Влияние шумовой температуры антенного обтекателя на изображение,формируемое матричными радиометрическими системами

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ISSN: 2225-4293

Учредитель: Учреждение Российской академии наук

“Научно-технологический центр уникального приборостроения”

Издатель: Учреждение Российской академии наук

“Научно-технологический центр уникального приборостроения”

Журнал зарегистрирован 15 февраля 2000 г.

Министерством Российской Федерации по делам печати, телерадиовещания и средств массовых коммуникаций Свидетельство о регистрации ПИ № 77-1685

РЕДКОЛЛЕГИЯ:

Пустовойт В.И. – гл. редактор, академик РАН, доктор физ.-мат. наук, профессор Кравченко В.Ф. – зам. гл. редактора, д.ф.-м.н., профессор;

Боритко С.В. – д.ф.-м.н., профессор;

Васильев В.П. – д.т.н., профессор;

Виноградов Е.А. – академик РАН, д.ф.-м.н., профессор;

Гуляев Ю.В. – академик РАН. д.ф.-м.н, профессор;

Дианов Е.М. – академик РАН, д.ф.-м.н., профессор;

Жижин Г.Н. – д.ф.-м.н., профессор.;

Компанец О.Н. – д.ф.-м.н., профессор;

Кошкин В.И. – д.ф.-м.н., профессор;

Крохин О.Н. – академик РАН, д.ф.-м.н.. профессор;

Мазур М.М. – д.т.н.;

EDITORIAL BOARD:

Pustovoit V.I. – Editor in Chief, academician RAS, Dr.Sci. (Phys.-Math.), Prof.

Kravchenko V.F. – Deputy Editor in Chief, Dr.Sci. (Phys.-Math.), Prof.

Boritko S.V. – Dr.Sci. (Phys.-Math.), Prof.

Vasiliev V.P. – Dr.Sci. (Techn.), Prof.

Vinogradov E.A. – academician RAS, Dr.Sci. (Phys.-Math.), Prof.

Gulyaev Yu.V. – academician RAS, Dr.Sci. (Phys.-Math.), Prof.

Dianov E.M. – academician RAS, Dr.Sci. (Phys.-Math.), Prof.

Zhizhin G.N. – Dr.Sci. (Phys.-Math.), Prof.

Kompanets O.N. – Dr.Sci. (Phys.-Math.), Prof.

Koshkin V.I. – Dr.Sci. (Phys.-Math.), Prof.

Krohin O.N. – academician RAS, Dr.Sci. (Phys.-Math.), Prof.

Mazur M.M. – Dr.Sci. (Techn.)

ɀɭɪɧɚɥ ɩɟɪɟɢɡɞɚɟɬɫɹ ɧɚ ɚɧɝɥɢɣɫɤɨɦ ɚɡɵɤɟ ɩɨɞ ɧɚɡɜɚɧɢɟɦ «Physical Base of Instrumentation»

Морозов А.Н. – д.ф.-м.н.. профессор;

Отливанчик Е.А. – к.ф.-м.н.;

Пожар В.Э. – д.ф.-м.н.;

Федоров И.Б. – академик РАН, д.т.н., профессор;

Филачев А.М. – чл.-корр. РАН, д.т.н., профессор;

Яковлев В.П. – д.ф.-м.н., профессор

Morozov A.N. – Dr.Sci. (Phys.-Math.), Prof.

Otlivanchik E.A. – Cd.Sci. (Phys.-Math.) Pozhar V.E. – Dr.Sci. (Phys.-Math.)

Fedorov I.B. – academician RAS, Dr.Sci. (Techn.), Prof.

Filachev A.M. – Associate of the Russian Academy of Sciences, Dr.Sci. (Techn.), Prof.

Yakovlev V.P. – Dr.Sci. (Phys.-Math.), Prof.

© ɇɌɐ ɍɉ ɊȺɇ, 201

Ⱥɞɪɟɫ ɪɟɞɚɤɰɢɢ: 117342, Ɇɨɫɤɜɚ, ɭɥ. Ȼɭɬɥɟɪɨɜɚ, ɞ. 15, ɤɨɦɧ. 232.

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ɋɞɚɧɨ ɜ ɧɚɛɨɪ 26.06.12. ɉɨɞɩɢɫɚɧɨ ɜ ɩɟɱɚɬɶ 20.06.2012

Ɏɨɪɦɚɬ ɛɭɦɚɝɢ (70×100)1/16. ɉɟɱɚɬɶ ɨɮɫɟɬɧɚɹ. ɉɟɱɚɬɧɵɯ ɥɢɫɬɨɜ 7.

Ɉɬɩɟɱɚɬɚɧɨ: ɈɈɈ «ȻɍȾɈɄȼȺɃ», 105062, ɝ. Ɇɨɫɤɜɚ, ɭɥ. ɉɨɤɪɨɜɤɚ, ɞ. 41, ɫɬɪ. 2 Ɍɢɪɚɠ 500 ɷɤɡ. ɐɟɧɚ ɞɨɝɨɜɨɪɧɚɹ.

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Ⱥɧɧɨɬɚɰɢɹ

Ɋɚɡɪɚɛɨɬɚɧ ɦɟɬɨɞ ɨɰɟɧɤɢ ɜɥɢɹɧɢɹ ɧɚɝɪɟɜɚ ɚɧ- ɬɟɧɧɨɝɨ ɨɛɬɟɤɚɬɟɥɹ ɧɚ ɬɟɤɭɳɟɟ ɢɡɨɛɪɚɠɟɧɢɟ, ɮɨɪ- ɦɢɪɭɟɦɨɟ ɦɚɬɪɢɱɧɨɣ ɪɚɞɢɨɦɟɬɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɨɣ ɧɚɜɢɝɚɰɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ. Ɉɫɨɛɟɧɧɨɫɬɶ ɦɟɬɨɞɚ ɫɨɫɬɨɢɬ ɜ ɭɱɟɬɟ ɦɧɨɝɨɫɥɨɣɧɨɣ ɫɬɪɭɤɬɭɪɵ ɨɛɬɟɤɚɬɟɥɹ ɢ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢ ɟɝɨ ɧɚɝɪɟɜɚ ɩɨ ɫɥɨ- ɹɦ ɢ ɨɛɪɚɡɭɸɳɟɣ, ɚ ɬɚɤɠɟ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɱɚɫɬɨɬ- ɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɢɡɥɭɱɟɧɢɹ ɜ ɫɬɟɧɤɟ ɨɛɬɟɤɚɬɟɥɹ.

Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɚɧɬɟɧɧɵɣ ɨɛɬɟɤɚɬɟɥɶ, ɬɟɤɭɳɟɟ ɢɡɨɛɪɚɠɟɧɢɟ, ɦɚɬɪɢɱɧɚɹ ɪɚɞɢɨɦɟɬɪɢɱɟɫɤɚɹ ɫɢɫɬɟ- ɦɚ ɧɚɜɢɝɚɰɢɢ, ɥɟɬɚɬɟɥɶɧɵɣ ɚɩɩɚɪɚɬ

© Ȼɝɭɩɫɶ, 2012

Антюфеев Валерий Иванович — доктор технических наук, ведущий научный сотрудник, Харьковский националь- ный университет им. В.Н. Каразина, радиофизический факультет, кафедра теоретической радиофизики.

Быков Виктор Николаевич — доктор технических наук, ведущий научный сотрудник, Харьковский национальный университет им. В.Н. Каразина, радиофизический факультет, кафедра теоретической радиофизики.

E-mail: [email protected]

Иванченко Дмитрий Дмитриевич — кандидат физико-математических наук, ведущий научный сотрудник, Харь- ковский национальный университет им. В.Н. Каразина, радиофизический факультет, кафедра теоретической ради- офизики. E-mail: [email protected]

УДК 621.396.67:629.7.028.6.001.4

ȽɆɃɚɈɃɀ ɓɎɇɉȽɉɄ ɍɀɇɊɀɋȻɍɎɋɖ ȻɈɍɀɈɈɉȾɉ ɉȼɍɀɅȻɍɀɆɚ ɈȻ ɃɂɉȼɋȻɁɀɈɃɀ, ɏɉɋɇɃɋɎɀɇɉɀ ɇȻɍɋɃɒɈɖɇɃ ɋȻȿɃɉɇɀɍɋɃɒɀɌɅɃɇɃ ɌɃɌɍɀɇȻɇɃ

ПРОБЛЕМЫ ОБРАБОТКИ СИГНАЛОВ И ИЗОБРАЖЕНИЙ В АКУСТООПТИКЕ И РАДИОФИЗИКЕ

ФИЗИЧЕСКИЕ ОСНОВЫ ПРИБОРОСТРОЕНИЯ. 2012 Том 1, № 1

ȼɜɟɞɟɧɢɟ

Ɋɚɞɢɨɩɪɨɡɪɚɱɧɵɟ ɨɛɬɟɤɚɬɟɥɢ ɚɧɬɟɧɧ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɪɚɞɢɨɦɟɬɪɢɱɟɫɤɢɯ (ɊɆ) ɫɢɫɬɟɦɚɯ ɧɚɜɢɝɚɰɢɢ ɥɟɬɚ- ɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ (ɅȺ), ɜ ɩɪɨɰɟɫɫɟ ɩɨɥɟɬɚ ɜ ɩɥɨɬɧɵɯ ɫɥɨɹɯ ɚɬɦɨɫɮɟɪɵ ɩɨɞɜɟɪɝɚɸɬɫɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɦɭ ɧɚɝɪɟɜɭ, ɤɨɬɨɪɵɣ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɪɚɜɧɨɦɟɪɧɵɦ ɤɚɤ ɩɨ ɬɨɥɳɢɧɟ ɫɬɟɧɤɢ, ɬɚɤ ɢ ɜɞɨɥɶ ɨɛɪɚɡɭɸɳɟɣ ɨɛɬɟɤɚɬɟɥɹ.

ɉɪɢ ɷɬɨɦ ɦɚɬɟɪɢɚɥ ɫɬɟɧɤɢ ɫɬɚɧɨɜɢɬɫɹ ɧɟɨɞɧɨɪɨɞɧɵɦ ɜ ɷɥɟɤɬɪɨɞɢɧɚɦɢɱɟɫɤɨɦ ɫɦɵɫɥɟ, ɬ.ɟ. ɞɢɷɥɟɤɬɪɢɱɟ- ɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɢ ɬɚɧɝɟɧɫ ɭɝɥɚ ɩɨɬɟɪɶ ɞɢɷɥɟɤɬɪɢɤɚ, ɢɡ ɤɨɬɨɪɨɝɨ ɢɡɝɨɬɨɜɥɟɧ ɨɛɬɟɤɚɬɟɥɶ, ɢɡɦɟɧɹɸɬɫɹ ɤɚɤ ɩɨ ɬɨɥɳɢɧɟ ɫɬɟɧɤɢ, ɬɚɤ ɢ ɩɨ ɨɛɪɚɡɭɸɳɟɣ. ɗɬɨ ɨɫɨɛɟɧɧɨ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɊɆ ɫɢɫɬɟɦɚɯ, ɮɭɧɤɰɢɨɧɢɪɭɸɳɢɯ ɜ ɤɨɪɨɬɤɨɜɨɥɧɨɜɨɣ ɱɚɫɬɢ ɪɚɞɢɨɞɢɚɩɚɡɨɧɚ — ɜ ɦɢɥɥɢɦɟɬɪɨɜɨɦ ɞɢɚɩɚɡɨɧɟ ɜɨɥɧ.

ɇɚɥɢɱɢɟ ɨɛɬɟɤɚɬɟɥɹ ɜ ɛɥɢɠɧɟɣ ɡɨɧɟ ɚɧɬɟɧɧɵ ɩɪɢɜɨɞɢɬ ɤ ɫɥɟɞɭɸɳɢɦ ɨɬɪɢɰɚɬɟɥɶɧɵɦ ɮɚɤɬɨɪɚɦ:

– ɫɨɛɫɬɜɟɧɧɨɟ ɢɡɥɭɱɟɧɢɟ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ ɢɡ-ɡɚ ɟɝɨ ɧɚɝɪɟɜɚ ɜɨɡɪɚɫɬɚɟɬ, ɱɬɨ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɭɯɭɞɲɟ- ɧɢɸ ɬɨɱɧɨɫɬɢ ɩɨɤɚɡɚɧɢɣ ɊɆ ɩɪɢɟɦɧɢɤɚ;

Abstract

Method of evaluation of radome heating inÀ u- ence on actual image formed by the matrix radiometric system of aircraft navigation was developed. The method allows to take into account the layered pattern of radome and heating irregular- ity from layer to layer and in direction of radome guiding line. Therefore method takes into account the interference of frequency components of radiation in radome wall.

Key words: antenna radome, image, matrix radiometric systems of navigation, aircraft

(4)

– ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɶ ɧɚɝɪɟɜɚ ɫɬɟɧɤɢ ɜɞɨɥɶ ɨɛɪɚɡɭɸɳɟɣ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɦɧɨɝɨɥɭɱɟɜɵɯ (ɦɚɬɪɢɱɧɵɯ) ɚɧɬɟɧɧ ɢɥɢ ɩɪɢ ɫɤɚɧɢɪɨɜɚɧɢɢ ɞɢɚɝɪɚɦɦɵ ɧɚɩɪɚɜɥɟɧɧɨɫɬɢ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɢɫɤɚɠɟɧɢɸ ɮɨɪɦɢɪɭɟɦɨɝɨ ɫɢɫɬɟɦɨɣ ɬɟɤɭɳɟɝɨ ɢɡɨɛɪɚɠɟɧɢɹ.

Ȼɨɥɶɲɢɧɫɬɜɨ ɪɚɛɨɬ ɩɨ ɜɨɩɪɨɫɭ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɥɢɹɧɢɹ ɨɛɬɟɤɚɬɟɥɹ ɧɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɪɚɞɢɨɬɟɯɧɢ- ɱɟɫɤɢɯ ɫɢɫɬɟɦ, ɜ ɬɨɦ ɱɢɫɥɟ ɧɚ ɊɆ ɫɢɫɬɟɦɵ ɡɟɦɥɟɨɛɡɨɪɚ, ɩɨɫɜɹɳɟɧɨ ɪɚɫɱɟɬɭ ɚɦɩɥɢɬɭɞɧɨ-ɮɚɡɨɜɨɝɨ ɪɚɫ- ɩɪɟɞɟɥɟɧɢɹ (ȺɎɊ) ɜ ɜɵɧɟɫɟɧɧɨɦ ɡɚ ɨɛɬɟɤɚɬɟɥɶ ɷɤɜɢɜɚɥɟɧɬɧɨɦ ɪɚɫɤɪɵɜɟ, ɪɚɫɱɟɬɭ ɞɢɚɝɪɚɦɦɵ ɧɚɩɪɚɜɥɟɧ- ɧɨɫɬɢ ɚɧɬɟɧɧɵ ɜ ɞɚɥɶɧɟɣ ɡɨɧɟ ɩɨ ɷɬɨɦɭ ȺɎɊ ɢ ɢɫɫɥɟɞɨɜɚɧɢɸ ɜɥɢɹɧɢɹ ɮɚɡɨɜɵɯ ɨɲɢɛɨɤ, ɜɨɡɧɢɤɚɸɳɢɯ ɩɪɢ ɧɚɝɪɟɜɟ ɨɛɬɟɤɚɬɟɥɹ [1–7]. ɉɪɢ ɪɚɫɱɟɬɚɯ, ɤɚɤ ɩɪɚɜɢɥɨ, ɩɪɟɧɟɛɪɟɝɚɸɬ ɩɨɬɟɪɹɦɢ ɜ ɫɬɟɧɤɟ ɡɚ ɫɱɟɬ ɡɚɬɭɯɚɧɢɹ ɢ ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ ɭɱɟɬɨɦ ɩɨɬɟɪɶ ɧɚ ɨɬɪɚɠɟɧɢɟ. ɉɨɫɤɨɥɶɤɭ ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɢ ɩɨɝɥɨɳɚɸɳɚɹ ɫɩɨɫɨɛɧɨɫɬɢ ɬɟɥɚ ɫɜɹɡɚɧɵ ɡɚɤɨɧɨɦ Ʉɢɪɯɝɨɮɚ, ɪɚɫɱɟɬ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɬɟɩɥɨɜɨɝɨ ɢɡɥɭɱɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɨɝɨ ɧɚɝɪɟɬɵɦ ɨɛɬɟɤɚɬɟɥɟɦ, ɞɨɥɠɟɧ ɩɪɨɜɨɞɢɬɶɫɹ ɫ ɭɱɟɬɨɦ ɩɨɝɥɨɳɟɧɢɹ ɷɧɟɪɝɢɢ ɜ ɫɬɟɧɤɟ.

ɋɭɳɟɫɬɜɭɸɳɢɟ ɦɟɬɨɞɢɤɢ ɪɚɫɱɟɬɚ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ» ɜ ɛɨɥɶɲɢɧ- ɫɬɜɟ ɫɥɭɱɚɟɜ ɨɫɧɨɜɚɧɵ ɧɚ ɦɨɞɟɥɢ ɪɚɜɧɨɦɟɪɧɨ ɧɚɝɪɟɬɨɝɨ ɨɛɬɟɤɚɬɟɥɹ [1, 3, 4]. ȼ ɪɚɛɨɬɟ [4] ɫɞɟɥɚɧɚ ɩɨɩɵɬɤɚ ɨɛɨɛɳɢɬɶ ɦɨɞɟɥɶ ɧɚ ɫɥɭɱɚɣ ɧɟɪɚɜɧɨɦɟɪɧɨɝɨ ɩɨ ɬɨɥɳɢɧɟ ɫɬɟɧɤɢ ɧɚɝɪɟɜɚ. Ɉɞɧɚɤɨ ɜɨɥɧɨɜɨɣ ɦɟɬɨɞ, ɫ ɩɨɦɨ- ɳɶɸ ɤɨɬɨɪɨɝɨ ɩɨɥɭɱɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɫɨɨɬɧɨɲɟɧɢɹ, ɧɟ ɭɱɢɬɵɜɚɟɬ ɩɟɪɟɨɬɪɚɠɟɧɢɣ ɜɧɭɬɪɢ ɫɬɟɧɤɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢɜɟɞɟɧɧɚɹ ɜ ɪɚɛɨɬɟ [4] ɮɨɪɦɭɥɚ ɧɟ ɭɱɢɬɵɜɚɟɬ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɱɚɫɬɨɬɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɢɡɥɭɱɟɧɢɹ ɜ ɫɬɟɧɤɟ, ɩɨɫɤɨɥɶɤɭ ɜ ɨɫɧɨɜɟ ɟɟ ɜɵɜɨɞɚ ɩɨɥɨɠɟɧɨ ɫɨɨɬɧɨɲɟɧɢɟ ɞɥɹ ɭɫɪɟɞɧɟɧɧɨɝɨ ɜ ɩɨɥɨɫɟ ɱɚɫɬɨɬ ɤɨɷɮ- ɮɢɰɢɟɧɬɚ ɢɡɥɭɱɟɧɢɹ. ɉɨɫɤɨɥɶɤɭ ɞɥɹ ɫɢɫɬɟɦ ɦɢɥɥɢɦɟɬɪɨɜɨɝɨ ɞɢɚɩɚɡɨɧɚ ɬɨɥɳɢɧɚ ɫɥɨɟɜ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ ɫɪɚɜɧɢɦɚ ɫ ɞɥɢɧɨɣ ɜɨɥɧɵ, ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɪɚɫɱɟɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɚɧɬɟɧɧɵ ɫ ɭɱɟɬɨɦ ɦɧɨɝɨɤɪɚɬ- ɧɵɯ ɨɬɪɚɠɟɧɢɣ ɜɧɭɬɪɢ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ, ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɝɪɚɞɢɟɧɬɨɦ ɷɥɟɤɬɪɨɮɢɡɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɩɨ ɬɨɥɳɢɧɟ ɫɬɟɧɤɢ.

ɐɟɥɶɸ ɢɫɫɥɟɞɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɡɪɚɛɨɬɤɚ ɦɟɬɨɞɚ ɪɚɫɱɟɬɚ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–

ɨɛɬɟɤɚɬɟɥɶ» ɫ ɭɱɟɬɨɦ ɨɬɪɚɠɟɧɢɣ ɜɧɭɬɪɢ ɫɬɟɧɤɢ ɩɪɢ ɟɟ ɧɟɪɚɜɧɨɦɟɪɧɨɦ ɧɚɝɪɟɜɟ ɤɚɤ ɩɨ ɬɨɥɳɢɧɟ, ɬɚɤ ɢ ɩɨ ɨɛɪɚɡɭɸɳɟɣ.

ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ

Ⱥɜɬɨɪɚɦɢ ɜ ɞɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɩɪɨɜɟɞɟɧ ɰɢɤɥ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɱɬɨ ɩɨɡɜɨɥɢɥɨ ɨɛɨɛɳɢɬɶ ɨɫɧɨɜɧɵɟ ɩɨɞɯɨɞɵ ɤ ɪɟɲɟɧɢɸ ɭɤɚɡɚɧɧɨɣ ɡɚɞɚɱɢ ɜ ɜɢɞɟ ɦɨɧɨɝɪɚɮɢɢ [8]. Ɉɞɧɚɤɨ ɧɟɤɨɬɨɪɵɟ ɢɡ ɜɨɩɪɨɫɨɜ ɨɫɬɚɥɢɫɶ ɧɟ- ɪɟɲɟɧɧɵɦɢ. ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ ɢɯ.

ɉɭɫɬɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɚɝɪɟɜɚ ɨɛɬɟɤɚɬɟɥɹ ɧɚɣɞɟɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ( ),T r rD ɜ ɨɛɥɚɫɬɢ D ɢ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ ɨɫɰɢɥɥɹɬɨɪɚ 4( )r ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ T. D — ɨɛ- ɥɚɫɬɶ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɡɚɧɢɦɚɟɦɨɝɨ ɬɟɥɨɦ ɨɛɬɟɤɚɬɟɥɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɞɥɹ ɡɚɞɚɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɨɛɬɟɤɚɬɟɥɹ ɧɚɣɞɟɧɵ ɬɟɦɩɟɪɚɬɭɪɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ ɞɥɹ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɞɢɷɥɟɤɬɪɢɱɟ- ɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɢ ɬɚɧɝɟɧɫɚ ɭɝɥɚ ɩɨɬɟɪɶ Hc Hc( ),T tgG tgG( )T , ɩɨ ɤɨɬɨɪɵɦ ɩɨɫɬɪɨɟɧɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ

( ), tg tg ( ) Hc Hc r G G r .

ȼ ɪɚɛɨɬɟ [8] ɫ ɭɱɟɬɨɦ ɩɨɥɨɠɟɧɢɣ ɪɚɛɨɬ [9, 10] ɩɨɥɭɱɟɧɨ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɲɭɦɨɜɨɣ ɬɟɦɩɟ- ɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ»

0 ( ) ( ) ( ) ( )2 .

a 2

D

T tg dV

kP_Z ^Z

ZH

³

4 ^r Hc ^r G ^{r E r}

D (1)

ɗɬɨ ɜɵɪɚɠɟɧɢɟ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɲɭɦɨɜɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɚɧɬɟɧɧɵ T_a^o ɨɬ ɬɟɩɥɨɜɨɝɨ ɢɡɥɭɱɟɧɢɹ ɨɛɬɟɤɚɬɟɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɨɥɟɣ ɦɨɳɧɨɫɬɢ ɢɡɥɭɱɟɧɢɹ ɚɧɬɟɧɧɵ, ɩɨɝɥɨɳɟɧɧɨɣ ɜ ɨɛɬɟɤɚɬɟɥɟ. ȼ ɜɵɪɚɠɟɧɢɢ (1) ɩɪɢɧɹɬɵ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ: Z 2Sf — ɤɪɭɝɨɜɚɹ ɱɚɫɬɨɬɚ ɢɡɥɭɱɟɧɢɹ ɩɪɢɧɢɦɚɟɦɨɝɨ ɫɢɝɧɚɥɚ, P_Z — ɫɩɟɤɬɪɚɥɶ- ɧɚɹ ɩɥɨɬɧɨɫɬɶ ɦɨɳɧɨɫɬɢ, ɢɡɥɭɱɚɟɦɚɹ ɚɧɬɟɧɧɨɣ ɩɪɢ ɩɢɬɚɧɢɢ ɟɟ ɬɨɤɨɦ, ɜɨɡɛɭɠɞɚɸɳɢɦ ɚɧɬɟɧɧɭ (ɩɪɢ ɪɚɛɨ- ɬɟ ɧɚ ɩɟɪɟɞɚɱɭ), H₀ 8,854 10 ⁹ Ɏ/ɦ — ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ; E (r)_Z — ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜɨɥɧɵ, ɩɚɞɚɸɳɟɣ ɧɚ ɨɛɬɟɤɚɬɟɥɶ (ɩɪɢ ɪɚɛɨɬɟ ɚɧɬɟɧɧɵ ɧɚ ɢɡɥɭɱɟɧɢɟ), ɜ ɫɢɥɭ ɬɟɨɪɟɦɵ ɜɡɚɢɦɧɨɫɬɢ, dV — ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɨɛɬɟɤɚɬɟɥɹ, k 1,38 10 ²³

ƒǂ

Ɠǆ ƳǀưƴK — ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ.

Ɏɨɪɦɭɥɚ (1) ɫɩɪɚɜɟɞɥɢɜɚ ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ, ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɜ ɥɸɛɨɣ ɡɨɧɟ ɚɧɬɟɧɧɵ: ɛɥɢɠɧɟɣ (ɥɭɱɟɜɨɣ, ɩɪɨɠɟɤɬɨɪɧɨɣ), ɩɪɨɦɟɠɭɬɨɱɧɨɣ (ɡɨɧɟ Ɏɪɟɧɟɥɹ) ɢɥɢ ɞɚɥɶɧɟɣ (ɡɨɧɟ Ɏɪɚɭɧɝɨɮɟɪɚ), ɧɨ ɬɨɥɶɤɨ ɞɥɹ G– ɤɨɪɪɟ- ɥɢɪɨɜɚɧɧɨɝɨ ɲɭɦɨɜɨɝɨ ɢɡɥɭɱɟɧɢɹ.

(5)

Ⱥɧɬɸɮɟɟɜ ȼ.ɂ., Ȼɵɤɨɜ ȼ.ɇ., ɂɜɚɧɱɟɧɤɨ Ⱦ.Ⱦ.

Ȼɭɞɟɦ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɨɩɪɟɞɟɥɟɧɢɹ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ» ɩɨ ɮɨɪɦɭɥɟ (1) ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɞɨɩɭɳɟɧɢɹɯ ɢ ɨɝɪɚɧɢɱɟɧɢɹɯ:

– ɪɚɫɤɪɵɜ ɚɧɬɟɧɧɵ (ɪɢɫ. 1) ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɩɥɨɫɤɢɦ, ɩɪɹɦɨɭɝɨɥɶɧɵɦ ɢ ɪɚɫɩɨɥɨɠɟɧɧɵɦ ɜ ɩɥɨɫɤɨɫɬɢ 0

y ɞɟɤɚɪɬɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ( , , )x y z G

>

ax ^2,ax ²

@

u

>

az ^2,az ²

@

;

Ɋɢɫ. 1. ɋɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ, ɫɜɹɡɚɧɧɚɹ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ ɪɚɫɤɪɵɜɚ

– ɜ ɨɛɥɚɫɬɢ G ɡɚɞɚɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɥɹ ɜ ɜɢɞɟ ɤɜɚɡɢɩɥɨɫɤɨɣ ɜɨɥɧɵ, ɩɨɥɹɪɢɡɨɜɚɧɧɨɣ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ x

–

0

( , ) ^iky; 1 ( , ) ^iky,

x z

E U x z e H U x z e

Z (2)

ɝɞɟ Z₀ P H₀ ₀ 120S [Ɉɦ ] — ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɚɤɭɭɦɚ;

– ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɥɹ ɜ ɪɚɫɤɪɵɜɟ G ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɫɢɦɦɟɬɪɢɱɧɵɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɣ x, z;

– ɫɪɟɞɚ, ɡɚɩɨɥɧɹɸɳɚɹ ɩɪɨɫɬɪɚɧɫɬɜɨ ɦɟɠɞɭ ɪɚɫɤɪɵɜɨɦ ɢ ɨɛɬɟɤɚɬɟɥɟɦ, ɹɜɥɹɟɬɫɹ ɨɞɧɨɪɨɞɧɨɣ, ɫ ɩɨɫɬɨɹɧ- ɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɪɟɥɨɦɥɟɧɢɹ

c c c

N H P const; (3)

ɨɬɪɚɠɟɧɢɹɦɢ ɷɧɟɪɝɢɢ ɨɬ ɩɥɨɫɤɨɫɬɢ ɪɚɫɤɪɵɜɚ ɤ ɨɛɬɟɤɚɬɟɥɸ ɩɪɟɧɟɛɪɟɝɚɟɦ;

ɬɨɥɳɢɧɚ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ ɜ ɥɸɛɨɦ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɨɞɢɧɚɤɨɜɚ ɢ ɪɚɜɧɚ d;

ɜɧɭɬɪɟɧɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɨɛɬɟɤɚɬɟɥɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɨɜɟɪɯɧɨɫɬɶ ɜɪɚɳɟɧɢɹ, ɩɨɥɭɱɟɧɧɭɸ ɩɭɬɟɦ ɜɪɚɳɟɧɢɹ ɜɵɩɭɤɥɨɣ ɝɥɚɞɤɨɣ ɤɪɢɜɨɣ ɜɨɤɪɭɝ ɨɫɢ oy, ɢ ɨɩɢɫɵɜɚɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

( , , ) 0

F x y z . (4)

ȼ ɫɢɥɭ ɫɢɦɦɟɬɪɢɢ ɡɚɞɚɱɢ ɛɭɞɟɦ ɢɧɬɟɝɪɢɪɨɜɚɬɶ ɬɨɥɶɤɨ ɩɨ ɱɚɫɬɢ ɪɚɫɤɪɵɜɚ G0

>

0,a_x 2

@

u

>

0,a_z 2

@

G. Ɋɚɡɨɛɶɟɦ ɨɛɥɚɫɬɶ G₀ ɧɚ ɫɨɜɨɤɭɩɧɨɫɬɶ ɹɱɟɟɤ Gjk '

>

j x j^{, (} ' u '¹⁾ x

@ >

k z k^{, (} '¹⁾ z

@

, ɬɚɤ ɱɬɨ ₀ ¹ ¹

0 0

J K

jk

j k

G G

**

^,

ɝɞɟ ' x a_x (2 ),J ' z a_z (2 )K .

Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɨɛɬɟɤɚɬɟɥɶ ɪɚɫɩɨɥɨɠɟɧ ɜ ɛɥɢɠɧɟɣ (ɥɭɱɟɜɨɣ) ɡɨɧɟ ɚɧɬɟɧɧɵ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɜ ɷɬɨɣ ɡɨɧɟ ɜɨɡɦɨɠɧɨ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɥɹ ɥɭɱɟɜɵɦ ɦɟɬɨɞɨɦ [5], ɬ.ɟ. ɫ ɭɱɟɬɨɦ ɜɵɫɲɢɯ ɩɪɢɛɥɢɠɟɧɢɣ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ — ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɞɢɮɪɚɤɰɢɢ. ɉɪɢɛɥɢɠɟɧɢɸ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɥɭ- ɱɚɣ, ɤɨɝɞɚ ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ ɝɥɚɜɧɵɦ ɱɥɟɧɨɦ ɥɭɱɟɜɨɣ ɚɫɢɦɩɬɨɬɢɤɢ. ɉɨɥɟ ɜ ɩɪɢɛɥɢɠɟɧɢɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ ɪɚɫɩɚɞɚɟɬɫɹ ɧɚ ɫɨɜɨɤɭɩɧɨɫɬɶ ɥɭɱɟɜɵɯ ɬɪɭɛɨɤ, ɩɨ ɤɚɠɞɨɣ ɢɡ ɤɨɬɨɪɵɯ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɷɥɟɤɬɪɨ- ɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ, ɩɪɢɱɟɦ ɫɨɫɟɞɧɢɟ ɥɭɱɟɜɵɟ ɬɪɭɛɤɢ ɧɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɦɟɠɞɭ ɫɨɛɨɣ.

ȼɨɡɶɦɟɦ ɜ ɤɚɱɟɫɬɜɟ ɥɭɱɟɜɨɣ ɬɪɭɛɤɢ ɩɪɢɡɦɭ ɫ ɨɫɧɨɜɚɧɢɟɦ G_jk (ɪɢɫ. 1) ɢ ɛɨɤɨɜɵɦɢ ɝɪɚɧɹɦɢ, ɨɛɪɚɡɨɜɚɧ- ɧɵɦɢ ɩɥɨɫɤɨɫɬɹɦɢ

, ( 1) ,

, ( 1) .

j k

x x j x x j x

z z k z z k z

' '

' ' (5)

(6)

ȼ ɩɪɢɛɥɢɠɟɧɢɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ ɩɥɨɫɤɨɫɬɹɦɢ (5) ɧɚ ɜɧɭɬɪɟɧɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ 6 ɨɛɬɟɤɚɬɟɥɹ ɜɵɫɟɤɚɟɬɫɹ ɱɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ 6_jk, ɤɨɬɨɪɭɸ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɵɯ ' 'x, z ɦɨɠɧɨ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɩɚ- ɪɚɥɥɟɥɨɝɪɚɦɦɨɦ ɜ ɤɚɫɚɬɟɥɶɧɨɣ ɤ 6 ɜ ɬɨɱɤɟ (x z_j, _k) ɩɥɨɫɤɨɫɬɢ Q_jk (ɪɢɫ. 1), ɩɥɨɳɚɞɶ ɤɨɬɨɪɨɝɨ ɩɪɢ ɭɫɥɨɜɢɢ

0 ( , , )

y jk

F w w z F y x y z 6 ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ [11]:

²

² ; ;

1 .

j k j k

jk x y z y x x z z y x x z z

S x z F F F F x z F F

' | ' ' ' ' (6)

ɉɪɟɞɫɬɚɜɢɦ ɢɧɬɟɝɪɚɥ (1) ɜ ɜɢɞɟ ɢɧɬɟɝɪɚɥɶɧɨɣ ɫɭɦɦɵ ɩɨ ɨɛɥɚɫɬɢ G₀

1 1

0

0 0

2

J K

a jk

j k

B

T k P_Z

ZH _:

¦¦

D , (7)

^{( )}

^{( )} ^{( )} ^{( )}²

jk

jk V

T H tgG _Z dV

: 4

³

^r c ^r ^{r E r} ^, ⁽⁸⁾

ɝɞɟ V_jk — ɨɛɥɚɫɬɢ, ɜɵɫɟɤɚɟɦɵɟ ɜ ɬɟɥɟ ɨɛɬɟɤɚɬɟɥɹ ɩɥɨɫɤɨɫɬɹɦɢ (5).

Ⱦɥɹ ɪɚɫɱɟɬɚ ɩɨɥɹ ɜɧɭɬɪɢ ɫɬɟɧɤɢ ɦɟɬɨɞ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ ɧɟɩɪɢɦɟɧɢɦ, ɬɚɤ ɤɚɤ ɨɧ ɧɟ ɭɱɢɬɵɜɚɟɬ ɨɬɪɚɠɟɧɢɣ ɨɬ ɧɟɨɞɧɨɪɨɞɧɨɫɬɟɣ ɫɪɟɞɵ, ɤɨɬɨɪɨɣ ɡɚɩɨɥɧɟɧɚ ɫɬɟɧɤɚ ɨɛɬɟɤɚɬɟɥɹ [10].

Ɉɛɳɚɹ ɩɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɩɪɢ ɜɵɲɟɭɤɚɡɚɧɧɵɯ ɞɨɩɭɳɟɧɢɹɯ ɢ ɨɝɪɚɧɢɱɟ- ɧɢɹɯ ɬɪɟɛɭɟɬɫɹ ɜɵɱɢɫɥɢɬɶ ɢɧɬɟɝɪɚɥɶɧɭɸ ɫɭɦɦɭ (7) ɫ ɭɱɟɬɨɦ ɨɬɪɚɠɟɧɢɣ ɜɧɭɬɪɢ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ.

Ɋɟɞɭɤɰɢɹ ɡɚɞɚɱɢ

ɉɨɫɬɚɜɥɟɧɧɚɹ ɡɚɞɚɱɚ ɪɟɞɭɰɢɪɭɟɬɫɹ ɤ ɬɪɟɦ ɩɨɞɡɚɞɚɱɚɦ:

— ɩɨ ɡɚɞɚɧɧɨɦɭ ȺɎɊ (2) ɜɵɱɢɫɥɢɬɶ ɩɨɥɟ E_Z_jk ɩɚɞɚɸɳɟɣ ɧɚ ɜɧɭɬɪɟɧɧɸɸ ɫɬɟɧɤɭ ɨɛɬɟɤɚɬɟɥɹ ɜɨɥɧɵ ɜ ɬɨɱɤɚɯ M_jk (x y_j, _jk,z_k)6, j0,J 1;k0,K1, ɝɞɟ y_jk ɟɫɬɶ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ F x y z( _j, , _k) 0;

— ɞɥɹ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ V_jk ɩɨɫɬɪɨɢɬɶ ɩɥɨɫɤɨɫɬɶ ɩɚɞɟɧɢɹ ɜɨɥɧɵ ɧɚ ɨɛɬɟɤɚɬɟɥɶ ɜ ɬɨɱɤɟ M_jk, ɜɵɱɢɫ- ɥɢɬɶ ɭɝɨɥ ɩɚɞɟɧɢɹ T_jk, ɤɨɦɩɨɧɟɧɬɵ ɩɨɥɹ E_s_Z,E_A_Z ɜɧɭɬɪɢ ɷɥɟɦɟɧɬɚ V_jk, ɥɟɠɚɳɢɟ ɜ ɩɥɨɫɤɨɫɬɢ ɩɚɞɟɧɢɹ ɢ ɜ ɨɪɬɨɝɨɧɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɚ ɬɚɤɠɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (8) ɢɧɬɟɝɪɚɥ

^

^{( )} ^{( )} ^{( )} ^{( )}² ^{( )}²

`

jk

jk s

V

T H tgG E_Z E_A_Z dV

:

³

4 ^r c ^r ^r u ^r ^r ⁽⁹⁾

ɫ ɭɱɟɬɨɦ ɨɬɪɚɠɟɧɢɣ ɜ ɫɥɨɟ;

— ɩɨ ɡɚɞɚɧɧɨɦɭ ȺɎɊ (2) ɜ ɪɚɫɤɪɵɜɟ ɪɚɫɫɱɢɬɚɬɶ ɫɩɟɤɬɪɚɥɶɧɭɸ ɩɥɨɬɧɨɫɬɶ ɦɨɳɧɨɫɬɢ P_Z, ɢɡɥɭɱɚɟɦɨɣ ɚɧɬɟɧɧɨɣ.

Ɂɚɞɚɱɚ 1. ȼ ɪɚɦɤɚɯ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɞɢɮɪɚɤɰɢɢ ɪɟɲɟɧɢɟ ɞɥɹ ɤɚɠɞɨɝɨ ɥɭɱɟɜɨɝɨ ɩɨɥɹ ɡɚɞɚɟɬɫɹ [5]

ɜ ɮɨɪɦɟ:

ik L0

V Ae , (10)

ɝɞɟ L L x y z( , , ) — ɷɣɤɨɧɚɥ, A A x y z k( , , , _c) — ɚɦɩɥɢɬɭɞɚ; V x y z( , , ) — ɫɨɫɬɚɜɥɹɸɳɚɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɢɥɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ; k_c N_cZ c k; ₀ Z c.

Ɋɟɲɟɧɢɟ ɢɳɟɬɫɹ ɜ ɜɢɞɟ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɝɨ ɪɹɞɚ ɩɨ ɫɬɟɩɟɧɹɦ kc¹

0

( , , ) (1 _c)^j _j( , , )

j

A x y z ik A x y z

¦

f ^{. (11)}

Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɥɹ (11) ɧɟɨɛɯɨɞɢɦɨ ɫɧɚɱɚɥɚ ɪɟɲɢɬɶ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɷɣɤɨɧɚɥɚ

2 2

(L( ))r N_c( )r , (12)

ɚ ɡɚɬɟɦ ɫɢɫɬɟɦɭ ɪɟɤɭɪɪɟɧɬɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɟɪɟɧɨɫɚ ɞɥɹ ɫɨɫɬɚɜɥɹɸɳɢɯ ɥɭɱɟɜɨɝɨ ɪɚɡɥɨɠɟɧɢɹ

1 1

2( L, A_n) 'LA_n 'A_n ,n 0,1, 2...,'A 0. (13) ȼ ɫɢɥɭ ɭɫɥɨɜɢɹ (3) ɥɭɱɢ, ɩɨ ɤɨɬɨɪɵɦ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɷɧɟɪɝɢɹ, ɹɜɥɹɸɬɫɹ ɩɪɹɦɵɦɢ ɥɢɧɢɹɦɢ [5], ɫɢɦ- ɦɟɬɪɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɪɚɫɤɪɵɜɭ ɜɥɟɱɟɬ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɶ ɷɬɢɯ ɥɢɧɢɣ ɩɥɨɫɤɨɫɬɢ y 0, ɬ.ɟ. ɭɪɚɜɧɟɧɢɹ ɥɭɱɟɣ ɢɦɟɸɬ ɜɢɞ:

(7)

, ( , )

0 1 0

x x y z z

x z G

c c

c c , ɚ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (11) ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

( , , ) 0( , ) _c , ( , ) ,

L x y z L x z N y x z G (14)

ɝɞɟ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (3), L x z₀( , ) argU x z( , ).

ȼ [5] ɩɨɤɚɡɚɧɨ, ɱɬɨ ɞɥɹ ɫɥɭɱɚɹ ɩɥɨɫɤɨɣ ɢɡɥɭɱɚɟɦɨɣ ɜɨɥɧɵ ɩɨɩɪɚɜɤɢ ɤ ɩɪɢɛɥɢɠɟɧɢɸ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ ɜɨɡɪɚɫɬɚɸɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɪɚɫɤɪɵɜɚ ɢ ɩɨɥɭɱɟɧɵ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɷɬɢɯ ɩɨɩɪɚɜɨɤ.

Ƚɥɚɜɧɵɣ ɱɥɟɧ ɚɫɢɦɩɬɨɬɢɤɢ ɢɦɟɟɬ ɜɢɞ

0( , , ) ( , )

A x y z U x z , (15)

ɬ.ɟ. ɚɦɩɥɢɬɭɞɚ ɜ ɩɪɢɛɥɢɠɟɧɢɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ y ɢ ɜ ɝɥɚɜɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɩɪɨɢɫɯɨ- ɞɢɬ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɟɪɟɧɨɫ ȺɎɊ ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ. ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɩɨ ɦɟɪɟ ɭɞɚɥɟɧɢɹ ɨɬ ɪɚɫɤɪɵɜɚ ɢɡ-ɡɚ ɞɢɮɪɚɤɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɥɭɱɟɜɵɯ ɬɪɭɛɨɤ ɩɨɥɟ ɞɟɮɨɪɦɢɪɭɟɬɫɹ. Ⱦɥɹ ɫɥɟɞɭɸɳɟɝɨ ɱɥɟɧɚ ɚɫɢɦɩɬɨɬɢɤɢ ɩɨɥɭɱɟɧɨ ɜɵɪɚɠɟɧɢɟ

1( , , ) ( 2) ( , )

A x y z y 'U x z . (16)

Ɋɚɫɫɬɨɹɧɢɟ yc, ɧɚ ɤɨɬɨɪɨɦ ɟɳɟ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɜɬɨɪɵɦ ɱɥɟɧɨɦ ɚɫɢɦɩɬɨɬɢɤɢ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭ- ɥɨɣ

2 0 ( , ) ( , )

yc k U x z 'U x z . (17)

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (9), (11), (13), (15), (16) ɪɟɲɟɧɢɟ ɩɟɪɜɨɣ ɡɚɞɚɱɢ ɞɥɹ ɤɨɦɩɨɧɟɧɬɵ ɷɥɟɤ- ɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢɦɟɟɬ ɜɢɞ

0

( ) 1 , ,

2

c jk

j k

ik y jk

jk x jk x x z z

c

E E M e y U

ik

§ ·

'

¨ ¸

ɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɬɨɪɨɣ ɢɡ ɮɨɪɦɭɥ (2).

Ɂɚɞɚɱɚ 2. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ Q_ij ɤɚɫɚɬɟɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ (4) ɜ ɬɨɱɤɟ M_jk (ɪɢɫ. 1). ɉɨɫɤɨɥɶ- ɤɭ ɧɚɩɪɚɜɥɹɸɳɢɣ ɜɟɤɬɨɪ ɥɭɱɚ, ɜɵɯɨɞɹɳɟɝɨ ɢɡ ɬɨɱɤɢ M_jk ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ, ɪɚɜɟɧ

(0,1, 0)

ejk , ɬɨ ɭɝɨɥ ɩɚɞɟɧɢɹ ɧɚ ɫɬɟɧɤɭ ɨɛɬɟɤɚɬɟɥɹ, ɬ.ɟ. ɭɝɨɥ ɦɟɠɞɭ ɭɤɚɡɚɧɧɵɦ ɧɚɩɪɚɜɥɹɸɳɢɦ ɜɟɤɬɨɪɨɦ ɢ ɧɨɪɦɚɥɶɸ n_jk ɤ 6, ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

, ,

2 2 2

arccos , arccos .

jk

jk jk y

jk x j x y y z k z

jk jk x y z

F

F F F

T _' _'

e n

e n (19)

ȿɫɥɢ 6 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɨɜɟɪɯɧɨɫɬɶ ɜɪɚɳɟɧɢɹ ɜɨɤɪɭɝ ɨɫɢ y, ɬɨ ɨɫɶ y ɩɪɢɧɚɞɥɟɠɢɬ ɩɥɨɫɤɨɫɬɢ ɩɚ- ɞɟɧɢɹ P_jk. ȿɫɥɢ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɚɪɚɥɥɟɥɟɧ ɨɫɢ ox ɢ ɚɦɩɥɢɬɭɞɚ ɩɨɥɹ ɜ ɬɨɱɤɟ

Mjk ɪɚɜɧɚ A_jk, ɬɨ ɚɦɩɥɢɬɭɞɚ ɫɨɫɬɚɜɥɹɸɳɟɣ ɩɨɥɹ, ɥɟɠɚɳɟɣ ɜ ɩɥɨɫɤɨɫɬɢ ɩɚɞɟɧɢɹ, ɪɚɜɧɚ A_jkcosG_jk, ɚ ɨɪɬɨ- ɝɨɧɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ — A_jksinG_jk, ɝɞɟ G_jk arctg z_k x_j.

ȼ ɩɥɨɫɤɨɫɬɢ ɩɚɞɟɧɢɹ P_jk ɜɜɟɞɟɦ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ (ɪɢɫ. 2), ɨɫɶ z ɤɨɬɨɪɨɣ ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɧɨɪɦɚɥɢ n_jk, ɚ ɨɫɶ x ɥɟɠɢɬ ɜ ɤɚɫɚɬɟɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ Q_jk.

Ɋɢɫ. 2. Ɇɧɨɝɨɫɥɨɣɧɚɹ ɦɨɞɟɥɶ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ

(8)

Ȼɭɞɟɦ ɩɪɟɞɫɬɚɜɥɹɬɶ ɥɨɤɚɥɶɧɨ ɱɚɫɬɶ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ M_jk ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɵɦ ɫɥɨɟɦ. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɢɧɬɟɝɪɚɥɚ ɩɨ V_jk ɜ ɮɨɪɦɭɥɟ (9) ɪɚɡɨɛɶɟɦ ɫɥɨɣ ɩɨ ɬɨɥɳɢɧɟ ɧɚ n2 ɷɥɟɦɟɧɬɚɪɧɵɯ ɫɥɨɟɜ ɪɚɜɧɨɣ ɬɨɥɳɢɧɵ 'd_jk d ^ª¬(n2) cosT_jk^º¼ ɢ ɡɚɩɢɲɟɦ ɜɵɪɚɠɟɧɢɟ (9) ɜ ɜɢɞɟ ɢɧɬɟɝɪɚɥɶɧɨɣ ɫɭɦɦɵ

2 2 2

0

,

n

m m m m m

jk jk jk jk s jk jk jk jk

m

T H T tgG T E_Z E _Z S d

: |

¦

4 c u A ' ' ⁽²⁰⁾

ɝɞɟ T_jk^m T x m d z( _j, ' , _k), d 2

d n

' , 'S_jk ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ (6).

ɑɬɨɛɵ ɨɩɪɟɞɟɥɢɬɶ ɩɨɥɟ ɜɧɭɬɪɢ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ, ɪɚɫɫɦɨɬɪɢɦ ɫɥɟɞɭɸɳɭɸ ɡɚɞɚɱɭ. ɉɭɫɬɶ ɧɚ ɩɥɨɫɤɨɩɚ- ɪɚɥɥɟɥɶɧɵɣ ɫɥɨɣ ɢɡ ɫɪɟɞɵ ɫ ɧɨɦɟɪɨɦ n ɩɨɞ ɭɝɥɨɦ T_jk T (ɢɧɞɟɤɫɵ ɨɩɭɫɬɢɦ) ɤ ɧɨɪɦɚɥɢ ɩɚɞɚɟɬ ɩɨɥɹɪɢɡɨ- ɜɚɧɧɚɹ ɨɪɬɨɝɨɧɚɥɶɧɨ ɤ ɩɥɨɫɤɨɫɬɢ ɩɚɞɟɧɢɹ ɜɨɥɧɚ ɱɚɫɬɨɬɵ Z

1 1

( ) ( )

1 ( ) ( )

0

1 ( ) ( )

0

,

cos ,

sin ,

j j j j j

i z z i z z i x

yj j j

i z z i z z i x

xj j j j j

i z z i z z i x

zj j j j j

E C e B e e

H Z C e B e e

D D V

T T

ª º

¬ ¼

ª º

¬ ¼

ª º

¬ ¼

1,

j j

z¬ªz z º¼, D_j k_zj k_jcosT_j, V_j k_xj k_jsinT_j,

1 2 0 0

, ( )

j aj aj j j

k c

c

Z H P Z H P H P ,

0 0

j j j

Z Z P H — ɜɨɥɧɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ j-ɝɨ ɫɥɨɹ.

ɂɡ ɭɫɥɨɜɢɹ ɧɟɩɪɟɪɵɜɧɨɫɬɢ ɬɚɧɝɟɧɰɢɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɩɨɥɹ ɧɚ ɝɪɚɧɢɰɚɯ ɫɥɨɟɜ ɫɥɟɞɭɸɬ ɪɚɜɟɧɫɬɜɚ

sin sin , 1,

j j n

k T k T j n (21)

(ɡɚɤɨɧ ɋɧɟɥɥɢɭɫɚ), ɚ ɬɚɤɠɟ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ [10]:

2 2 2 2

1 1 1 1

2 2 2 2

1 1 1 1

1 2 2

2 3 2 3

1 1

1 2 1 2 2 1 2

2 3 2 3 2

3 2 3

1 1

0,

0, , 0, 0,

n n n n

i d i d

n n n n

i d i d

n n

C C B

C e C B e B

C e B e B C

C C Z Z B Z Z

C e C Z Z B e B Z Z

C e B e

D D

A A A A

A A

""""""""""""""""

""""""""""""""

1 3 1 3 ,

n n n n

B ZÂ ZÂ C ZÂ ZÂ

°

°°

®°

°°

¯

(22)

ɝɞɟ ₁, ⁰ cos

n n n j j j

d z z Z^A Z T , ɚɦɩɥɢɬɭɞɚ ɩɚɞɚɸɳɟɣ ɜɨɥɧɵ C_n E⁰_jksinG_jk, E⁰_jk ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟ- ɧɢɟɦ (18), ɚ ɜ ɫɪɟɞɟ ɫ ɧɨɦɟɪɨɦ 1 ɨɬɪɚɠɟɧɧɚɹ ɜɨɥɧɚ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɨɬɫɭɬɫɬɜɭɸɳɟɣ.

ɂɡ (21) ɫɥɟɞɭɟɬ

² ²

²

cosT_j 1 k_n k_j sin T 1 H P H P_n _n _j _j sin T. ȼ ɫɥɭɱɚɟ ɜɨɥɧɵ, ɩɨɥɹɪɢɡɨɜɚɧɧɨɣ ɜ ɩɥɨɫɤɨɫɬɢ ɩɚɞɟɧɢɹ, ɢɦɟɟɦ

1 1

( ) ( )

( ) ( ) 0

,

cos ,

sin ,

j j j j j

i z z i z z i x

yj j j

i z z i z z i x

xj j j j j

i z z i z z i x

zj j j j j

H C e B e e

E C e B e Z e

D D V

T T

ª º

¬ ¼

ª º

¬ ¼

ª º

¬ ¼

(9)

ɚ ɫɢɫɬɟɦɚ (22) ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ

2 2 2 2

1 1 1 1

2 2 2 2

1 1 1 1

1 2 2

2 3 2 3

1 1

1 2 2 1 2 2 1

2 3 3 2 2

3 3 2

1 1

0,

0, , 0, 0,

n n n n

i d i d

n n n n

s s s s

i d s s i d

s s

i d i d

n n

C C B

C e C B e B

C e B e B C

C C Z Z B Z Z C e C Z Z B e

B Z Z

C e B e

D D

""""""""""""""""

"""""""""""""""

1 1,

s s s s

n n n n n n

B Z Z C Z Z

°

°°

®°

°°

¯

(23)

ɝɞɟ Z^s_j Z⁰_jcosT_j, C_n (1 Z₀)E⁰_jkcosG_jk.

ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦ (22), (23) ɞɥɹ ɤɚɠɞɨɣ ɢɡ ɩɨɥɹɪɢɡɚɰɢɣ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɥɨɤɚɥɶɧɵɣ ɤɨɷɮ- ɮɢɰɢɟɧɬ ɨɬɪɚɠɟɧɢɹ R_jk B C_n _n ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɡɪɚɱɧɨɫɬɢ ɫɥɨɹ t_jk B C₁ _n.

Ɂɚɞɚɱɚ 3. ɋɩɟɤɬɪɚɥɶɧɭɸ ɩɥɨɬɧɨɫɬɶ ɦɨɳɧɨɫɬɢ ɢɡɥɭɱɟɧɢɹ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɤɚɤ ɩɨɬɨɤ ɜɟɤɬɨɪɚ ɉɨɣɧɬɢɧ- ɝɚ ɱɟɪɟɡ ɱɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɤɪɵɜɚ G₀, ɬ.ɟ.

(24)

ɝɞɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɥɹ ɜ ɪɚɫɤɪɵɜɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ (2), Z_c Z₀ P H_c _c . Ɋɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ

ɑɢɫɥɟɧɧɵɟ ɪɚɫɱɟɬɵ ɩɨ ɮɨɪɦɭɥɚɦ (7), (8) ɫ ɭɱɟɬɨɦ ɪɟɞɭɤɰɢɢ ɡɚɞɚɱɢ ɩɪɨɜɟɞɟɧɵ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɞɨɩɭ- ɳɟɧɢɹɯ ɢ ɨɝɪɚɧɢɱɟɧɢɹɯ:

– ɩɪɨɫɬɪɚɧɫɬɜɨ ɦɟɠɞɭ ɨɛɬɟɤɚɬɟɥɟɦ ɢ ɪɚɫɤɪɵɜɨɦ ɡɚɩɨɥɧɟɧɨ ɜɨɡɞɭɯɨɦ, ɞɥɹ ɤɨɬɨɪɨɝɨ H_c |1, P_c 1, tgG |0; – ɜɧɭɬɪɟɧɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɨɛɬɟɤɚɬɟɥɹ 6 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɜɟɪɯɧɸɸ ɱɚɫɬɶ ɜɵɬɹɧɭɬɨɝɨ ɷɥɥɢɩɫɨɢɞɚ ɜɪɚɳɟɧɢɹ ɜɨɤɪɭɝ ɨɫɢ y, ɨɩɢɫɵɜɚɟɦɨɝɨ ɭɪɚɜɧɟɧɢɟɦ

–

2 2 2

0

2 2

( )

y y 1, x z

u g

t , (25)

ɝɞɟ y₀ — ɪɚɫɫɬɨɹɧɢɟ, ɧɚ ɤɨɬɨɪɨɟ ɫɦɟɳɟɧɚ ɩɥɨɫɤɨɫɬɶ ɪɚɫɤɪɵɜɚ ɚɧɬɟɧɧɵ ɨɬ ɰɟɧɬɪɚ ɷɥɥɢɩɫɨɢɞɚ;

– ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɥɹ ɜ ɩɪɹɦɨɭɝɨɥɶɧɨɦ ɪɚɫɤɪɵɜɟ ɚɧɬɟɧɧɵ, ɥɟɠɚɳɟɦ ɜ ɩɥɨɫɤɨɫɬɢ y 0, ɹɜɥɹɟɬɫɹ ɫɢɧ- ɮɚɡɧɵɦ ɢ ɡɚɞɚɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

–U x z^{( , )} ^cos

Sx ax ^cos Sz az

^{, arg}U x z^{( , )} const^; (26) – ɨɛɬɟɤɚɬɟɥɶ ɢɡɝɨɬɨɜɥɟɧ ɢɡ ɤɜɚɪɰɟɜɨɝɨ ɫɬɟɤɥɚ (Ʉɋ) ɢɥɢ ɢɡ ɨɤɢɫɢ ɛɟɪɢɥɥɢɹ (ɈȻ), ɩɪɢɱɟɦ ɦɚɬɟɪɢɚɥ ɜɬɨ-

ɪɨɝɨ ɬɢɩɚ ɨɬɥɢɱɚɟɬɫɹ ɛɨɥɟɟ ɜɵɫɨɤɢɦɢ ɩɨɬɟɪɹɦɢ;

– ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɜɧɭɬɪɢ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɢɡɜɟɫɬɧɵɦ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟ- ɧɢɹ ɡɚɞɚɱɢ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɚɝɪɟɜɚ ɨɛɬɟɤɚɬɟɥɹ ɢ ɫɢɦɦɟɬɪɢɱɧɵɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɨɛɬɟɤɚɬɟɥɹ, ɡɚɞɚɧɨ ɜ ɜɢɞɟ ɦɚɬɪɢɰɵ [T_ij] ɜ ɭɡɥɚɯ ɩɨɥɹɪɧɨɣ ɫɟɬɤɢ ɞɥɹ ɤɚɠɞɨɣ ɫɟɤɭɧɞɵ ɩɨɥɟɬɚ ɅȺ [8].

ɇɚ ɪɢɫ.3 ɩɪɢɜɟɞɟɧɵ ɫɟɦɟɣɫɬɜɚ ɡɚɜɢɫɢɦɨɫɬɟɣ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ» ɞɥɹ ɦɨɞɟɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɬɨɥɳɢɧɟ ɫɬɟɧɤɢ

( ) 0 ( 2)

T y T K yd , (27)

ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬ K ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɝɪɚɞɢɟɧɬ ɬɟɦɩɟɪɚɬɭɪɵ. ɋɥɭɱɚɣ K 0 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɜɧɨɦɟɪɧɨɦɭ ɪɚɫ- ɩɪɟɞɟɥɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɫɬɟɧɤɟ, ɤɨɝɞɚ ɜɧɭɬɪɟɧɧɢɟ ɩɟɪɟɨɬɪɚɠɟɧɢɹ ɧɟ ɭɱɢɬɵɜɚɸɬɫɹ.

(10)

Ʉɪɢɜɵɟ ɢɦɟɸɬ ɱɟɬɤɨ ɜɵɪɚɠɟɧɧɵɟ ɦɚɤɫɢɦɭɦɵ ɢ ɦɢɧɢɦɭɦɵ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɢɧɬɟɪɮɟɪɟɧɰɢɟɣ ɤɨɥɟɛɚɧɢɣ ɪɚɡɥɢɱɧɵɯ ɱɚɫɬɨɬ ɜ ɫɬɟɧɤɟ.

Ɉɬɦɟɬɢɦ, ɱɬɨ ɦɚɤɫɢɦɭɦɵ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɞɥɹ Ʉɋ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɫɦɟɳɚɸɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɝɪɚ- ɞɢɟɧɬɚ ɬɟɦɩɟɪɚɬɭɪɵ K, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɜ ɫɥɭɱɚɟ ɈȻ ɫɦɟɳɟɧɢɹ ɨɤɚɡɵɜɚɸɬɫɹ ɡɧɚɱɢɬɟɥɶɧɵɦɢ, ɱɬɨ ɡɚɬɪɭɞɧɹɟɬ ɜɵɛɨɪ ɨɩɬɢɦɚɥɶɧɨɣ ɬɨɥɳɢɧɵ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ.

Ɋɢɫ. 3. Ɂɚɜɢɫɢɦɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪɵ ɚɧɬɟɧɧɵ ɨɬ ɱɚɫɬɨɬɵ ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ ɤɜɚɪɰɟɜɨɝɨ ɫɬɟɤɥɚ (ɚ) ɢ ɨɤɢɫɢ ɛɟɪɢɥɥɢɹ (ɛ)

Ɋɢɫ. 4. Ɂɚɜɢɫɢɦɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪɵ ɚɧɬɟɧɧɵ ɨɬ ɱɚɫɬɨɬɵ ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ

ɢɡ ɤɜɚɪɰɟɜɨɝɨ ɫɬɟɤɥɚ (ɚ) ɢ ɨɤɢɫɢ ɛɟɪɢɥɥɢɹ (ɛ) ɞɥɹ ɰɟɧɬɪɚɥɶɧɨɝɨ (5–5) ɢ ɭɝɥɨɜɨɝɨ ɥɭɱɟɣ (1–1)

ȼ ɨɤɪɟɫɬɧɨɫɬɹɯ ɦɚɤɫɢɦɭɦɨɜ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɥɟɠɚɬ ɦɢɧɢɦɭɦɵ ɦɨɞɭɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɬɪɚɠɟɧɢɹ ɢ ɦɚɤɫɢɦɭɦɵ ɦɨɞɭɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɪɨɡɪɚɱɧɨɫɬɢ ɫɬɟɧɤɢ, ɩɨɷɬɨɦɭ ɫɪɟɞɧɸɸ ɪɚɛɨɱɭɸ ɱɚɫɬɨɬɭ ɊɆ ɩɪɢ- ɟɦɧɢɤɚ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɨɥɳɢɧɟ ɫɥɟɞɭɟɬ ɜɵɛɢɪɚɬɶ ɜɛɥɢɡɢ ɨɞɧɨɝɨ ɢɡ ɦɚɤɫɢɦɭɦɨɜ ɢɥɢ ɩɪɢ ɡɚɞɚɧɧɨɣ ɱɚɫɬɨɬɟ ɜɵɛɢɪɚɬɶ ɞɨɥɠɧɵɦ ɨɛɪɚɡɨɦ ɬɨɥɳɢɧɭ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ.

ɉɨ ɪɟɡɭɥɶɬɚɬɚɦ ɪɚɛɨɬɵ [8] ɛɵɥɢ ɩɪɨɜɟɞɟɧɵ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɢɥɢ ɨɰɟ- ɧɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ» ɨɬ ɱɚɫɬɨɬɵ ɩɪɢɧɢɦɚɟɦɨɝɨ ɊɆ ɫɢɝɧɚɥɚ ɞɥɹ ɰɟɧɬɪɚɥɶɧɨɝɨ ɥɭɱɚ (5–5) ɢ ɛɨɤɨɜɨɝɨ ɥɭɱɚ (1–1), ɦɚɤɫɢɦɚɥɶɧɨ ɭɞɚɥɟɧɧɨɝɨ ɨɬ ɰɟɧɬɪɚ ɦɚɬɪɢɱ- ɧɨɝɨ ɩɪɢɟɦɧɢɤɚ. Ɉɰɟɧɤɢ ɩɪɨɜɟɞɟɧɵ ɞɥɹ ɨɛɬɟɤɚɬɟɥɟɣ ɢɡ Ʉɋ ɢ ɈȻ (ɪɢɫ. 4). ɉɨɤɚɡɚɧɨ, ɱɬɨ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɶ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɤɚɞɪɭ ɢɡɨɛɪɚɠɟɧɢɹ (ɪɚɡɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪ ɞɥɹ ɰɟɧɬɪɚɥɶɧɨɝɨ (5–5) ɢ ɛɨɤɨɜɨɝɨ ɥɭɱɚ (1–1)) ɧɚ ɨɞɧɨɣ ɱɚɫɬɨɬɟ ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ ɤɜɚɪɰɟɜɨɝɨ ɫɬɟɤɥɚ ɫɨɫɬɚɜɥɹɟɬ GT|1,5K, ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ ɨɤɢɫɢ ɛɟɪɢɥɥɢɹ GT|13,5K . Ʉɪɢɜɵɟ ɞɥɹ ɛɨɤɨɜɨɝɨ ɥɭɱɚ (1–1) ɪɚɫɩɨɥɨɠɟɧɵ ɧɢɠɟ, ɱɟɦ ɞɥɹ ɰɟɧɬɪɚɥɶ- ɧɨɝɨ (5–5).

Ɉɰɟɧɟɧɨ ɜɥɢɹɧɢɟ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢ ɧɚɝɪɟɜɚ ɨɛɬɟɤɚɬɟɥɹ ɜɞɨɥɶ ɨɛɪɚɡɭɸɳɟɣ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɞɟɠ- ɧɨɫɬɢ ɦɟɫɬɨɨɩɪɟɞɟɥɟɧɢɹ ɪɚɞɢɨɦɟɬɪɢɱɟɫɤɢɦɢ ɫɢɫɬɟɦɚɦɢ ɧɚɜɢɝɚɰɢɢ. ɉɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɚɜɢɥɶɧɨɣ ɩɪɢɜɹɡɤɢ ɢɡɨɛɪɚɠɟɧɢɣ ɨɬ ɭɪɨɜɧɹ ɲɭɦɚ (ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɣ ɨɲɢɛɤɢ — ɋɄɈ) V ɜ ɢɡɨ-

ɚ) ɛ)

(11)

ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ

1. Ʉɚɩɥɭɧ ȼ.Ⱥ. Ⱥɧɬɟɧɧɵɟ ɪɚɞɢɨɩɪɨɡɪɚɱɧɵɟ ɨɛ- ɬɟɤɚɬɟɥɢ (ɷɬɚɩɵ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢ ɪɚɡɪɚɛɨɬɨɤ) //

Ɋɚɞɢɨɬɟɯɧɢɤɚ. 2002. ʋ 11. ɋ. 6–15.

2. Ʉɪɵɥɨɜ ȼ.ɉ. Ɇɟɬɨɞ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɩɪɨɮɢɥɢ- ɪɨɜɚɧɢɹ ɚɧɬɟɧɧɵɯ ɨɛɬɟɤɚɬɟɥɟɣ / ȼ. ɉ. Ʉɪɵɥɨɜ, ɂ. ȼ. ɉɨɞɨɥɶɯɨɜ, ȼ. Ƚ. Ɋɨɦɚɲɢɧ, Ⱥ. ɉ. ɒɚɞɪɢɧ // Ɋɚɞɢɨɬɟɯɧɢɤɚ. 2002. ʋ 11. ɋ. 20–24.

3. ȼɨɪɨɛɶɟɜ ȼ.Ⱥ. ɒɭɦɵ ɚɧɬɟɧɧɨɝɨ ɨɛɬɟɤɚɬɟɥɹ, ɩɨɞ- ɜɟɪɝɚɸɳɟɝɨɫɹ ɜɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɨɦɭ ɧɚɝɪɟɜɭ //

ɂɡɜ. ɜɭɡɨɜ. Ɋɚɞɢɨɷɥɟɤɬɪɨɧɢɤɚ. 1971. Ɍ. 1, ʋ 7.

ɋ. 839–840.

4. Ʉɚɥɚɲɧɢɤɨɜ ȼ.ɋ. ȼɥɢɹɧɢɟ ɲɭɦɨɜ ɚɧɬɟɧɧɨɝɨ ɨɛ- ɬɟɤɚɬɟɥɹ ɩɪɢ ɟɝɨ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɦ ɧɚɝɪɟɜɟ ɧɚ ɪɚɛɨɬɭ ɛɨɪɬɨɜɨɣ ɚɩɩɚɪɚɬɭɪɵ / ȼ.ɋ. Ʉɚɥɚɲɧɢɤɨɜ, ȼ.Ɏ. Ɇɢɯɚɣɥɨɜ // ɂɡɜ. ɜɭɡɨɜ. Ɋɚɞɢɨɷɥɟɤɬɪɨɧɢɤɚ.

1976. Ɍ. 19, ʋ 5. ɋ. 3–8.

5. Ɂɚɦɹɬɢɧ ȼ.ɂ. Ⱥɧɬɟɧɧɵɟ ɨɛɬɟɤɚɬɟɥɢ / ȼ.ɂ. Ɂɚɦɹ- ɬɢɧ, Ⱥ.ɋ. Ʉɥɸɱɧɢɤɨɜ, ȼ.ɂ. ɒɜɟɰ. Ɇɢɧɫɤ: ɂɡɞ- ɜɨ ȻȽɍ, 1980. 192 ɫ.

6. Rengarajan S.R. Gillespie. Asymptotic Approximations in Radome Analysis [Ɍɟɤɫɬ] / S.R.

Rengarajan, S. Edmond // IEEE Trans. Antenna Propagat. 1998. Vol. AP-36, No. 3. P. 635–644.

7. Yurchenko V.B. Numerical Optimization of a Cylindrical ReÀ ector-in-Radome Antenna System / V.B. Yurchenko, A. Ayhans, A.I. Nosich // IEEE Trans. Antenna Propagat. 1999. Vol. AP-47, No. 4.

P. 668–673.

8. Ⱥɧɬɸɮɟɟɜ ȼ.ɂ. ɉɪɢɦɟɧɟɧɢɟ ɩɪɢɧɰɢɩɨɜ ɪɚ- ɞɢɨɦɟɬɪɢɢ ɜ ɤɨɪɪɟɥɹɰɢɨɧɧɨ-ɷɤɫɬɪɟɦɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɧɚɜɢɝɚɰɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ:

Ɇɨɧɨɝɪɚɮɢɹ / ȼ.ɂ. Ⱥɧɬɸɮɟɟɜ, ȼ.ɇ. Ȼɵɤɨɜ, ɛɪɚɠɟɧɢɢ ɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɣ ɤɨɧɬɪɚɫɬɚ ɨɛɴɟɤɬ–ɮɨɧ 'T (ɪɢɫ. 5). Ɋɚɫɱɟɬɵ ɩɪɨɜɟɞɟɧɵ ɞɥɹ ɞɜɭɯ ɫɥɭ- ɱɚɟɜ: ɩɪɟɜɵɲɟɧɢɹ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɢɡɨɛɪɚɠɟɧɢɸ ɧɚɞ ɜɟɥɢɱɢɧɨɣ ɤɨɧɬɪɚɫɬɚ

4 13,5

T K GT K

' d ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ ɈȻ, ɜ ɬɨ ɠɟ ɜɪɟɦɹ ɞɥɹ ɫɥɭɱɚɹ ɩɪɟɜɵɲɟɧɢɹ ɤɨɧɬɪɚɫɬɚ ɧɚɞ ɧɟɪɚɜɧɨ- ɦɟɪɧɨɫɬɶɸ — ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ Ʉɋ GT 1,5Kd ' T 4K.

Ɋɢɫ. 5. Ɂɚɜɢɫɢɦɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɨɬ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɣ ɨɲɢɛɤɢ (ɋɄɈ) ɲɭɦɚ ɞɥɹ T' dGT ɢ T' tGT

ɍɜɟɥɢɱɟɧɢɟ ɜɟɥɢɱɢɧɵ ɤɨɧɬɪɚɫɬɚ, ɧɚɩɪɢɦɟɪ, ɞɨ ɡɧɚɱɟɧɢɣ GT 13,5Kd ' T 20K ɩɪɢɜɨɞɢɬ ɤ ɫɭɳɟɫɬɜɟɧ- ɧɨɦɭ ɩɨɜɵɲɟɧɢɸ ɜɟɪɨɹɬɧɨɫɬɢ ɦɟɫɬɨɨɩɪɟɞɟɥɟɧɢɹ (Pt0,9) ɞɥɹ ɨɛɨɢɯ ɬɢɩɨɜ ɦɚɬɟɪɢɚɥɨɜ ɨɛɬɟɤɚɬɟɥɹ.

Ⱦɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ Ʉɋ ɤɪɢɜɵɟ ɩɨɦɟɱɟɧɵ ɤɪɭɠɨɱɤɚɦɢ, ɞɥɹ ɨɛɬɟɤɚɬɟɥɹ ɢɡ ɈȻ — ɤɪɟɫɬɢɤɚɦɢ.

Ɂɚɤɥɸɱɟɧɢɟ

ȼ ɩɪɢɛɥɢɠɟɧɢɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɞɢɮɪɚɤɰɢɢ ɫ ɭɱɟɬɨɦ ɦɧɨɝɨɫɥɨɣɧɨɣ ɫɬɟɧɤɢ ɨɛɬɟɤɚɬɟɥɹ ɢ ɧɟ- ɪɚɜɧɨɦɟɪɧɨɝɨ ɟɝɨ ɧɚɝɪɟɜɚ ɩɨ ɬɨɥɳɢɧɟ ɢ ɜɞɨɥɶ ɨɛɪɚɡɭɸɳɟɣ, ɚ ɬɚɤɠɟ ɫ ɭɱɟɬɨɦ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɱɚɫɬɨɬɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɢɡɥɭɱɟɧɢɹ ɜ ɫɬɟɧɤɟ ɩɨɥɭɱɟɧɵ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɪɚɞɢɨɹɪɤɨɫɬɧɨɣ ɬɟɦɩɟɪɚɬɭ- ɪɵ ɩɚɪɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ», ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɹɸɬ ɨɰɟɧɢɬɶ ɜɥɢɹɧɢɟ ɲɭɦɨɜ ɨɛɬɟɤɚɬɟɥɹ ɧɚ ɮɨɪɦɢɪɨɜɚɧɢɟ ɬɟɤɭɳɟɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɦɚɬɪɢɱɧɨɣ ɪɚɞɢɨɦɟɬɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɧɚɜɢɝɚɰɢɢ. Ʉɨɥɢɱɟɫɬɜɟɧɧɵɟ ɨɰɟɧɤɢ ɩɨɤɚ- ɡɵɜɚɸɬ, ɱɬɨ ɩɪɢɦɟɧɟɧɢɟ ɞɚɧɧɨɝɨ ɦɟɬɨɞɚ ɪɚɫɱɟɬɚ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɜɵɫɢɬɶ ɬɨɱɧɨɫɬɶ ɪɚɫɱɟɬɚ ɲɭɦɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɫɢɫɬɟɦɵ «ɚɧɬɟɧɧɚ–ɨɛɬɟɤɚɬɟɥɶ» ɞɨ 2-ɯ ɪɚɡ, ɩɨɜɵɫɢɜ ɜɟɪɨɹɬɧɨɫɬɶ ɦɟɫɬɨɨɩɪɟɞɟɥɟɧɢɹ ɊɆ ɫɢ- ɫɬɟɦɵ ɧɚɜɢɝɚɰɢɢ, ɚ ɬɚɤɠɟ ɩɨɡɜɨɥɹɟɬ ɨɩɬɢɦɚɥɶɧɨ ɜɵɛɢɪɚɬɶ ɦɚɬɟɪɢɚɥ ɨɛɬɟɤɚɬɟɥɹ ɢ ɪɚɛɨɱɢɣ ɞɢɚɩɚɡɨɧ ɱɚɫɬɨɬ ɪɚɞɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɩɪɢɟɦɧɢɤɚ ɫɢɫɬɟɦɵ.

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Ⱥ.Ɇ. Ƚɪɢɱɚɧɸɤ, ȼ.Ⱥ. Ʉɪɚɸɲɤɢɧ, Ɋ.ɉ. Ƚɚɯɨɜ. Ɇ.:

Ɏɢɡɦɚɬɥɢɬ, 2009. 352 ɫ.

9. Ʌɟɜɢɧ Ɇ.Ʌ. Ɍɟɨɪɢɹ ɪɚɜɧɨɜɟɫɧɵɯ ɮɥɭɤɬɭɚɰɢɣ ɜ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɟ / Ɇ.Ʌ. Ʌɟɜɢɧ, ɋ.Ɇ. Ɋɵɬɨɜ. Ɇ.:

ɇɚɭɤɚ, 1967. 308 ɫ.

10. Ȼɪɟɯɨɜɫɤɢɯ Ʌ.Ɇ. ȼɨɥɧɵ ɜ ɫɥɨɢɫɬɵɯ ɫɪɟɞɚɯ. Ɇ.:

ɂɡɞ-ɜɨ Ⱥɤɚɞɟɦɢɢ ɧɚɭɤ ɋɋɋɊ, 1957. 503 ɫ.

11. Ⱦɭɛɪɨɜɢɧ Ȼ.Ⱥ. ɋɨɜɪɟɦɟɧɧɚɹ ɝɟɨɦɟɬɪɢɹ: Ɇɟɬɨɞɵ ɢ ɩɪɢɥɨɠɟɧɢɹ / Ȼ.Ⱥ. Ⱦɭɛɪɨɜɢɧ, ɋ.ɉ. ɇɨɜɢɤɨɜ, Ⱥ.Ɍ. Ɏɨɦɟɧɤɨ. Ɇ.: ɇɚɭɤɚ, 1979. 760 ɫ.

INFLUENCE OF NOISE TEMPERATURE OF ANTENNA RADOME ON IMAGE FORMED BY MATRIX RADIOMETRIC SYSTEMS

Antyufeev V.I., Bykov V.N., Ivanchenko D.D.

Radiotransparent radomes used in aircraft radiometric system during atmospheric À ight are exposed to heating.

This heating is irregular for depth of radome sidewall and for different point of radome guiding line. One needs to evaluate the inÀ uence of such irregular heating of radome which may be characterized by noise temperature on image formed by the matrix radiometric extreme-correlated aircraft navigation system placed on aircraft.

Based on geometrical optics approximation and analysis of radiation propagation through radome wall the formulas to determine of antenna–radome system temperature were developed. These formulas depend on frequency and takes into account interference of different frequency components of radiation in the radome wall.

Proposed method allows estimating the antenna–radome system temperature twice as accuracy. Therefore it may used to make an optimal choice of radome material and work frequency band of radiometric sensor system of aircraft navigation.