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Файл:Функции Грина и проводимость. Учебное пособие
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ɋ ɩɨɦɨɳɶɸ ɩɨɥɭɱɟɧɧɨɣ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɮɭɧɤɰɢɢ ߖ
ሺݐሻ
ɱɟɧɢɟ ɜɟɥɢɱɢɧɵ ݔ᪄
ɨɩɟɪɚɬɨɪɚ ݔො
. ȼ ɬɨɦ ɠɟ ɩɪɢɛɥɢɠɟɧɢɢ ɢɦɟɟɦ
ఈ
ൌ൫ܽ
ɤɚɤ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɞɢɚɝɨɧɚɥɶɧɵɣ ɦɚɬɪɢɱɧɵɣ ɷɥɟɦɟɧɬ
ఈ
ൌߖ
ȁ݉ۧ
݁
כ
ሺݍሻ
ఠ௧
ݔො
ఈߖ
ܽ
כ
ݔ᪄
ۦ݊ȁ
ሺݐሻ
ఈ
ݔො
ఈ
ሺݍሻ
ۦ݉ȁ
ɜɵɱɢɫɥɹɟɦ ɫɪɟɞɧɟɟ ɡɧɚ-
݀ݍൌ
ఠ௧
ȁ݊ۧ
ݔො
݁
ఈ
൯ൌ
ൌ
ͳ
ቈ
ʹ
ۦ݊ȁ
ݔො
ఈ
߱
ȁ݉ۧ
ൻ݉หݔො
െ߱െ݅ߜ
ห݊ൿ
ఉ
ۦ݉ȁ
ݔො
߱
ȁ݊ۧ
ൻ݊หݔො
ఈ
߱݅ߜ
ఉ
ห݉ൿ
ఉԜ݂ఉԜ݁
ିఠ௧
ܿǤܿǤሺͳǤͳͷ
ɋɪɚɜɧɢɜ ɷɬɨɬ ɪɟɡɭɥɶɬɚɬ ɫ (1.7), ɧɚɣɞɟɦ
߯
ఈఉ
ሺ߱ሻ
ȁ݉ۧ
ۦ݊ȁ
ͳ
ൌ
ቈ
ݔො
ఈ
߱
ൻ݉หݔො
ఉ
െ߱െ݅ߜ
ห݊ൿ
ۦ݉ȁ
ݔො
߱
ȁ݊ۧ
ൻ݊หݔො
ఈ
߱݅ߜ
ఉ
ห݉ൿ
ሺ
Ǥ
ͳǤͳ
ɉɨɤɚɠɟɦ ɬɟɩɟɪɶ, ɱɬɨ ɜɵɪɚɠɟɧɢɟ (1.16) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɮɭɪɶɟ-ɨɛɪɚɡ
ɮɭɧɤɰɢɢ
݅
ሺݐሻ
ఈఉ
ൌ൝
߯
ൻ݊หԜݔො
ሺݐሻ
ሺͲሻ
ݔො
ఈ
ఉ
െݔො
ఉ
ሺͲሻ
ሺݐሻ
ݔො
ఈ
Ԝห݊ൿǡ ݐͲǡ
ሺ
ͳǤͳ
Ͳǡ ݐ൏Ͳǡ
(ɷɬɨ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɡɚɜɢɫɢɬ, ɤɨɧɟɱɧɨ, ɬɨɥɶɤɨ ɨɬ ɪɚɡɧɨɫɬɢ ɦɨɦɟɧɬɨɜ ɜɪɟɦɟɧɢ, ɜ
ɢ ݔො
ɤɨɬɨɪɵɟ ɛɟɪɭɬɫɹ ɨɩɟɪɚɬɨɪɵ ݔො
). Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɜɵɱɢɫɥɹɹ ɦɚɬɪɢɱɧɵɣ ɷɥɟ-
ఈ
ఉ
ɦɟɧɬ, ɢɦɟɟɦ ɩɪɢ ݐͲ
߯
ఈఉ
ሺݐሻ
ൌ
ൣۦ݊ȁݔො
ሺݐሻ
ȁ݉ۧ
ఈ
ൻ݉หݔො
ሺͲሻ
ఉ
ห݊ൿെൻ݊หݔො
ሺͲሻ
ఉ
ห݉ൿۦ݉ȁݔො
ሺݐሻ
ȁ݊ۧ
൧
ఈ
ǡሺͳǤͳͺ
݅
ɭɱɢɬɵɜɚɹ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɜɪɟɦɟɧɢ ɞɥɹ ɦɚɬɪɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɢɦɟɟɬ ɜɢɞ
ۦ݊ȁ
ሺݐሻ
ݔො
ఈ
ȁ݉ۧൌۦ݊ȁ
ݔො
ఈ
ȁ݉ۧ
Ԝ݁
ఠ௧
ǡ
ሺ
ͳǤͳͻ
ɩɨɥɭɱɚɟɦ
ሻ
ሻ
ሻ
ሻ
ሻ
߯
ఈఉ
ሺݐሻ
݅
ൌ
ൣۦ݊ȁݔො
ఈ
ȁ݉ۧ
ൻ݉หݔො
ఉ
ห݊ൿ݁
ఠ௧
െൻ݊หݔොఉห݉ൿۦ݉ȁݔො
ఠ௧
ȁ݊ۧ
݁
ఈ
൧ǡሺͳǤʹͲ
ɮɭɪɶɟ-ɨɛɪɚɡ ɷɬɨɣ ɮɭɧɤɰɢɢ, ɫ ɭɱɟɬɨɦ, ɱɬɨ ɨɧɚ ɨɬɥɢɱɧɚ ɨɬ ɧɭɥɹ ɩɪɢ ݐͲ, ɜɵɱɢɫ-
ɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ
ஶ
න݁
ఠ௧
݀ݐൌ
݅
߱݅ߜ
ሺ
ͳǤʹͳ
11
ሻ
ሻ
ɢ ɫɨɜɩɚɞɚɟɬ ɫ (1.16). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɥɭɱɚɟɦ
ஶ
݅
߯
ఈఉ
ሺ߱ሻ
ൌ
න݁
ఠ௧
ൻ݊หԜݔො
ሺݐሻ
ሺͲሻ
ݔො
ఈ
ఉ
െݔො
ఉ
ሺͲሻ
ሺݐሻ
ݔො
Ԝห݊ൿԜ݀ݐǤ
ఈ
ሺ
ͳǤʹʹ
ሻ
Ȼɭɞɭɱɢ ɫɩɪɚɜɟɞɥɢɜɨɣ ɩɪɢ ɭɫɪɟɞɧɟɧɢɢ ɩɨ ɜɫɹɤɨɦɭ ɡɚɞɚɧɧɨɦɭ ɫɬɚɰɢɨɧɚɪɧɨɦɭ
ɫɨɫɬɨɹɧɢɸ ɫɢɫɬɟɦɵ, ɷɬɚ ɮɨɪɦɭɥɚ ɨɫɬɚɟɬɫɹ ɛɟɡ ɢɡɦɟɧɟɧɢɣ ɩɨɫɥɟ ɭɫɪɟɞɧɟɧɢɹ ɩɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɢɛɛɫɚ. ɍɫɪɟɞɧɟɧɢɟ ɩɨ Ƚɢɛɛɫɭ ɨɛɨɡɧɚɱɢɦ ɩɨɫɪɟɞɫɬɜɨɦ ɫɤɨɛɨɤ:
ሺ
ۦǥۧ
ൌݓ
்
ۦ݊ȁǥȁ݊ۧ
ǡ
ͳǤʹ͵
ሻ
ɝɞɟ
ͳ
ሺబሻ
ିఉா
Ȁ
ݓ
ൌ
݁
ܼ
ǡԜԜԜܼൌ݁
ିఉா
ሺబሻ
Ȁ
ǡԜԜԜߚൌȀܶǡ
ሺ
ͳǤʹͶ
ሻ
ɢ ɩɪɢɦɟɦ ɜɨ ɜɧɢɦɚɧɢɟ ɨɛɨɡɧɚɱɟɧɢɟ ɞɥɹ ɤɨɦɦɭɬɚɬɨɪɚ ɞɜɭɯ ɨɩɟɪɚɬɨɪɨɜ ൣܣመǡܤ൧ൌ
ൌܣመܤെܤܣ
መ
, ɬɨɝɞɚ ɩɨɥɭɱɢɦ ɨɤɨɧɱɚɬɟɥɶɧɨ ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɣ (ɨɛɨɛɳɟɧɧɨɣ) ɜɨɫ-
ɩɪɢɢɦɱɢɜɨɫɬɢ ɫɢɫɬɟɦɵ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ܶ ɮɨɪɦɭɥɭ Ʉɭɛɨ:
ஶ
݅
ሺ߱ሻ
ఈఉ
ൌ
߯
ɉɨɥɭɱɢɦ ɬɚɤɠɟ ɩɨɥɟɡɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɞɥɹ ߯
න݁
ఠ௧
ൻԜൣݔො
ሺݐሻ
ሺͲሻ
ǡݔො
൧Ԝൿ
ఈ
ఉ
Ԝ݀ݐǤ
்
ሺ߱ሻ
, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɩɨɥɭ-
ఈఉ
ሺ
ͳǤʹͷ
ሻ
ɱɢɬɶ ɢɡ (1.16) ɜ ɫɥɭɱɚɟ ɭɫɪɟɞɧɟɧɢɹ ɩɨ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɢɛɛɫɚ. ɂɦɟɟɦ
ȁ݉ۧ
ͳ
ሺ߱ሻ
ൌ
߯
ఈఉ
ݓ
ۦ݊ȁ
ቈ
ݔො
ఈ
߱
ൻ݉หݔො
ఉ
െ߱െ݅ߜ
ห݊ൿ
ۦ݉ȁ
ݔො
߱
ȁ݊ۧ
ൻ݊หݔො
ఈ
߱݅ߜ
ఉ
ห݉ൿ
ǡ
ሺ
ͳǤʹ
ɪɚɫɫɦɨɬɪɢɦ ɨɬɞɟɥɶɧɨ ɜɤɥɚɞ ɨɬ ɩɟɪɜɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɢɡ ɤɜɚɞɪɚɬɧɨɣ ɫɤɨɛɤɢ ɢ ɩɨɦɟ-
ɧɹɟɦ ɦɟɫɬɚɦɢ ɢɧɞɟɤɫɵ ɫɭɦɦɢɪɨɜɚɧɢɹ ݊՞݉
ͳ
݁
ܼ
ͳ
ൌ
ܼ
݁
ି
ఉா
ିఉா
ሺబሻ
ȁ݉ۧ
ۦ݊ȁ
ԜԜ
Ȁ
ԜԜ
ݔො
߱
ۦ݉ȁ
ఈ
ൻ݉หݔො
െ߱െ݅ߜ
ȁ݊ۧ
ݔො
ఈ
߱
െ߱െ݅ߜ
ఉ
ൻ݊หݔො
ห݊ൿ
ఉ
ൌ
ห݉ൿ
ǡ
ሺ
ͳǤʹ
ሺబሻ
ɞɚɥɟɟ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɦɨɠɧɨ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɬɚɤ
ͳ
െ
ܼ
݁
ିఉா
ሺబሻ
ۦ݉ȁ
Ȁ
ԜԜ
ݔො
߱
ൻ݊หݔො
ఈ
߱݅ߜ
ఉ
ห݉ൿ
Ԝ݁
ିఉఠ
ǡ
ሺ
ͳǤʹͺ
ȁ݊ۧ
12
ሻ
ሻ
ሻ
ɩɨɞɫɬɚɜɥɹɹ ɜ (1.26), ɜ ɢɬɨɝɟ ɩɨɥɭɱɢɦ
ȁ݊ۧ
ͳ
ሺ߱ሻ
ൌ
߯
ఈఉ
ݓ
ǡ
ۦ݉ȁ
ԜԜ
ݔො
߱
ൻ݊หݔො
ఈ
߱݅ߜ
ఉ
ห݉ൿ
൫ͳെ݁
ିఉఠ
൯ǡ
ɷɬɨ ɢ ɟɫɬɶ ɢɫɤɨɦɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ.
Ʌɢɬɟɪɚɬɭɪɚ
Ɉɫɧɨɜɧɨɟ ɫɨɞɟɪɠɚɧɢɟ ɷɬɨɣ ɝɥɚɜɵ ɨɫɧɨɜɚɧ ɧɚ ɦɚɬɟɪɢɚɥɚɯ ɭɱɟɛɧɢɤɚ [2] ɝɥ. 12,
§ 123, 126.
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ
1. ɉɭɫɬɶ ɜɟɥɢɱɢɧɵ ݂ఈሺݐሻ (ɮɨɪɦɭɥɚ (1.2)) ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɤɨɦɩɨɧɟɧɬɵ
ɜɟɤɬɨɪɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɤɚɤɨɣ ɫɦɵɫɥ ɛɭɞɭɬ ɢɦɟɬɶ ɜɟɤɬɨɪ ݔ᪄
ሺ߬ሻ
?
߯
ఈఉ
2. ɉɭɫɬɶ ɜɟɥɢɱɢɧɵ ݂
ሺݐሻ (ɮɨɪɦɭɥɚ (1.2)) ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɤɨɦɩɨɧɟɧɬɵ
ఈ
ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɤɚɤɨɣ ɫɦɵɫɥ ɛɭɞɭɬ ɢɦɟɬɶ ɜɟɤɬɨɪ ݔ᪄
ሺ߬ሻ
?
߯
ఈఉ
3. ɋɮɨɪɦɭɥɢɪɨɜɚɬɶ ɩɪɢɧɰɢɩ ɩɪɢɱɢɧɧɨɫɬɢ.
4. Ʉɚɤɢɟ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ߯
ሺ߱ሻ
ɤɚɤ ɮɭɧɤɰɢɢ ɤɨɦɩɥɟɤɫɧɨɝɨ ɩɟɪɟ-
ఈఉ
ɦɟɧɧɨɝɨ ɫɥɟɞɭɸɬ ɢɡ ɩɪɢɧɰɢɩɚ ɩɪɢɱɢɧɧɨɫɬɢ?
5. Ʉɚɤ ɫɜɹɡɚɧɚ ɷɧɟɪɝɢɹ, ɞɢɫɫɢɩɢɪɭɟɦɚɹ ɜ ɫɢɫɬɟɦɟ ɩɨɞ ɜɥɢɹɧɢɟɦ ɜɨɡɦɭɳɟɧɢɹ
ሺ߱ሻ
ሺݐሻ ɫ ɦɧɢɦɨɣ ɱɚɫɬɶɸ ɮɭɧɤɰɢɢ ߯
݂
ఈ
ఈఉ
?
ሺݐሻ ɢ ɬɟɧɡɨɪ
ఈ
ሺݐሻ ɢ ɬɟɧɡɨɪ
ఈ
ሺ
ͳǤʹͻ
ሻ
13
Ƚɥɚɜɚ 2
ɆȺɐɍȻȺɊɈȼɋɄȺə
ȼɈɋɉɊɂɂɆɑɂȼɈɋɌɖ
2.1. Ɇɚɰɭɛɚɪɨɜɫɤɨɟ ɜɪɟɦɹ
Ɉɫɧɨɜɧɚɹ ɡɚɞɚɱɚ, ɪɟɲɚɟɦɚɹ ɜ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɮɢɡɢɤɟ ɪɚɜɧɨɜɟɫɧɵɯ ɫɢɫɬɟɦ, ɫɨ-
ɫɬɨɢɬ ɜ ɧɚɯɨɠɞɟɧɢɢ ɫɪɟɞɧɢɯ ɩɨ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɢɛɛɫɚ, ɤɨɬɨɪɵɟ ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ
ൻܣመǥܤൿ
ൌݓ
்
ൻ݊หܣመǥܤห݊ൿǡ
ɝɞɟ ɢɧɞɟɤɫ ܶ ɭɤɚɡɵɜɚɟɬ ɧɚ ɬɨ, ɱɬɨ ɫɪɟɞɧɟɟ ɛɟɪɟɬɫɹ ɩɨ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɜɟɪɨɹɬɧɨɫɬɟɣ ɪɚɡɥɢɱɧɵɯ ɫɨɫɬɨɹɧɢɣ ɩɪɢ ɤɨɧɟɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ܶ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ݓ
ɞɚɟɬɫɹ ɮɨɪɦɭɥɚɦɢ (1.24)
ఉா
ͳ
ି
ൌ
ݓ
݁
ܼ
ǡԜԜԜܼൌ݁
ఉா
ି
ǡԜԜԜߚൌȀܶǤ
ȼɵɪɚɠɟɧɢɟ (2.1) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
ఉு
ି
ቇ
Ǥ
ఉு
ି
ൻܣመǥܤൿ
Tr ቆܣመǥܤ݁
ൌ
்
TrԜ݁
Ɍɟɨɪɢɹ ɜɨɡɦɭɳɟɧɢɣ, ɩɨɡɜɨɥɹɸɳɚɹ ɧɚɯɨɞɢɬɶ ɩɨɞɨɛɧɵɟ ɫɪɟɞɧɢɟ, ɧɚɡɵɜɚɟɬɫɹ
ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɞɢɚɝɪɚɦɦɧɨɣ ɬɟɯɧɢɤɨɣ. Ɉɧɚ ɫɬɪɨɢɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ, ɩɪɟɞ-
ɫɬɚɜɢɦ ɝɚɦɢɥɶɬɨɧɢɚɧ ɜ ɜɢɞɟ ܪൌܪ
ܸ, ɝɞɟ ܸ
ɜɨɡɦɭɳɟɧɢɟ ɢ ɩɪɢɦɟɦ ɜɨ ɜɧɢ-
ɦɚɧɢɟ ɚɧɚɥɨɝɢɸ ɦɟɠɞɭ ɨɩɟɪɚɬɨɪɧɨɣ ɷɤɫɩɨɧɟɧɬɨɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɢɛɛɫɚ
࣯
ൌെ
ఉ
ߚ
൫ܪ
ܸ൯൨
ɢ ɤɜɚɧɬɨɜɨɦɟɯɚɧɢɱɟɫɤɢɦ ɨɩɟɪɚɬɨɪɨɦ ɷɜɨɥɸɰɢɢ
ݐ
Ԝ൫ܪ
ܸ൯൨Ǥ
ɉɟɪɟɯɨɞ ɨɬ ܷ
ሺݐሻ
ൌെ݅
ܷ
ሺݐሻ
ɤ ࣯
ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɨɫɬɨɣ ɡɚɦɟɧɨɣ ݐ՜െ݅ߚ. Ɉɤɚɡɵɜɚ-
ఉ
ɟɬɫɹ, ɱɬɨ ɬɚɤɚɹ ɚɧɚɥɨɝɢɹ ɢɦɟɟɬ ɞɚɥɟɤɨ ɢɞɭɳɢɟ ɩɨɫɥɟɞɫɬɜɢɹ. Ⱥ ɢɦɟɧɧɨ ɪɚɫɫɦɨɬ-
ɪɢɦ ɷɜɨɥɸɰɢɸ ɫɢɫɬɟɦɵ ɜɨ ɦɧɢɦɨɦ ɜɪɟɦɟɧɢ ݐൌെ݅߬ (߬ ɧɚɡɵɜɚɸɬ ɬɚɤɠɟ ɦɚɰɭɛɚ-
ɪɨɜɫɤɢɦ ɜɪɟɦɟɧɟɦ). ȼɜɟɞɟɦ ɝɟɣɡɟɧɛɟɪɝɨɜɫɤɢɟ ɨɩɟɪɚɬɨɪɵ
ெ
መ
ሺ߬ሻ
ܣ
ൌ݁
ఛுȀ
ܣመ݁
ିఛுȀ
Ǥ
ሺ
ሺ
ሺ
ሺ
ሺ
ሺ
ʹǤͳ
ʹǤʹ
ʹǤ͵
ʹǤͶ
ʹǤͷ
ʹǤ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
14
ɗɜɨɥɸɰɢɹ ɷɬɢɯ ɨɩɟɪɚɬɨɪɨɜ ɜɨ ɦɧɢɦɨɦ ɜɪɟɦɟɧɢ ɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
ெ
መ
݀ܣ
݀߬
ൌൣܪǡܣ
Ԝ
ெ
መ
൧Ǥ
ሺ
ʹǤ
Ⱦɚɥɟɟ ɜɜɟɞɟɦ ɦɚɰɭɛɚɪɨɜɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ఛு
Ȁ
ൌ݁
బ
መ
ሺ߬ሻ
ܣ
ܣመ݁
ିఛு
Ȁ
బ
ǡ
ሺ
ʹǤͺ
ɢ ɨɩɪɟɞɟɥɢɦ ɦɚɰɭɛɚɪɨɜɫɤɭɸ ܵ-ɦɚɬɪɢɰɭ
ఛு
Ȁ݁ିఛுȀ
ൌ݁
బ
Ǥ
ሺ
ʹǤͻ
መ
ሺ߬ሻ
࣭
Ʌɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɱɬɨ ɷɬɚ ܵ-ɦɚɬɪɢɰɚ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ
መ
ሺ߬ሻ
݀ܵ
Ԝ
݀߬
ൌെܸ
ሺ߬ሻ
መ
ሺ߬ሻ
࣭
ǡ
ሺ
ʹǤͳͲ
ɝɞɟ
ఛு
ൌ݁
బ
ሺ߬ሻ
ܸ
Ȁ
ିఛு
Ȁ
ܸ݁
బ
ሺ
ʹǤͳͳ
ɨɩɟɪɚɬɨɪ ɜɨɡɦɭɳɟɧɢɹ, ɡɚɩɢɫɚɧɧɵɣ ɜ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. Ɋɟɲɟɧɢɟ
ɭɪɚɜɧɟɧɢɹ (2.10) ɢɦɟɟɬ ɜɢɞ
ఛ
ͳ
නܸ
ሺ߬ሻ
݀߬ቇǤ
ሺ
ʹǤͳʹ
ɋɢɦɜɨɥ T
መ
ሺ߬ሻ
࣭
ɨɛɨɡɧɚɱɚɟɬ ɯɪɨɧɨɥɨɝɢɱɟɫɤɨɟ ɭɩɨɪɹɞɨɱɟɧɢɟ ɨɩɟɪɚɬɨɪɨɜ ɩɨ ɦɚɰɭɛɚ-
ఛ
ൌT
ቆെ
ఛ
ɪɨɜɫɤɨɦɭ ɜɪɟɦɟɧɢ ߬.
Ɏɨɪɦɭɥɵ (2.6), (2.9) ɢ (2.12) ɩɨɡɜɨɥɹɸɬ ɜɵɪɚɡɢɬɶ «ɬɨɱɧɵɣ» ɦɚɰɭɛɚɪɨɜɫɤɢɣ
ɨɩɟɪɚɬɨɪ ɱɟɪɟɡ ɨɩɟɪɚɬɨɪ ɜ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɢɡ
(2.9) ɢɦɟɟɦ
ൌ݁
ఛு
బ
ି
መ
ሺ߬ሻ
Ԝ࣭
ǡ
ሺ
ʹǤͳ͵
ఛு
ି
݁
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ɨɛɪɚɳɚɹ ɨɩɟɪɚɬɨɪɵ ɜ ɩɪɚɜɨɣ ɢ ɥɟɜɨɣ ɱɚɫɬɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ
ఛு
ିଵ
መ
݁
ൌ࣭
ሺ߬ሻ
ఛு
బ
Ԝ݁
ǡ
ɢɫɩɨɥɶɡɭɹ ɷɬɢ ɞɜɚ ɪɚɜɟɧɫɬɜɚ, ɩɨɥɭɱɚɟɦ
ெ
መ
ሺ߬ሻ
ܣ
ൌ࣭
ିଵ
መ
ሺ߬ሻ
መ
መ
ሺ߬ሻ
ሺ߬ሻ
Ԝܣ
Ԝ࣭
Ǥ
ɋ ɩɨɦɨɳɶɸ ɷɬɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɫɪɟɞɧɢɟ (2.3) ɦɨɠɧɨ ɥɟɝɤɨ ɩɟɪɟɩɢɫɚɬɶ ɜ ɜɢɞɟ
ఉு
బ
ି
መ
ሺߚሻ
ሺߚሻ
መ
࣭
ି
Ԝ݁
ሺߚሻ
ఉு
݁
ቇ
బ
ቇ
Ǥ
ൻܣመǥܤൿ
መ
ሺߚሻ
Tr ቆܣ
ൌ
்
ǥܤ
Tr ቆ࣭
15
ሺ
ʹǤͳͶ
ሺ
ʹǤͳͷ
ሺ
ʹǤͳ
ሻ
ሻ
ሻ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ۦ
ۧ
ɝɞɟ
ɨɛɨɡɧɚɱɚɟɬ ɫɪɟɞɧɟɟ ɩɨ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɢɛɛɫɚ ɫ ɧɟɜɨɡɦɭɳɟɧɧɵɦ ɝɚ-
ǤǤǤ
்ǡ
ɦɢɥɶɬɨɧɢɚɧɨɦ ܪ
መ
ሺߚሻ
ൻܣ
ൻܣመǥܤൿ
.
ൌ
்
ǥܤ
ൻ࣭
መ
ሺߚሻ
ሺߚሻ
መ
ሺߚሻ
࣭
ൿ
்ǡ
ൿ
்ǡ
ǡ
ሺ
ʹǤͳ
2.2. Ɇɚɰɭɛɚɪɨɜɫɤɢɣ ɚɧɚɥɨɝ ɮɨɪɦɭɥɵ Ʉɭɛɨ
Ɋɚɫɫɦɨɬɪɢɦ ɫɢɫɬɟɦɭ ɫ ɝɚɦɢɥɶɬɨɧɢɚɧɨɦ ܪ
ɧɢɟ (1.1). Ȼɭɞɟɦ ɬɟɩɟɪɶ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɧɟɲɧɢɟ ɫɢɥɵ ݂
ɨɬ ɦɚɰɭɛɚɪɨɜɫɤɨɝɨ ɜɪɟɦɟɧɢ ߬, ɩɪɢ ɷɬɨɦ െߚ൏߬൏ߚ, ɚ ɫɢɥɵ ɩɟɪɢɨɞɢɱɧɵ ɫ ɩɟɪɢɨɞɨɦ ߚ:
, ɧɚ ɤɨɬɨɪɭɸ ɧɚɥɨɠɟɧɨ ɜɨɡɦɭɳɟ-
ɜ ɷɬɨɦ ɜɨɡɦɭɳɟɧɢɢ ɡɚɜɢɫɹɬ
ఈ
ሻ
ሺ
߬ߚሻൌ݂
݂
ఈ
ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɢɯ ɫɢɥ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ ݔ᪄
ሺ߬ሻ
Ǥ
ఈ
ሺ߬ሻ
ɛɭɞɭɬ ɨɬɥɢɱɧɵ ɨɬ ɧɭɥɹ ɢ ɛɭ-
ఈ
ሺ
ʹǤͳͺ
ɞɭɬ ɥɢɧɟɣɧɨ ɡɚɜɢɫɟɬɶ ɨɬ ɩɪɢɥɨɠɟɧɧɵɯ ɫɢɥ, ɬɚɤ ɱɬɨ ɢɦɟɟɬ ɦɟɫɬɨ
ఉ
ሺ߬ሻ
ɢ ݂
ெ
ሺ
ሻ
ሺ
߬െ߬
ఈఉ
ெ
ఈఉ
ఉ
ଵ
ሺ߬ሻ
ɧɚɡɵɜɚɟɬɫɹ ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɜɨɫɩɪɢ-
ሺ߬ሻ
ɦɚɰɭɛɚɪɨɜɫɤɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɩɟ-
ሻ
݂
߬
݀߬
ఉ
Ǥ
ଵ
ଵ
ሺ
ʹǤͳͻ
ሺ߬ሻ
ൌන߯
ݔ᪄
ఈ
əɞɪɨ ɷɬɨɝɨ ɥɢɧɟɣɧɨɝɨ ɨɩɟɪɚɬɨɪɚ ߯
ɢɦɱɢɜɨɫɬɶɸ. Ʉɚɤ ɢ ɮɭɧɤɰɢɢ ݔ᪄
ఉ
ఈ
ɪɢɨɞɢɱɧɚ ɩɨ ߬ ɫ ɩɟɪɢɨɞɨɦ ߚ, ɩɨɷɬɨɦɭ ɷɬɢ ɮɭɧɤɰɢɢ ɦɨɠɧɨ ɪɚɡɥɨɠɢɬɶ ɜ ɪɹɞ Ɏɭɪɶɟ
ɩɨ ɝɚɪɦɨɧɢɤɚɦ ɫ ɱɚɫɬɨɬɚɦɢ ߞ
ஶ
ሺ߬ሻ
ൌ݂
݂
ఈ
௦ୀିஶ
ൌʹߨݏȀߚൌʹߨݏܶȀ, ɝɞɟ ݏ ɰɟɥɨɟ ɱɢɫɥɨ:
௦
ஶ
ିೞఛ
ሺݏሻ
Ԝ݁
ఈ
ெ
ሺ߬ሻ
ఈఉ
ൌ߯
௦ୀିஶ
Ԝ߯
ሺ߬ሻ
ఈ
ெ
ఈఉ
ൌݔ᪄
௦ୀିஶ
ሺ
ሻ
ߞ
Ԝ݁
௦
ǡԜԜԜݔ᪄
ஶ
ିೞఛ
ሺݏሻ
ఈ
Ǥ
Ԝ݁
ିೞఛ
ǡԜԜ
ሺ
ʹǤʹͲ
Ɍɨɝɞɚ ɢɡ (2.19) ɫɥɟɞɭɟɬ
ሺݏሻ
ൌ߯
ݔ᪄
ఈ
ɇɚɲɚ ɰɟɥɶ ɫɨɫɬɨɢɬ ɬɟɩɟɪɶ ɜ ɬɨɦ ɱɬɨɛɵ, ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ, ɩɨɥɭɱɢɬɶ ɞɥɹ
ெ
ሺ
ሻ
ߞ
߯
ɧɨɜɢɬɶ ɫɜɹɡɶ ɦɟɠɞɭ ߯
ɫɨɨɬɧɨɲɟɧɢɟ ɚɧɚɥɨɝɢɱɧɨɟ ɮɨɪɦɭɥɟ Ʉɭɛɨ (1.25), ɚ ɫ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ ɭɫɬɚ-
௦
ఈఉ
ெ
ሺ
ሻ
ߞ
ɢ ɞɢɧɚɦɢɱɟɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶɸ ߯
௦
ఈఉ
ெ
ሺ
ሻ
ሺݏሻ
ߞ
݂
Ǥ
௦
ఈఉ
ఉ
ఉ
ఈఉ
ሺ߱ሻ
ሺ
ʹǤʹͳ
. ɇɚɱɧɟɦ
ɫ ɩɟɪɜɨɣ ɡɚɞɚɱɢ.
ሻ
ሻ
ሻ
ሻ
16
ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ ɢɦɟɟɦ
ఉு
ି
ெ
Tr ൭݁
ሺ߬ሻ
ൌ
ݔ᪄
ఈ
Tr ቆ݁
ሺ߬ሻ
൱
Ԝݔො
ఈ
ǡ
ఉு
ି
ቇ
ɝɞɟ
ఛு
ఛு
ெ
ሺ߬ሻ
ݔො
ൌ݁
ି
ݔො݁
ǡԜԜԜܪൌܪ
ሺ߬ሻ
Ǥ
ܸ
ɋɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (2.15) ɢɦɟɟɦ
ெ
ሺ߬ሻ
ݔො
ఈ
ൌ࣭
ିଵ
መ
ሺ߬ሻ
Ԝݔොሺ߬ሻԜ࣭
መ
ሺ߬ሻ
ǡ
ɝɞɟ
ݔොሺ߬ሻൌ݁
ఛு
బ
ݔොԜ݁
ఛு
బ
ି
ǡ
ɩɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (2.22) ɢ ɭɱɢɬɵɜɚɹ (2.13), ɩɨɥɭɱɢɦ
ఉு
బ
ି
Tr ൭݁
ሺ߬ሻ
ݔ᪄
ൌ
ఈ
Tr ൭݁
ିଵ
መ
መ
ሺ߬ሻ
ሺߚሻ
࣭
࣭
ఉு
బ
ି
መ
ሺߚሻ
࣭
መ
ሺ߬ሻ
ሺ߬ሻ
ݔො
࣭
ఈ
൱
Ǥ
൱
Ɍɟɩɟɪɶ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɮɨɪɦɭɥɨɣ (2.12) ɢ ɪɚɡɥɨɠɢɦ ɷɤɫɩɨɧɟɧɬɭ ɞɨ ɩɟɪɜɨɝɨ
ɩɨɪɹɞɤɚ ɩɨ ܸ
, ɬɨɝɞɚ
ఉ
ൌͳെ
ͳ
නܸ
ͳ
ఛ
නܸ
ఛ
ሺ
߬
ሺ
ሻ
߬
݀߬
ǡ
ଵ
ଵ
ሻ
݀߬
ǡ
ଵ
ଵ
ିଵ
መ
መ
ሺߚሻ
࣭
ሺ߬ሻ
࣭
መ
ሺ߬ሻ
࣭
ൌͳെ
ɝɞɟ, ɫɨɝɥɚɫɧɨ (1.1)
ሺ
ʹǤʹʹ
ሺ
ʹǤʹ͵
ሺ
ʹǤʹͶ
ሺ
ʹǤʹͷ
ሺ
ʹǤʹ
ሺ
ʹǤʹ
ሺ
ʹǤʹͺ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
ሺ߬ሻ
ܸ
ൌെݔො
ሺ߬ሻ
ሺ߬ሻ
Ԝ݂
ఉ
ఉ
ǡ
ఉ
ɩɨɞɫɬɚɜɥɹɟɦ ɷɬɢ ɫɨɨɬɧɨɲɟɧɢɹ ɜ (2.26) ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ Tr ቀ݁
ିఉு
Ȁ
బ
ሺ߬ሻ
ܸ
Tr ቀ݁
ቁൌͲ, ɩɨɥɭɱɢɦ
ሺ߬ሻ
ൌൽቆͳെ
ݔ᪄
ఈ
ͳ
නܸ
ఉ
ሺ
ሻ
߬
݀߬
ଵ
ఛ
ଵ
ቇݔො
ሺ߬ሻ
ቆͳെ
ఈ
ͳ
ఛ
නܸ
ሺ
߬
ଵ
17
ሻ
ିఉு
݀߬
బ
ቇඁ்ൌ
ଵ
ሺ
ʹǤʹͻ
Ȁ
ݔොሺ߬ሻቁൌͲ ɢ
ሻ
ൌെ
ͳ
ఉ
ൽන ܸ
ఛ
ఛ
ሺ
ሻ
߬
ଵ
݀߬
ሺ߬ሻ
ݔො
Ԝݔො
ଵ
ఈ
ఈ
ሺ߬ሻ
Ԝනܸ
ሺ
ሻ
߬
݀߬
ඁ்ൌ
ଵ
ଵ
ఉ
ൽනݔො
ఛ
ఉ
ఉ
߬ଵ݂
ሺ
߬
ఉ
ଵ
ሺ
߬
ఉ
ଵ
ͳ
ൌ
ሻ
Ԝ݂
ఉ
ሻ
Ԝൻߠሺ߬
නൻTఛݔො
ఉ
ൌ
ͳ
ൌ
ͳ
න݀
ఉ
Ɂɞɟɫɶ ɦɵ ɜ ɨɛɨɡɧɚɱɟɧɢɢ
ሺ
߬
ଵ
ଵ
ۦǥۧ
ሻ
ఉ
ሺ߬ሻ
Ԝ݀߬
ଵ
െ߬ሻݔො
்ǡ
ݔො
Ԝݔො
ఈ
ሺ
ሻ
߬
Ԝݔො
ఉ
ଵ
ఈ
ሺ߬ሻ
ሺ
ݔො
ఈ
߬
ఉ
ଵ
ɞɥɹ ɩɪɨɫɬɨɬɵ ɮɨɪɦɭɥ ɨɩɭɫɤɚɟɦ ɢɧɞɟɤɫ «Ͳ»,
ሺ߬ሻ
Ԝනݔො
ఈ
ሺ߬ሻߠሺ
ሻ
ൿ
Ԝ݂
ఉ
்
ఛ
߬െ߬
ሺ
߬
ሺ
ሻ
ሺ
߬
ఉ
ଵ
ଵ
ሻ
Ԝ݀߬
ଵ
ሻ
Ԝ݂
߬
Ԝ݀߬
ఉ
ଵ
ଵ
ሻ
ሺ߬ሻ
ݔො
Ǥ
ଵ
ሺ
ݔො
ఈ
߬
ఉ
ଵ
ɬɨ ɟɫɬɶ
ఉு
బ
ି
TrԜ݁
ሺǥሻ
Ǥ
ఉு
బ
ି
ۦǥۧ
TrԜ݁
ൌ
்
ɋɪɚɜɧɢɜɚɹ (2.30) ɫ (2.19), ɩɨɥɭɱɚɟɦ ɢɫɤɨɦɨɟ ɫɨɨɬɧɨɲɟɧɢɟ
ሺ߬ሻ
ͳ
ൌ
ൻTఛݔො
ሺ߬ሻ
ሺͲሻ
ݔො
ൿ
ఈ
ǡ
ఉ
்
ெ
߯
ఈఉ
ɢɥɢ ɞɥɹ ɮɭɪɶɟ-ɤɨɦɩɨɧɟɧɬ
ఉ
ெ
߯
ఈఉ
ͳ
න݁
ೞఛ
ൻTఛݔො
ఈ
ሺ߬ሻ
ሺͲሻ
ݔො
ൿ
Ԝ݀߬Ǥ
ఉ
்
ሺ
ሻ
ߞ
ൌ
௦
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɹɜɥɹɟɬɫɹ ɦɚɰɭɛɚɪɨɜɫɤɢɦ ɚɧɚɥɨɝɨɦ ɮɨɪɦɭɥɵ Ʉɭɛɨ (1.25).
2.3. ɋɜɹɡɶ ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ
ɫ ɞɢɧɚɦɢɱɟɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶɸ
Ⱦɥɹ ɪɟɲɟɧɢɹ ɜɬɨɪɨɣ ɡɚɞɚɱɢ ɧɚɯɨɠɞɟɧɢɹ ɫɜɹɡɢ ɦɟɠɞɭ ɮɭɧɤɰɢɹɦɢ ߯
ሺ߱ሻ
߯
ɩɨ ɫɨɛɫɬɜɟɧɧɵɦ ɮɭɧɤɰɢɹɦ ɝɚɦɢɥɶɬɨɧɢɚɧɚ ܪ
ɜɵɪɚɡɢɦ ɩɟɪɜɭɸ ɮɭɧɤɰɢɸ ɱɟɪɟɡ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɨɩɟɪɚɬɨɪɨɜ ݔො
ఈఉ
.
ൌ
߯
ெ
ఈఉ
ͳ
ሺ
ሻ
ߞ
௦
ఉ
න݀
ൌ
߬݁
ͳ
ೞఛ
ఉ
න݁
ݓ
ೞఛ
ൽTఛ݁
ൻ݊ห݁
ఛு
ఛு
బ
బ
ݔොఈ݁
Ȁ
ି
ݔොఈ݁
ఛு
బ
ݔොఉඁ்Ԝ݀߬ൌ
ିఛு
Ȁ
బ
ݔොఉห݊ൿൌ
ඁ
ൌ
்
ሻ
ൿ
ൌ
்
ሺ
ሻ
ʹǤ͵Ͳ
ሺ
ሻ
ʹǤ͵ͳ
ሺ
ሻ
ʹǤ͵ʹ
ሺ
ሻ
ʹǤ͵͵
ெ
ሺ
ሻ
ߞ
ɢ
௦
ఈఉ
ఈ
18
ఉ
ɝɞɟ ݓ
ൌ݁
ିఉா
ͳ
න݀
ൌ
ൌ
ሺబሻ
Ȁ
Ȁܼ. ɉɟɪɟɨɛɨɡɧɚɱɢɦ ɬɟɩɟɪɶ ݉՞݊ ɢ ɭɱɬɟɦ, ɱɬɨ
ͳ
ݓ
߬݁
ೞఛ
ݓ
ۦ݊ȁ
ȁ݉ۧ
ݔො
ఈ
݅ߞ
௦߱
ݓ
ൌݓ
ఛఠ
݁
ൻ݉หݔො
݁
ఉఠ
ۦ݊ȁ
ఉ
ห݊ൿ
ȁ݉ۧ
ݔො
ൻ݉หݔො
ห݊ൿൌ
ఉ
െͳ൯ǡ
ሺ
ʹǤ͵Ͷ
ሺ
ʹǤ͵ͷ
ఈ
ఉఠ
൫݁
ǡ
ɬɨɝɞɚ ɢɦɟɟɦ
ۦ݉ȁ
ȁ݊ۧ
ݔො
ൻ݊หݔො
ȁ݊ۧ
ൻ݊หݔො
ఉ
ห݉ൿ
ห݉ൿ
ఉ
ఉఠ
൫݁
൫ͳെ݁
െͳ൯ൌ
ିఉఠ
൯ǡ
ሺ
ʹǤ͵
ݓ
ൌݓ
ۦ݉ȁ
ఈ
݅ߞ
௦߱
ݔො
ఈ
݅ߞ
௦߱
ɜ ɢɬɨɝɟ
ۦ݉ȁ
ȁ݊ۧ
ݔො
ൻ݊หݔො
ெ
߯
ఈఉ
ͳ
ሺ
ሻ
ߞ
ൌ
ݓ
௦
ఈ
݅ߞ
௦߱
ఉ
ห݉ൿ
൫ͳെ݁
ିఉఠ
൯Ǥ
ሺ
ʹǤ͵
ɋɪɚɜɧɢɦ ɷɬɨ ɫ ɮɨɪɦɭɥɨɣ (1.29)
ȁ݊ۧ
ͳ
ሺ߱ሻ
ൌ
߯
ఈఉ
ݓ
ǡ
ۦ݉ȁ
ԜԜ
ݔො
߱
ൻ݊หݔො
ఈ
߱݅ߜ
ఉ
ห݉ൿ
൫ͳെ݁
ିఉఠ
൯ǡ
ሺ
ʹǤ͵ͺ
ɩɨɥɭɱɚɟɦ
ெ
ሺ
ሻ
߯
ߞ
௦
ఈఉ
ൌ߯
ఈఉ
ሺ
݅ߞ
ሻ
Ǥ
௦
ሺ
ʹǤ͵ͻ
ɋɨɨɬɧɨɲɟɧɢɟ (2.39) ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɢɫɤɨɦɭɸ ɫɜɹɡɶ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɨɩɪɟ-
ɞɟɥɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ߯
ሺ߱ሻ
ɧɚɞɨ ɩɨɫɬɪɨɢɬɶ ɮɭɧɤɰɢɸ ɚɧɚ-
ఈఉ
ɥɢɬɢɱɟɫɤɭɸ ɜ ɜɟɪɯɧɟɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɩɟɪɟɦɟɧɧɨɣ ߱, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɨɣ ɜ ɞɢɫ-
ெ
ሺ
ሻ
ɤɪɟɬɧɵɯ ɬɨɱɤɚɯ ߱ൌ݅ߞ
ɧɚ ɜɟɪɯɧɟɣ ɦɧɢɦɨɣ ɩɨɥɭɨɫɢ ɫɨɜɩɚɞɚɸɬ ɫ ߯
௦
ఈఉ
ߞ
௦
ɋɨɝɥɚɫɧɨ ɢɡɜɟɫɬɧɨɣ ɬɟɨɪɟɦɟ ɬɟɨɪɢɢ ɮɭɧɤɰɢɣ ɤɨɦɩɥɟɤɫɧɨɝɨ ɩɟɪɟɦɟɧɧɨɝɨ, ɬɚɤɚɹ
ɮɭɧɤɰɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɨɞɧɨɡɧɚɱɧɨ, ɬɚɤ ɤɚɤ ɦɧɨɠɟɫɬɜɨ ɞɢɫɤɪɟɬɧɵɯ ɱɚɫɬɨɬ
߱ൌ݅ߞ
ɢɦɟɟɬ ɬɨɱɤɭ ɫɝɭɳɟɧɢɹ ݖஶൌλ. ɉɨɥɭɱɟɧɧɚɹ ɮɭɧɤɰɢɹ ɢ ɛɭɞɟɬ ɞɢɧɚɦɢɱɟ-
௦
ɫɤɨɣ (ɨɛɨɛɳɟɧɧɨɣ) ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶɸ ɫɢɫɬɟɦɵ.
Ʌɢɬɟɪɚɬɭɪɚ
Ɉɩɪɟɞɟɥɟɧɢɟ ɦɚɰɭɛɚɪɨɜɫɤɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɞɚɧɨ ɜ [4] ɝɥ. 10 § 91, ɬɚɦ ɠɟ
ɭɫɬɚɧɨɜɥɟɧɚ ɫɜɹɡɶ ɦɟɠɞɭ ߯
ெ
ఈఉ
ሺ
ሻ
ɢ ߯
ఈఉ
ሺ߱ሻ
.
ߞ
௦
ሻ
ሻ
ሻ
ሻ
ሻ
ሻ
.
19
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ
1. ȼ ɤɚɤɢɯ ɩɪɟɞɟɥɚɯ ɢɡɦɟɧɹɟɬɫɹ ɦɚɰɭɛɚɪɨɜɫɤɨɟ ɜɪɟɦɹ ߬?
2. ȼ ɤɚɤɢɯ ɬɨɱɤɚɯ ɤɨɦɩɥɟɤɫɧɨɣ ɩɥɨɫɤɨɫɬɢ ߱ ɨɩɪɟɞɟɥɟɧɚ ɦɚɰɭɛɚɪɨɜɫɤɚɹ ɜɨɫ-
ɩɪɢɢɦɱɢɜɨɫɬɶ?
ܸ
3. Ʉɚɤ ɝɢɛɛɫɨɜɫɤɨɟ ɫɪɟɞɧɟɟ ɫ ɝɚɦɢɥɶɬɨɧɢɚɧɨɦ ܪ
ɛɫɨɜɫɤɨɟ ɫɪɟɞɧɟɟ ɫ ɝɚɦɢɥɶɬɨɧɢɚɧɨɦ ܪ
4. Ʉɚɤɨɣ ɫɦɵɫɥ ɢɦɟɟɬ ɫɢɦɜɨɥ T
?
ɜ ɜɵɪɚɠɟɧɢɢ (2.12) ɞɥɹ ࣭
ఛ
5. Ɂɚɩɢɫɚɬɶ ɦɚɰɭɛɚɪɨɜɫɤɢɣ ɚɧɚɥɨɝ ɮɨɪɦɭɥɵ Ʉɭɛɨ.
ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɝɢɛ-
መ
ሺ߬ሻ
?
20
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