɧɚɱɢɥɢ
െ݅ߞሺݐሻ՜ߞሺݐሻǡ᩷݅ߞ
݅
ߪොଷߜሺݐെݐ
ݒ
ሺ
ݐǡݐԢ
ఠ
ᇱ
ሻ
ൌെ
ሺାሻ
݅ߞ
ᇱ
ሻ
Ǥ
ሻ
, ɜɵɞɟɥɹɹ ɧɟɤɨɬɨɪɵɟ ɦɧɨɠɢɬɟɥɢ ɞɥɹ
݅
ݒ
ᇱ
ሺ
ሻ
ݐǡݐ
ఠ
ሺାሻ
ǡ
ሺݐሻ
ߪො
ߞ
՜ߞ
݃ො
ᇱ
ሻ
כ
ଷ
כ
כ
כ
ሺݐሻ
ǡ
ሺݐሻ
ሺݐሻǤ
ሺିሻ
Ԝߪො
൧ܩ
ᇱ
ሺ
ሻ
ݐǡݐ
ఠ
െ
ሺ
ሺ
ሺିሻ
Ԝߪො
൧݃ො
ᇱ
ሺ
ሻ
ݐǡݐ
ఠ
ሺ
ሺ
ͺǤ͵Ͷ
ͺǤ͵ͷ
ͺǤ͵
ͺǤ͵
ሻ
ሻ
ሻ
ሻ
Ʉɚɤ ɮɭɧɤɰɢɢ ɧɨɜɨɣ ɩɟɪɟɦɟɧɧɨɣ ݐ, ɫɥɭɱɚɣɧɵɟ ɩɨɥɹ ߟሺݐሻ ɢ ߞሺݐ
ሻ
ɢɦɟɸɬ ɫɥɟɞɭ-
ɸɳɢɟ ɤɨɪɪɟɥɹɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ
ͳ
ۦߞሺݐ
ۦߟሺݐ
ሻ
ۧ
ൌͲǡ᩷ۦߞሺݐሻߞ
ሻ
ۧ
ൌͲǡ᩷ۦߟሺݐሻߟሺݐ
כ
ᇱ
ሺ
ሻ
ۧ
ݐ
ൌ
ᇱ
ͳ
Ԝߜሺݐെݐ
߬
ଶ
ሻ
ۧ
ൌ
Ԝߜሺݐെݐ
߬
ଵ
ᇱ
ሻ
ᇱ
ሻ
ǡ
ǡ᩷ۦߞሺݐሻߞሺݐ
ᇱ
ሻ
ۧ
ൌͲǤሺͺǤ͵ͻ
ሺ
ͺǤ͵ͺ
ȼɜɟɞɟɦ ɨɛɨɡɧɚɱɟɧɢɟ
ܮ
ሺݐሻ
ൌ݅߱ߪො
ఠ
െ݅ߟሺݐሻߪොଷߞሺݐሻԜߪො
ଷ
݅߱െ݅ߟሺݐ
ൌ൬
כ
ሺݐሻ
ߞ
ሻ
ሺାሻ
ߞሺݐ
െ݅߱݅ߟሺݐ
Ƀ
ሻ
ሻ
൰ǡ
כ
ሺݐሻ
ሺିሻ
Ԝߪො
ൌ
ሺ
ͺǤͶͲ
ɬɨɝɞɚ ɭɪɚɜɧɟɧɢɟ ɧɚ ɮɭɧɤɰɢɸ Ƚɪɢɧɚ ɩɪɢɦɟɬ ɜɢɞ
μ
Ԝ݃ො
μݐ
ɉɪɨɢɧɬɟɝɪɢɪɭɟɦ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɩɨ ɢɧɬɟɪɜɚɥɭ
ᇱ
ሺ
ሻ
݃ො
ݐǡݐ
ఠ
ൌ݃ො
ሺ
ఠ
ᇱ
ሻ
ൌܮ
௧
න݀
௧
బ
ሺݐሻ
ఠ
ሺ߬ሻ
߬ܮ
ఠ
ሺ
ݐǡݐ
ఠ
ᇱ
ሻ
ݐ
ǡݐ
ᇱ
ሺ
Ԝ݃ො
ሻߜሺ
ݐǡݐ
ఠ
ሺ
ݐ
ᇱ
ሺ
Ԝ݃ො
ሻߠሺ
߬ǡݐ
ఠ
ݐെݐ
ሻ
ǡݐ
, ɩɨɥɭɱɢɦ
ᇱ
ሻ
ݐെݐ
െݐ
ሻǤሺ
ሺ
ͺǤͶͳ
ͺǤͶʹ
Ǥ
ᇱ
ᇱ
ሻߠሺ
ݐ
Ɏɨɪɦɚɥɶɧɨ, ɪɟɲɚɹ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɦɟɬɨɞɨɦ ɢɬɟɪɚɰɢɣ, ɬɚɤ ɠɟ ɤɚɤ ɷɬɨ ɞɟɥɚɟɬɫɹ
ɜ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɩɨɥɹ, ɩɪɢ ɜɵɜɨɞɟ ܵ-ɦɚɬɪɢɰɵ ɜ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɜɡɚɢɦɨɞɟɣ-
ɫɬɜɢɹ, ɩɟɪɟɩɢɲɟɦ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɜ ɮɨɪɦɟ
ሻ
ሻ
ሻ
ሻ
ሻ
82
݃ො
ᇱ
ሻ
ൌܵ
መ
ሺ
ሻ
ݐǡݐ
ఠ
݃ො
ሺ
ݐǡݐ
ఠ
ᇱ
ሺ
ሻ
ݐ
ܵ
ǡݐ
ఠ
ᇱ
መ
ሺ
ሻߠሺ
ݐǡݐ
ఠ
ݐെݐ
ᇱ
ሻߠሺ
ᇱ
ሻǤሺ
ݐ
െݐ
ͺǤͶ͵
Ɂɞɟɫɶ ɩɨɹɜɢɥɫɹ ɨɩɟɪɚɬɨɪ ɷɜɨɥɸɰɢɢ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɜɵɪɚɠɟɧɢɟɦ
መ
ሺ
ݐǡݐ
ܵ
ఠ
ɨɩɟɪɚɬɨɪ ɯɪɨɧɨɥɨɝɢɱɟɫɤɨɝɨ ɭɩɨɪɹɞɨɱɟɧɢɹ. ɗɬɨ ɢ ɟɫɬɶ ܵ-ɦɚɬɪɢɰɚ. ɋɪɚɡɭ
ɝɞɟ
௧
ሻ
ൌ
௧
௧
ቊන݀
௧
బ
߬ܮ
ሺ߬ሻ
ቋ
ǡ
ఠ
ሺ
ͺǤͶͶ
ɨɬɦɟɬɢɦ ɨɱɟɜɢɞɧɨɟ ɩɨɥɭɝɪɭɩɩɨɜɨɟ ɫɜɨɣɫɬɜɨ ܵ-ɦɚɬɪɢɰɵ
መ
ሺ
ሻ
ݐǡݐ
ܵ
ఠ
ൌܵ
Ⱦɥɹ ɨɛɪɚɬɧɨɣ ɦɚɬɪɢɰɵ ܵ
መ
መ
ఠ
ܵ
ఠ
ିଵ
መ
ሺ
ሻ
ሺ
ݐǡݐ
ܵ
ଵ
ሺ
ሻ
ݐǡݐ
, ɨɩɪɟɞɟɥɟɧɧɨɣ ɨɛɵɱɧɵɦ ɨɛɪɚɡɨɦ:
ିଵ
መ
ሺ
ݐǡݐ
ఠ
ሻ
ݐ
ܵ
ଵǡݐ
መ
ఠ
ሺ
ݐǡݐ
ǡ᩷ɩɪɢ᩷ݐݐ
ሻ
ൌͳǡ
ఠ
ሻ
ଵݐ
Ǥ
ሺ
ͺǤͶͷ
ሺ
ͺǤͶ
ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɟɞɫɬɚɜɥɟɧɢɟ
௧
ሺ߬ሻ
ቋ
߬ܮ
௧
బ
ǡ
ఠ
ሺ
ͺǤͶ
ɝɞɟ
ିଵ
መ
ሺ
ݐǡݐ
ܵ
ఠ
ିଵ
ɨɩɟɪɚɬɨɪ ɚɧɬɢɭɩɨɪɹɞɨɱɟɧɢɹ ɩɨ ݐ. ɂɡ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɪɚɬɧɨɣ ɦɚɬɪɢ-
௧
ିଵ
ሻ
ൌ
ቊെන݀
௧
ɰɵ (8.46) ɢ ɩɨɥɭɝɪɭɩɩɨɜɨɝɨ ɫɜɨɣɫɬɜɚ (8.45) ɩɨɥɭɱɚɟɬɫɹ ɫɜɨɣɫɬɜɨ «ɤɨɦɩɟɧɫɚɰɢɢ»:
ܵ
መ
ሺ
ݐ
ఠ
ଵǡݐ
ሻ
ൌܵ
ିଵ
መ
ఠ
መ
ሺ
ሻ
ሺ
ݐǡݐ
ܵ
ଵ
ሻ
ݐǡݐ
ఠ
ǡ᩷ɩɪɢ᩷ݐݐ
ଵݐ
Ǥ
ሺ
ͺǤͶͺ
ɋ ɩɨɦɨɳɶɸ ɷɬɨɝɨ ɫɜɨɣɫɬɜɚ ɢɡ ɭɪɚɜɧɟɧɢɹ (8.43) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɭɪɚɜɧɟɧɢɟ ɫ
ɨɛɪɚɬɧɨɣ ɦɚɬɪɢɰɟɣ
݃ො
ǡݐ
ሻ
ൌܵ
መ
ሺ
ሻ
ݐǡݐ
ఠ
ሺ
݃ො
ݐǡݐ
ఠ
ሺ
ݐ
ఠ
ିଵ
ᇱ
ିଵ
ᇱ
ሻ
െܵ
ᇱ
መ
ሺ
ሻߠሺ
ݐ
ǡݐ
ఠ
ݐെݐ
ᇱ
ሻߠሺ
ᇱ
ሻǤሺ
ݐ
െݐ
ͺǤͶͻ
ɋɜɨɣɫɬɜɚ S-ɦɚɬɪɢɰɵ
Ɋɚɡɨɛɶɟɦ ɨɬɪɟɡɨɤ
ɷɬɨɦ ɨɛɨɡɧɚɱɢɦ ߜൌݐ
ǡݐሿ ɧɚ ܰ ɪɚɜɧɵɯ ɱɚɫɬɟɣ ݐ൏ݐଵ൏ڮݐ
ݐ
ାଵെݐ
ൌሺݐെݐ
ሻ
Ȁܰ, ɬɨɝɞɚ ɢɧɬɟɝɪɚɥ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ܵ-ɦɚɬ-
ேିଵ൏ݐே
ൌݐ, ɩɪɢ
ሾ
ɪɢɰɵ (8.44) ɦɨɠɧɨ ɡɚɦɟɧɢɬɶ ɢɧɬɟɝɪɚɥɶɧɨɣ ɫɭɦɦɨɣ
ሺ߬ሻ
ே
ൌܮ
ୀଵ
ఠ
ǡ
ሺ
ͺǤͷͲ
௧
න݀
௧
బ
߬ܮ
ఠ
ɝɞɟ
ܮ
ൌ݅߱ߜԜߪොଷെ݅ߟԜߪොଷߞԜߪො
ఠ
ሺାሻ
ߞ
݅߱ߜെ݅ߟ
ሺିሻ
כ
Ԝߪො
ൌ൬
כ
ߞ
െ݅߱ߜ݅ߟ
ߞ
൰ሺͺǤͷͳ
ɢ ɜɜɟɞɟɧɵ ɨɛɨɡɧɚɱɟɧɢɹ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ߟ
ൌߟሺݐ
ሻ
ߜǡ᩷ߞ
83
ൌߞሺݐ
ሻ
ߜǤ
ሺ
ͺǤͷʹ
ሻ
ɗɬɢ ɫɥɭɱɚɣɧɵɟ ɩɟɪɟɦɟɧɧɵɟ ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɟ ɫɪɟɞɧɢɟ ɩɨ ɪɟɚɥɢɡɚɰɢɢ ɫɥɭ-
ɱɚɣɧɨɝɨ ɩɨɥɹ
ۦߟ
ۧ
ൌۦߞ
ൌͲǡ᩷ۦߟߟ
ۧ
ۧൌߜ
ߜ
ǡ᩷ۦߞߞ
߬
ଵ
כ
ۧ
ൌߜ
ߜ
ǤሺͺǤͷ͵
߬
ଶ
ɂɫɩɨɥɶɡɭɹ (8.50), ܵ-ɦɚɬɪɢɰɭ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɩɪɟɞɟɥɚ ɨɬ ɤɨɧɟɱɧɨɝɨ
ɩɪɨɢɡɜɟɞɟɧɢɹ ɦɚɬɪɢɰ
ே
ܵ
መ
ሺ
ݐǡݐ
ఠ
ሻ
ൌ
ෑ݁
௧
ɉɨɫɤɨɥɶɤɭ, ɨɱɟɜɢɞɧɨ, ܮ
ୀଵ
ഘ
ൌ݁
ൌͲ ɬɨ ݁
ఠ
ܵ
ഘಿ
ഘಿషభ
݁
መ
ሺ
ݐǡݐ
ఠ
ഘమ
ഘభ
݁
ൌͳ ɢ ɫɥɟɞɨɜɚɬɟɥɶɧɨ
ሻ
ڮ݁
ഘ
ൌͳǡ
ǡ᩷ܰ՜λǡߜ՜ͲǤሺͺǤͷͶ
ሺ
ͺǤͷͷ
ሻ
ሻ
ሻ
ɬɨ ɟɫɬɶ ܵ-ɦɚɬɪɢɰɚ ɭɧɢɦɨɞɭɥɹɪɧɚ, ɤɪɨɦɟ ɬɨɝɨ ɢɡ (8.40) ɦɨɠɧɨ ɭɜɢɞɟɬɶ, ɱɬɨ ɦɚɬɪɢɰɵ ܮ
ɢ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ܵ
ɩɪɢɧɚɞɥɟɠɚɬ ɚɥɝɟɛɪɟ Ʌɢ ݏݑሺͳǡͳሻ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɤɚɠɞɚɹ ɦɚɬɪɢɰɚ ݁
ఠ
መ
ሺ
ሻ
ݐǡݐ
ɩɪɢɧɚɞɥɟɠɚɬ ɝɪɭɩɩɟ ܷܵሺͳǡͳ
ఠ
ɩɪɢ ɥɢɧɟɣɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɧɚ ʠ
ଶ
ɫɨɯɪɚɧɹɸɬ ɮɨɪɦɭ
ሻ
. Ɇɚɬɪɢɰɵ ɢɡ ɷɬɨɣ ɝɪɭɩɩɵ
ଶ
ȁ
ȁ
ݖ
ଵ
െȁݖ
ଶ
ȁ
ɢ ɨɛɥɚɞɚɸɬ
ଶ
ɫɜɨɣɫɬɜɨɦ
ܵ
መ
ఠԜଶଶ
ൌܵ
כ
መ
ఠԜଵଵ
ǡ᩷᩷ܵ
መ
ఠԜଶଵ
ൌܵ
כ
መ
ఠԜଵଶ
ǡ᩷᩷หܵ
መ
ఠԜଵଵ
หଶെหܵ
መ
หଶൌͳǤሺͺǤͷ
ఠԜଵଶ
Ⱥɧɚɥɨɝɢɱɧɨ ɨɛɪɚɬɧɚɹ ɦɚɬɪɢɰɚ ɩɪɟɞɫɬɚɜɢɦɚ ɜ ɜɢɞɟ
ே
ܵ
ିଵ
መ
ሺ
ݐǡݐ
ఠ
ିଵ
ሻ
ൌ
௧
ෑ݁
ୀଵ
ି
ഘ
ൌ݁
ഘభ
ି
݁
ഘమ
ڮ݁
ି
ഘಿషభ
ି
ഘಿ
݁
ǡܰ՜λǡԜ߂՜ͲሺͺǤͷ
ɟɟ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɫ ɭɱɟɬɨɦ ɭɧɢɦɨɞɭɥɹɪɧɨɫɬɢ ɜɵɪɚɠɚɸɬɫɹ ɱɟɪɟɡ ɦɚɬɪɢɱ-
ɧɵɟ ɷɥɟɦɟɧɬɵ ܵ
መ
ɨɛɵɱɧɵɦ ɨɛɪɚɡɨɦ:
ఠ
ିଵ
መ
ܵ
ఠ
ൌቆ
መ
ܵ
െܵ
ఠԜଶଶ
መ
ఠԜଶଵ
െܵ
ܵ
መ
ఠԜଵଶ
መ
ఠԜଵଵ
ቇǤ
ሺ
ͺǤͷͺ
ɉɪɢ ɜɵɱɢɫɥɟɧɢɢ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɛɭɞɟɬ ɩɨɥɟɡɧɵɦ ɫɥɟɞɭɸ-
ɳɟɟ «ɤɚɥɢɛɪɨɜɨɱɧɨɟ» ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ܵ-ɦɚɬɪɢɰɵ (ɮɢɝɭɪɧɵɦɢ ɫɤɨɛɤɚɦɢ ɨɛɨɡɧɚɱɟɧɚ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ܵ-ɦɚɬɪɢɰɵ ɨɬ ɩɨɥɟɣ ߞሺݐሻ ɢ ߞ
݁
ఠభఙ
ෝ
௧
య
መ
ܵ
൫ݐǡݐᇱǡ൛ߞ
ఠିఠ
భ
כ
ሚ
ሚ
ǡߞ
ൟ൯݁
ఠ
ఠ
భ
భ
ିఠభఙ
ᇲ
ෝ
௧
య
መ
ሺ
ൌܵ
ఠ
ݐǡݐ
ᇱ
ǡሼߞǡߞ
כ
ሺݐሻ
)
כ
ሻ
ሽ
ሺ
ǡ
ͺǤͷͻ
ɝɞɟ
ߞ
ሚ
ሺݐሻൌߞሺݐሻ
ఠ
భ
ିଶఠభ௧
݁
ǡ᩷᩷ߞ
כ
ሚ
ሺݐሻ
ఠ
భ
ൌߞ
כ
ଶఠభ௧
ሺݐሻ
݁
Ǥ
ሺ
ͺǤͲ
ഘ
ሻ
ሻ
ሻ
ሻ
ሻ
84
Ɋɚɫɩɢɲɟɦ ɞɥɹ ɫɫɵɥɨɤ ɮɨɪɦɭɥɭ (8.59) ɞɥɹ ɦɚɬɪɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ
݁
ିఠభ௧
݁
݁
ఠభ௧
ఠభ௧
݁
ିఠభ௧
መ
ܵ
ఠିఠభԜଵଵ
መ
ܵ
ఠିఠభԜଵଶ
መ
ܵ
ఠିఠభԜଶଵ
መ
ܵ
ఠିఠభԜଶଶ
൫ݐǡݐᇱǡ൛ߞ
൫ݐǡݐᇱǡ൛ߞ
൫ݐǡݐᇱǡ൛ߞ
൫ݐǡݐᇱǡ൛ߞ
כ
ሚ
ሚ
ǡߞ
ൟ൯݁
ఠ
ఠ
భ
భ
כ
ሚ
ሚ
ǡߞ
ఠ
ఠ
భ
భ
כ
ሚ
ሚ
ǡߞ
ൟ൯݁
ఠ
ఠ
భ
భ
כ
ሚ
ሚ
ǡߞ
ఠ
ఠ
భ
భ
ൟ൯݁
ൟ൯݁
ିఠభ௧
ఠభ௧
ିఠభ௧
ఠభ௧
ᇲ
ᇲ
ᇲ
ᇲ
መ
ൌܵ
ఠԜଵଵ
መ
ൌܵ
ఠԜଵଶ
መ
ൌܵ
ఠԜଶଵ
መ
ൌܵ
ఠԜଶଶ
ᇱ
כ
ǡሼߞǡߞ
ǡሼߞǡߞ
ǡሼߞǡߞ
ǡሼߞǡߞ
ሻ
ሽ
כ
ሻ
ሽ
ሺ
ͺǤͳ
כ
ሻ
ሽ
כ
ሻ
ሽ
ሺ
ݐǡݐ
ᇱ
ሺ
ݐǡݐ
ᇱ
ሺ
ݐǡݐ
ᇱ
ሺ
ݐǡݐ
8.3. ȼɵɪɚɠɟɧɢɟ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɱɟɪɟɡ ɷɥɟɦɟɧɬɵ
S-ɦɚɬɪɢɰɵ
ȼɵɪɚɡɢɦ ɬɟɩɟɪɶ ɮɭɧɤɰɢɢ Ƚɪɢɧɚ ɱɟɪɟɡ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ܵ-ɦɚɬɪɢɰɵ. ɗɬɨ
ɧɭɠɧɨ ɞɟɥɚɬɶ ɨɬɞɟɥɶɧɨ ɞɥɹ ɡɚɩɚɡɞɵɜɚɸɳɟɣ ɢ ɨɩɟɪɟɠɚɸɳɟɣ ɮɭɧɤɰɢɣ. ɇɚɱɧɟɦ
ɫ ɡɚɩɚɡɞɵɜɚɸɳɟɣ ɮɭɧɤɰɢɢ. ɂɫɯɨɞɢɦ ɢɡ ɭɪɚɜɧɟɧɢɹ (8.43), ɤɨɬɨɪɨɟ ɡɚɩɢɲɟɦ
ɡɞɟɫɶ ɜ ɢɧɞɟɤɫɚɯ (ɩɨ ɩɨɜɬɨɪɹɸɳɢɦɫɹ ɢɧɞɟɤɫɚɦ ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ ɫɭɦɦɢɪɨɜɚɧɢɟ)
݃ො
ோ
ఠԜఓఔ
ሺ
ݐǡݐ
ᇱ
ሻ
ൌܵ
መ
ఠԜఓఒ
ሺ
ݐǡݐ
ோ
ሻ
݃ො
ఠԜఒఔ
ᇱ
ǡݐ
ሻ
ܵ
መ
ఠԜఓఔ
ሺ
ݐ
ᇱ
ሺ
ሻߠሺ
ݐǡݐ
ݐെݐ
ᇱ
ሻߠሺ
ᇱ
ሻǤሺ
ݐ
െݐ
ͺǤʹ
ሻ
ሻ
ɍɫɬɪɟɦɢɦ ɬɟɩɟɪɶ ݐ
՜െλ ɢ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (8.32),
ɬɨɝɞɚ
݃ො
ோ
ఠԜఓఔ
ᇱ
ሻ
ൌܵ
መ
ఠԜఓଶ
ሺ
ݐǡെλሻ݃ො
ሺ
ݐǡݐ
ோ
ఠԜଶఔ
ሺ
െλǡݐ
ᇱ
መ
ሻ
ܵ
ఠԜఓఔ
ᇱ
ሺ
ሻߠሺ
ݐǡݐ
ݐെݐ
ᇱ
ሻǡሺ
ͺǤ͵
ɬɟɩɟɪɶ ɜɵɛɟɪɟɦ ߤൌʹ, ɫɞɟɥɚɟɦ ɩɪɟɞɟɥɶɧɵɣ ɩɟɪɟɯɨɞ ݐ՜λ, ɫɨɝɥɚɫɧɨ (8.32), ɩɨ-
ɥɭɱɢɦ
Ͳൌܵ
መ
ఠԜଶଶ
ሺ
λǡെλሻ݃ො
ோ
ఠԜଶఔ
ሺ
െλǡݐ
ᇱ
መ
ሻ
ܵ
ఠԜଶఔ
ሺ
λǡݐ
ᇱ
ሻ
ǡ
ሺ
ͺǤͶ
ɨɬɤɭɞɚ
݃ො
ோ
ఠԜଶఔ
ሺ
െλǡݐ
ᇱ
ሻ
ൌെ
መ
ܵ
መ
ܵ
ఠԜଶఔ
ఠԜଶଶ
ሺ
λǡݐ
ሺ
λǡെλ
ᇱ
ሻ
ǡ
ሻ
ሺ
ͺǤͷ
ɩɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (8.63), ɩɨɥɭɱɚɟɦ
݃ො
ோ
ఠԜఓఔ
መ
ሺ
ܵ
ݐǡെλሻԜܵ
ൌെ
ఠԜఓଶ
መ
ܵ
ᇱ
ሺ
ሻ
ݐǡݐ
ఠԜଶଶ
መ
ሺ
λǡെλ
ఠԜଶఔ
ሺ
ሻ
λǡݐ
ᇱ
ሻ
ܵ
መ
ఠԜఓఔ
ᇱ
ሺ
ሻߠሺ
ݐǡݐ
ݐെݐ
ᇱ
ሻ
ǡሺͺǤሻ
ɷɬɚ ɮɨɪɦɭɥɚ ɜɟɪɧɚ ɩɪɢ ɥɸɛɨɦ ɡɧɚɱɟɧɢɢ ɚɪɝɭɦɟɧɬɨɜ, ɟɫɥɢ ɩɪɢ ɷɬɨɦ ݐ൏ݐԢ, ɬɨ
݃ො
ோ
ఠఓఔ
መ
ሺ
ܵ
ݐǡെλሻԜܵ
ൌെ
ఠԜఓଶ
መ
ܵ
ᇱ
ሺ
ሻ
ݐǡݐ
ఠԜଶଶ
መ
ሺ
λǡെλ
ఠԜଶఔ
ሺ
ሻ
λǡݐ
ᇱ
ሻ
ǡ᩷ɩɪɢ᩷ݐ൏ݐᇱǤ
ሺ
ͺǤ
ɋɨɜɟɪɲɟɧɧɨ ɚɧɚɥɨɝɢɱɧɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɩɪɢɜɨɞɹɬ ɤ ɫɥɟɞɭɸɳɢɦ ɜɵɪɚɠɟɧɢɹɦ
ɞɥɹ ɨɩɟɪɟɠɚɸɳɟɣ ɮɭɧɤɰɢɢ Ƚɪɢɧɚ
85
ሻ
ሻ
ሻ
ሻ
݃ො
݃ො
ఠԜఓఔ
ሺ
ݐǡݐ
ఠԜఓఔ
ᇱ
ሺ
ሻ
ݐǡݐ
ൌെ
ᇱ
ሻ
መ
ܵ
ఠԜఓଵ
ൌെ
ሺ
ݐǡെλሻԜܵ
መ
ܵ
ఠԜଵଵ
መ
ܵ
ఠԜఓଵ
መ
ሺ
λǡെλ
ሺ
ݐǡെλሻԜܵ
መ
ܵ
ఠԜଵଵ
ఠԜଵఔ
ሺ
ሺ
λǡݐ
ሻ
መ
ఠԜଵఔ
λǡെλ
ᇱ
ሺ
ሻ
ሻ
λǡݐ
ܵ
ᇱ
መ
ఠԜఓఔ
ሻ
ᇱ
ሺ
ሻߠሺ
ݐǡݐ
ݐെݐ
ǡ᩷ɩɪɢ᩷ݐ൏ݐᇱǤ
ᇱ
ሻǡሺ
ͺǤͺ
ሺ
ͺǤͻ
ɇɚɦ ɩɨɬɪɟɛɭɸɬɫɹ ɜ ɞɚɥɶɧɟɣɲɟɦ «ɭɤɨɪɨɱɟɧɧɵɟ» ɮɨɪɦɭɥɵ ɬɢɩɚ (8.67) ɢ (8.69)
ɞɥɹ ɤɨɦɛɢɧɚɰɢɢ ɚɪɝɭɦɟɧɬɨɜ ݐݐԢ. ɂɯ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɭɪɚɜɧɟɧɢɹ ( 8.49) ɫ ɦɚɬ-
ିଵ
መ
ሺ
ሻ
ݐǡݐ
ɪɢɰɟɣ ܵ
ఠ
݃ො
݃ො
, ɜɵɜɨɞ ɚɧɚɥɨɝɢɱɧɵɣ ɩɪɨɞɟɥɚɧɧɨɦɭ ɞɚɟɬ
ோ
ఠԜఓఔ
ఠԜఓఔ
ሺ
ሺ
ݐǡݐ
ݐǡݐ
ିଵ
መ
ሺ
ܵ
ఠԜఓଵ
ᇱ
ሻ
ൌ
ିଵ
መ
ሺ
ܵ
ఠԜఓଶ
ᇱ
ሻ
ൌ
λǡݐሻԜܵ
ିଵ
መ
ܵ
ఠԜଵଵ
λǡݐሻԜܵ
ିଵ
መ
ܵ
ఠԜଶଶ
ିଵ
መ
ఠԜଵఔ
ሺ
λǡെλ
ିଵ
መ
ఠԜଶఔ
ሺ
λǡെλ
ሺ
ሺ
ᇱ
ݐ
ሻ
ᇱ
ݐ
ሻ
ǡെλ
ǡെλ
ሻ
ሻ
ǡ᩷ɩɪɢ᩷ݐݐᇱǡ
ǡ᩷ɩɪɢ᩷ݐݐᇱǤ
ሺ
ͺǤͲ
ሺ
ͺǤͳ
Ɏɨɪɦɭɥɵ (8.67), (8.69), (8.70), (8.71) ɪɟɲɚɸɬ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ ɜɵɪɚɠɟ-
ɧɢɹ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ ɱɟɪɟɡ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ܵ-ɦɚɬɪɢɰɵ.
8.4. ȼɵɪɚɠɟɧɢɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɞɧɨɦɟɪɧɨɝɨ ɦɟɬɚɥɥɚ
ɱɟɪɟɡ ɷɥɟɦɟɧɬɵ ࡿ-ɦɚɬɪɢɰɵ
ɋɬɚɪɬɭɟɦ ɫ ɨɞɧɨɦɟɪɧɨɝɨ ɜɚɪɢɚɧɬɚ ɮɨɪɦɭɥɵ (4.65) (ɡɞɟɫɶ ൌͳ, ɩɨɫɥɟ ɞɟɣ-
ɫɬɜɢɹ ɨɩɟɪɚɬɨɪɨɜ ɧɭɠɧɨ ɩɨɥɨɠɢɬɶ ݕൌݖ ɢ ݕ
ஶ
ିஶ
ோ
ሺ
߱ߗǡݕǡݖ
ሻ
ɱɟɪɟɡ ɞɥɢɧɧɨɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ Ƚɪɢɧɚ ܩ
ଵ
ఓିଵ
ሻ
:
ఔୀଵǡଶఓୀଵǡଶ
݀݊
ி
߱Ԝቆ
݀߱
ሻ
ܩ
ଵ
బఎഋ௭ିబఎഌ௭
ߪሺߗǡݖሻൌ
ͺߨ݉
ܩ
ȼɵɪɚɡɢɦ ɮɭɧɤɰɢɢ ܩሺݖǡݖ
ɢɫɩɨɥɶɡɭɹ ɫɢɦɜɨɥ ߟ
ܩሺݖǡݖ
ଶ
݁
ൌሺെͳ
ఓ
ଶ
ଵ
Ԝන݀ݖଵԜන ݀
ሻ
ൌ݁
ɩɨɞɫɬɚɜɥɹɹ ɜ (8.72) ɢ ɞɟɣɫɬɜɭɹ ɨɩɟɪɚɬɨɪɚɦɢ ɬɨɥɶɤɨ ɧɚ ɛɵɫɬɪɨ ɦɟɧɹɸɳɢɟɫɹ ɷɤɫ-
ɩɨɧɟɧɬɵ ݁
ߪሺߗሻൌെ
బఎഋ௭
, ɩɨɫɥɟ ɧɟɫɥɨɠɧɨɝɨ ɜɵɱɢɫɥɟɧɢɹ ɩɨɥɭɱɢɦ
ଶ
݁
ʹߨ݉
ଶ
Ԝන݀ݖଵԜන ݀
ଶ
ିஶ
ஶ
߱Ԝቆ
݀݊
ி
݀߱
ሺ߱ሻ
ቇԜൣܩ
ɉɨɫɥɟ ɭɫɪɟɞɧɟɧɢɹ ɡɚɜɢɫɢɦɨɫɬɶ ߪሺߗǡݖሻ ɨɬ ݖ ɢɫɱɟɡɧɟɬ, ɢ ɦɵ ɧɟ ɛɭɞɟɦ ɟɟ ɭɤɚ-
ɡɵɜɚɬɶ. ȼɵɪɚɡɢɦ ɮɭɧɤɰɢɢ ܩ ɱɟɪɟɡ ݃ො ɩɨ ɮɨɪɦɭɥɟ (8.35), ɩɨɥɭɱɢɦ
)
ଵൌݖଵ
ሺ߱ሻ
ቇ൫௭െ௬൯൫
ሺ
߱ǡݕ
ǡݖሻǤ
ଵ
ᇲ
ܩ
ோ
ሺ
ఠାఆ
ఓఔ
ݖǡݖ
ሺ
ଵ
ݖǡݖ
ሻ
െ
௬
భ
భ
ሺ
ݖ
ǡݖሻߪොଷ൧ǤሺͺǤͶ
ଵ
൯Ԝ
ሺ
ͺǤʹ
ሺ
ݖǡݖ
ఓఔ
ଵ
ሺ
ͺǤ͵
௭
ሻ
ǡ
ଵ
ߪො
ܩ
ଷ
ఠ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
,
ሻ
ሻ
86
ஶ
ିஶ
߱Ԝቆ
݀݊
ி
݀߱
ሺ߱ሻ
ቇԜሾ݃ො
ோ
ఠାఆ
ݐǡݐ
ሻ
ሺ
ሻ
ݐ
ଵ
ǡݐ
ሿ
ǤሺͺǤͷ
݃ො
ଵ
ఠ
ሺ
ߪሺߗሻൌ
ଶ
ݒ
݁
Ԝන݀ݐଵԜන ݀
ʹߨ
ȼɵɪɚɠɟɧɢɟ ɩɨɞ ɜ (8.75) ɮɚɤɬɢɱɟɫɤɢ ɧɚ ɡɚɜɢɫɢɬ ɨɬ ߱, ɢ ɜ ɧɟɦ ɦɵ ɩɨɥɨɠɢɦ
߱ൌͲ, ɬɨɝɞɚ ɢɧɬɟɝɪɚɥ ɩɨ ɱɚɫɬɨɬɟ ߱ ɪɚɜɟɧ െͳ, ɜ ɢɬɨɝɟ ɩɨɥɭɱɢɦ
ଶ
ݒ
݁
ߪሺߗሻൌെ
Ԝන݀ݐଵԜሾ݃ො
ʹߨ
ோ
ఆ
ሺ
ݐǡݐ
ሻ
ሺ
ሻ
݃ො
ଵ
ሿ
ݐ
ǡݐ
Ǥ
ଵ
ሺ
ͺǤ
ሻ
ሻ
Ɋɚɡɛɢɜɚɟɦ ɢɧɬɟɝɪɚɥ ɩɨ ݐ
ߪሺߗሻൌെ
ɧɚ ɞɜɚ ɨɬ െλ ɞɨ ݐ ɢ ɨɬ ݐ ɞɨ λ:
ଵ
௧
ଶ
݁
ݒ
ʹߨ
ஶ
න ݀
௧
ቊ
න݀
ିஶ
ݐଵԜԜሾ݃ො
ݐଵԜሾ݃ො
ோ
ሺ
ݐǡݐ
ఆ
ோ
ሺ
ݐǡݐ
ఆ
ሻ
ሺ
݃ො
ଵ
ሻ
ሺ
ሻ
݃ො
ଵ
ሻ
ݐ
ǡݐ
ଵ
ሿ
ݐ
ǡݐ
ଵ
ሿ
ቋ
ɢ ɢɫɩɨɥɶɡɭɟɦ ɮɨɪɦɭɥɵ (8.67), (8.69), (8.70), (8.71) ɞɥɹ ɮɭɧɤɰɢɣ ݃, ɩɨɥɭɱɢɦ
መ
ఆԜఓଶ
መ
ܵ
ݐଵԜ
ሺ
ݐǡെλሻԜܵ
መ
ܵ
ఆԜଶଶ
ିଵ
ఆԜఓଵ
ሺ
ሺ
λǡെλ
ଶ
ݒ
ߪሺߗሻൌ
݁
ʹߨ
ஶ
න ݀
௧
ቊ
න݀
ݐଵԜ
௧
ିஶ
ܵ
ɂɫɩɨɥɶɡɭɹ ɬɟɩɟɪɶ ɮɨɪɦɭɥɭ (8.58), ɜɵɪɚɡɢɦ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ܵ
ቊ
መ
, ɩɨɥɭɱɢɦ
ஶ
න݀
ିஶ
ߠሺݐെݐ
ݐ
ଵ
ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ܵ
ଶ
݁
ߪሺߗሻൌ
ݒ
ʹߨ
λǡݐሻԜܵ
ିଵ
መ
ܵ
ఆԜଵଵ
መ
ఆԜଶఔ
ሻ
ܭ
ଵ
መ
ܵ
ିଵ
መ
ఆԜଵఔ
ሺ
λǡെλ
ሺ
λǡݐ
ሻ
ሺݐሻ
ఆ
ఆԜଶଶ
ሺ
ݐ
ǡെλ
ଵ
ሻ
ିଵ
መ
ሻ
ܵ
ଵ
Ԝఔଶ
ሺ
ሻߠሺ
ܮ
ݐ
ఆ
ଵ
ሺ
λǡെλሻܵ
ሻ
ሺ
λǡݐ
ܵ
መ
Ԝଵଵ
Ԝ
መ
ܵ
Ԝଶଶ
መ
ିଵ
Ԝఔଵ
ݐ
ଵ
ሺ
ሺ
ݐ
ଵ
መ
ܵ
Ԝଵଵ
ିଵ
መ
ሻ
Ԝܵ
ଵ
Ԝଶఓ
ሺ
λǡെλ
െݐሻܭ
λǡെλ
ǡെλሻԜܵ
ሺ
λǡെλ
ሺ
ݐǡെλ
ሻ
ሺ
ݐ
ఆ
ଵ
ሻ
መ
ሻ
Ԝଵఓ
ܮ
ఆ
ሻ
ሺ
ሻ
ቋ
ሺݐሻ
λǡݐ
Ǥ
ିଵ
መ
ቋ
ǡሺͺǤͻ
ሻ
ɝɞɟ
ሺ
λǡݐሻܵ
መ
መ
Ԝଵଶ
መ
መ
ఆԜଵଶ
ିଵ
ఆԜఓଵ
Ԝఔଵ
ሺ
ሺ
λǡݐሻൌ
λǡݐሻܵ
ሺ
ݐǡെλሻൌ
ሺ
ݐǡെλሻܵ
መ
ఆԜଶଵ
መ
Ԝଶଵ
ሺ
λǡݐሻǡ
ሺ
ݐǡെλሻǤ
ൌܵ
ൌܵ
መ
ఆԜଶଶ
መ
ሺ
Ԝଵଵ
ܮ
ఆ
ሺ
ݐǡെλሻܵ
ሺݐሻ
ܭ
ఆ
λǡݐሻܵ
ሺݐሻ
መ
ൌܵ
መ
ఆԜଶଶ
ିଵ
መ
ൌܵ
ఆԜଵఔ
ሺ
ݐǡെλሻെܵ
Ԝଵଵ
መ
Ԝଵఓ
ሺ
λǡݐሻെܵ
ሺ
ݐǡെλሻܵ
Ɏɨɪɦɭɥɵ (8.79), (8.80), (8.81) ɞɚɸɬ ɢɫɤɨɦɵɟ ɜɵɪɚɠɟɧɢɹ, ɫɜɹɡɵɜɚɸɳɢɟ ɩɪɨ-
ɜɨɞɢɦɨɫɬɶ ɫ ɷɥɟɦɟɧɬɚɦɢ ܵ-ɦɚɬɪɢɰɵ.
Ʌɢɬɟɪɚɬɭɪɚ
Ɍɟɯɧɢɤɚ ܵ-ɦɚɬɪɢɰɵ, ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɞɧɨɦɟɪɧɵɯ ɢ ɤɜɚɡɢ-ɨɞ-
ɧɨɦɟɪɧɵɯ ɦɟɬɚɥɥɨɜ ɢɡɥɨɠɟɧɚ ɜ [7].
87
ሺ
ͺǤ
ሺ
ͺǤͺ
ɱɟɪɟɡ
ሺ
ͺǤͺͲ
ሺ
ͺǤͺͳ
ሻ
ሻ
ሻ
ሻ
ሻ
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ
1. Ʉɚɤɢɦ ɝɪɚɧɢɱɧɵɦ ɭɫɥɨɜɢɹɦ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɨɩɟɪɟɠɚ-
ɸɳɟɣ ɢ ɡɚɩɚɡɞɵɜɚɸɳɟɣ ɮɭɧɤɰɢɣ Ƚɪɢɧɚ?
2. ȼɵɩɢɫɚɬɶ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ܵመ ɢ ܵ
3. Ʉɚɤɨɣ ɝɪɭɩɩɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɪɨɫɬɪɚɧɫɬɜɚ ʠ
4. ȼɵɩɢɫɚɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɫɬɚɬɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɱɟɪɟɡ ɷɥɟɦɟɧɬɵ
መ
ܵ
-ɦɚɬɪɢɰɵ.
ିଵ
መ
ɦɚɬɪɢɰ.
ଶ
ɩɪɢɧɚɞɥɟɠɢɬ ܵ
መ
-ɦɚɬɪɢɰɚ?
88
Ƚɥɚɜɚ 9
ɋɌȺɌɂɑȿɋɄȺə ɉɊɈȼɈȾɂɆɈɋɌɖ
ɈȾɇɈɆȿɊɇɈȽɈ ɆȿɌȺɅɅȺ
ɉɨɥɭɱɟɧɧɵɟ ɮɨɪɦɭɥɵ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ (8.79), (8.80), (8.81) ɞɨɜɨɥɶɧɨ ɫɥɨɠ-
ɧɵ. Ɉɧɢ ɫɭɳɟɫɬɜɟɧɧɨ ɭɩɪɨɳɚɸɬɫɹ ɩɪɢ ߗൌͲ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ܭ
ሺݐሻ
ɢ ɜ ɮɨɪɦɭɥɟ (8.79) ɢɧɬɟɝɪɚɥ ɩɨ ɜɫɟɣ ɨɫɢ ɧɭɠɧɨ ɡɚɦɟɧɢɬɶ ɧɚ ɢɧɬɟɝɪɚɥ ɩɨ ɤɨɧɟɱɧɨɦɭ
ɨɛɪɚɡɰɭ ɞɥɢɧɵ ܮ, ɩɪɢ ɷɬɨɦ ɞɥɹ ɭɞɨɛɫɬɜɚ ɜɜɟɞɟɦ «ɜɪɟɦɹ» ݐ
ൌܮȀݒ
. Ɍɨɝɞɚ ɞɥɹ ɩɪɨ-
ɜɨɞɢɦɨɫɬɢ ɦɵ ɩɨɥɭɱɢɦ ɫɪɚɜɧɢɬɟɥɶɧɨ ɩɪɨɫɬɨɟ ɜɵɪɚɠɟɧɢɟ
ଶ
݁
ܮ
ߪሺͲሻൌ
ʹߨ
ൣܵ
መ
Ԝଶଶ
መ
ሺ
ݐ
ǡͲሻܵ
Ԝଵଵ
ሺ
ݐ
ǡͲሻ൧ିଵǤ
Ɉɛɨɡɧɚɱɢɦ
ൌܮ
ሺݐሻ
ൌͳ,
ሺ
ͻǤͳ
ሻ
ܴሺݐ
ሻ
ൌൣܵ
መ
Ԝଶଶ
መ
ሺ
ݐ
ǡͲሻܵ
Ԝଵଵ
ሺ
ݐ
ǡͲሻ൧ିଵǡ
ሺ
ͻǤʹ
ɬɨɝɞɚ
ଶ
݁
ܮ
ߪሺͲሻൌ
ʹߨ
ܴሺݐ
ሻ
ǡ
ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɡɚɞɚɱɚ ɫɜɟɥɚɫɶ ɤ ɭɫɪɟɞɧɟɧɢɸ ɜɟɥɢɱɢɧɵ ܴሺݐ
ሻ
ɩɨ ɫɥɭɱɚɣɧɵɦ ɩɨ-
ሺ
ͻǤ͵
ɥɹɦ ߟ ɢ ߞ. Ɇɵ ɪɟɲɢɦ ɷɬɭ ɡɚɞɚɱɭ ɫɜɟɞɟɧɢɟɦ ɟɟ ɤ ɡɚɞɚɱɟ ɨ ɫɥɭɱɚɣɧɵɯ ɛɥɭɠɞɚɧɢɹɯ
ɧɚ ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ.
9.1. S-ɦɚɬɪɢɰɚ ɢ ɫɥɭɱɚɣɧɨɟ ɛɥɭɠɞɚɧɢɟ
ɧɚ ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ
ɂɞɟɹ ɷɬɨɝɨ ɩɨɞɯɨɞɚ ɫɨɫɬɨɢɬ ɜ ɫɥɟɞɭɸɳɟɦ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ܵ-ɦɚɬɪɢɰɵ ɜ ɜɢɞɟ ݐ-ɭɩɨɪɹɞɨɱɟɧɧɨɝɨ ɩɪɨɢɡɜɟɞɟɧɢɹ (8.54). ȼɵɩɢɲɟɦ ɞɥɹ ɭɞɨɛɫɬɜɚ ɟɝɨ
ɟɳɟ ɪɚɡ, ɨɩɭɫɤɚɹ ɢɧɞɟɤɫ 0, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɱɚɫɬɨɬɟ ߗൌͲ
ே
መ
ሺ
ܵ
ݐǡݐ
ሻ
ൌ
ෑ݁
௧
ୀଵ
ɝɞɟ
ൌെ݅ߟԜߪොଷߞԜߪො
ܮ
ɚ ɫɥɭɱɚɣɧɵɟ ɜɟɥɢɱɢɧɵ ߟ
Ʉɚɠɞɚɹ ɦɚɬɪɢɰɚ ݁
ɢ ߞ
ɜ ɷɬɨɦ ɩɪɨɢɡɜɟɞɟɧɢɢ ɹɜɥɹɟɬɫɹ ɛɥɢɡɤɨɣ ɤ ɟɞɢɧɢɱɧɨɣ ɭɧɢ-
ɦɨɞɭɥɹɪɧɨɣ ɦɚɬɪɢɰɟɣ ɜɢɞɚ
ಿ
ሺାሻ
݁
ߞ
ൌ݁
ɢɦɟɸɬ ɤɨɪɪɟɥɹɬɨɪɵ (8.53).
ಿషభ
ڮ݁
כ
మ
భ
݁
ǡ᩷ܰ՜λǡԜߜ՜Ͳǡ
െ݅ߟ
ߞ
כ
ߞ
݅ߟ
൰ǡ
ሺିሻ
Ԝߪො
ൌ൬
ሺ
ሺ
ͻǤͶ
ͻǤͷ
ሻ
ሻ
ሻ
ሻ
89
ܽ
ൌ൬
ܾ
כ
ܾ
൰Ǥ
כ
ܽ
ሺ
ͻǤ
݁
ɉɨɫɬɚɜɢɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɷɬɨɣ ɦɚɬɪɢɰɟ ɞɪɨɛɧɨ-ɥɢɧɟɣɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɤɨɦɩɥɟɤɫɧɨɣ ɩɥɨɫɤɨɫɬɢ
ܽ
ݖܾ
ݖհݓ
ሺݖሻ
ൌ
ܾ
כ
ݖܽ
Ǥ
כ
ሺ
ͻǤ
ɇɟɬɪɭɞɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɞɪɨɛɧɨ-ɥɢɧɟɣɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɬɚɤɨɜɨ ɜɢɞɚ, ɜɨɩɟɪɜɵɯ, ɩɟɪɟɜɨɞɢɬ ɟɞɢɧɢɱɧɵɣ ɤɪɭɝ
ȁݖȁ
ͳ ɜ ɫɟɛɹ, ɚ ɜɨ-ɜɬɨɪɵɯ ɹɜɥɹɸɬɫɹ ɞɜɢɠɟ-
ɧɢɟɦ ɦɟɬɪɢɤɢ
ଶ
݀ݏ
ଶ
ൌͶԜ
ሺ
ͳെȁݖ
݀ݖ݀ݖ᪄
ȁ
ଶሻଶ
ൌͶԜ
݀ݔ
ሾ
ͳെሺݔ
݀ݕ
ଶݕଶ
ଶ
ሺ
ଶ
ሻ
ሿ
ͻǤͺ
ɨɩɪɟɞɟɥɟɧɧɨɣ ɜɧɭɬɪɢ ɤɪɭɝɚ. ɉɨɫɥɟɞɧɟɟ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɟɫɥɢ ݓ ɢ ݖ ɫɜɹɡɚɧɵ ɫɨɨɬɧɨ-
ɲɟɧɢɟɦ (9.7), ɬɨ
݀ݓ݀ݓ᪄
ሺ
ͳെȁݓ
ȁ
ଶሻଶ
ൌ
ሾͳെȁݖȁ
݀ݖ݀ݖ᪄
ଶሿଶ
Ǥ
ሺ
ͻǤͻ
ȿɞɢɧɢɱɧɵɣ ɤɪɭɝ ɜɦɟɫɬɟ ɫ ɦɟɬɪɢɤɨɣ (9.8) ɹɜɥɹɟɬɫɹ ɦɨɞɟɥɶɸ Ʉɥɟɣɧɚ ɝɟɨɦɟɬɪɢɢ
Ʌɨɛɚɱɟɜɫɤɨɝɨ. ȼ ɷɬɨɣ ɦɨɞɟɥɢ ɩɪɹɦɵɦɢ ɹɜɥɹɸɬɫɹ ɞɭɝɢ ɨɤɪɭɠɧɨɫɬɟɣ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɟ ɝɪɚɧɢɱɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɟɞɢɧɢɱɧɨɝɨ ɤɪɭɝɚ (ɷɬɨ ɝɪɚɧɢɱɧɚɹ ɨɤɪɭɠɧɨɫɬɶ
ɧɚɡɵɜɚɟɬɫɹ ɚɛɫɨɥɸɬɨɦ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɪɨɛɧɨ-ɥɢɧɟɣɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɜɢɞɚ
(9.7) ɹɜɥɹɸɬɫɹ ɞɜɢɠɟɧɢɹɦɢ ɜ ɝɟɨɦɟɬɪɢɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ, ɨɧɢ ɩɟɪɟɜɨɞɹɬ ɩɪɹɦɵɟ ɜ
ɩɪɹɦɵɟ ɢ ɫɨɯɪɚɧɹɸɬ
ɪɚɫɫɬɨɹɧɢɹ ɜ ɦɟɬɪɢɤɟ (9.8).
Ɇɵ ɦɨɠɟɦ ɬɟɩɟɪɶ ܵ-ɦɚɬɪɢɰɟ (9.4) ɩɨɫɬɚɜɢɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɤɨɦɩɨɡɢɰɢɸ ɫɥɭ-
ɱɚɣɧɵɯ ɞɪɨɛɧɨ-ɥɢɧɟɣɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ
ሻ
ሻ
ሻ
ሻ
ݓෝ
לݓෝ
ே
לڮלݓෝଶלݓෝଵǡ
ேିଵ
ሺ
ͻǤͳͲ
ɢ ɪɚɫɫɦɨɬɪɟɬɶ ɷɬɭ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɚɤ ɪɟɚɥɢɡɚɰɢɸ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɧɚ
ɩɥɨɫɤɨɫɬɢ Ʌɨɛɚɱɟɜɫɤɨɝɨ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɨɬɨɛɪɚɠɟɧɢɟ (9.10) ɟɫɬɶ ɨɬɨɛɪɚɠɟɧɢɟ
ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ ɩɨɫɥɟ ɩɟɪɜɵɯ ܰ ɲɚɝɨɜ ɛɥɭɠɞɚɧɢɹ. ȿɫɥɢ ݖ
ɧɟɤɨɬɨɪɚɹ ɩɪɨɢɡ-
ɜɨɥɶɧɚɹ ɧɚɱɚɥɶɧɚɹ ɬɨɱɤɚ, ɬɨ
ሺ
ሻሺ
ݖேൌݓෝேלڮלݓෝ
ݖ
ଵ
ɟɫɬɶ ܰ-ɹ ɬɨɱɤɚ ɬɪɚɟɤɬɨɪɢɢ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɫ ɧɚɱɚɥɨɦ ɜ ݖ
, ɚ ɩɨɫɥɟɞɨɜɚ-
ͻǤͳͳ
ɬɟɥɶɧɨɫɬɶ
ݖ
ǡԜݖଵǡԜݖଶǡԜǥǡԜݖேǡ
ሺ
ͻǤͳʹ
ɡɚɞɚɟɬ ɜɫɸ ɬɪɚɟɤɬɨɪɢɸ ɫɥɭɱɚɣɧɨɝɨ ɛɥɭɠɞɚɧɢɹ ɢɡ ܰ ɲɚɝɨɜ (ɪɢɫ. 9.1).
90
ሻ
ሻ
ሻ
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