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Volume 25, Sofia, 2013 Space Research and Technology Institute Bulgarian Academy of Sciences Volume 25, Sofia, 2013 Space Research and Technology Institute Bulgarian Academy of Sciences Editorial Board Prof. Garo Mardirossian (Editor-in-Chief) Chief Assistant Lyudmila Todorieva (English Language Editor) Tsveta Srebrova, MS (Technical Editor) Acad. Valeri Bondour – Russia Prof. Gerassimos Papadopoulos – Greece Prof. Stefano Tinti – Italy Prof. Rupert Gertzer – Germany Corr. Member Filip Filipov Corr. Member Petar Velinov Prof. Petar Getsov Prof. Petko Nenovski Prof. Eugenia Roumenina Assoc. Prof. Tania Ivanova Assoc. Prof. Lachezar Filipov Assoc. Prof. Stefan Chapkunov Assoc. Prof. Dimitar Teodossiev Address AEROSPACE RESEARCH IN BULGARIA Space Research and Technology Institute bl. 1, Acad. G. Bonchev St., Sofia 1113, Bulgaria e-mail: [email protected] Pre-Publication Processing Tsveta Srebrova © Space Research and Technology Institute – Bulgarian Academy of Sciences ISSN 1313 – 0927 Bulgarian Academy of Sciences ISSN 1313 – 0927 Aerospace Research in Bulgaria 25 Sofia, 2013 C o n t e n t s 1. Dimitar Dimitrov ANALYTICAL COMPUTATION OF TWO INTEGRALS, APPEARING IN THE THEORY OF ELLIPTICAL ACCRETION DISCS. I. SOLVING OF THE AUXILIARY INTEGRALS, EMERGING DURING THEIR DERIVATIONS. 5 2. Dimitar Dimitrov ANALYTICAL COMPUTATION OF TWO INTEGRALS, APPEARING IN THE THEORY OF ELLIPTICAL ACCRETION DISCS. II. SOLVING OF SOME AUXILIARY INTEGRALS, CONTAINING LOGARITHMIC FUNCTIONS INTO THEIR INTEGRANDS. .35 3. Peter Velinov, Simeon Asenovski, Lachezar Mateev, Eduard Vashenyuk, Aleksander Mishev INVESTIGATION OF MIDDLE ATMOSPHERE IONIZATION DURING GLE 70 EVENT FROM DECEMBER 2006 BY MEANS OF CORIMIA MODEL AND NORMALIZED CR SPECTRA. .62 4. Maria Abunina, Anatoly Abunin, Anatoly Belov, Sergey Gaidash, Yordan Tassev, Peter Velinov, Lachezar Mateev, Peter Tonev GEOEFFECTIVITY OF SOLAR CORONAL HOLES WITH DIFFERENT MAGNETIC FIELD POLARITY. 70 5. Tsvetan Dachev, Nikolay Bankov, Borislav Tomov, Yury Matviichuk, Plamen Dimitrov SPACE RADIATION PECULIARITIES IN THE EXTRA VEHICULAR ENVIRONMENT OF THE INTERNATIONAL SPACE STATION (ISS). 78 6. Tsvetan Dachev, Borislav Tomov, Yury Matviichuk, Plamen Dimitrov, Nikolay Bankov, Vladislav Petrov, Viacheslav Shurshakov, Olga Ivanova, Donat-Peter Häder, Michael Lebert, Martin Schuster, Günter Reitz, Gerda Horneck, Ondrej Ploc PRELIMINARY RESULTS FOR THE RADIATION ENVIRONMENT OBSERVED BY RD3-B3 RADIOMETER-DOSIMETER INSIDE BION- M № 1 SPACECRAFT. .109 7. Tatjana Zenchenko, Malina Jordanova, Lilia Poskotinova, Anna Medvedeva, Todor Uzunov, Alexandra Alenikova, Tamara Breus SYNCHRONIZATION OF HEART RATES AND GEOMAGNETIC FIELD VARIATIONS: A PILOT STUDY. 125 8. Lachezar Filchev DETECTION AND ASSESSMENT OF ABIOTIC STRESS OF CONIFEROUS LANDSCAPES CAUSED BY URANIUM MINING (USING HYPERSPECTRAL EO-1/HYPERION DATA). .138 9. Vassil Vassilev CROP INVESTIGATION USING HIGH-RESOLUTION WORLDVIEW-1 AND QUICKBIRD-2 SATELLITE IMAGES ON A TEST SITE IN BULGARIA. 154 10. Vassil Vassilev CROP MONITORING USING SPOT-VGT NDVIs S10 TIME-SERIES PRODUCT FOR THE ARABLE LAND OF BULGARIA. 172 11. Vanya Naydenova, Stefan Stamenov LANDFORM CLASSIFICATION USING ASTER GDEM AND OPTICAL HIGH RESOLUTION SATELLITE IMAGES OF SOFIA CITY DISTRICT. .183 12. Maria Dimitrova, Iva Ivanova, Mariana Zaharinova, Roumen Nedkov APPLICATION OF AEROSPACE METHODS FOR MONITORING OF FOREST FIRES AND EVALUATION OF BURNED AREA IN HASKOVO REGION IN THE SUMMER OF 2011. 194 13. Peter Getzov, Zoia Hubenova, Dimitar Yordanov, Wiliam Popov MODELING OF THE HUMAN – OPERATOR IN A COMPLEX SYSTEM FUNCTIONING UNDER EXTREME CONDITIONS. 206 14. Peter Petkov, Еlisaveta Аlexandrova NEW CONSTRUCTION KU-BAND ANTENNA WITH IMPROVED RADIATION DIAGRAM FOR SATELLITE BROADCASTING RECEIVING EARTH STATION. .228 15. Zhivko Zhelezov, Rоumen Nedkov, Dimitar Teodosiev, Maria Bivolarska, Neven Georgiev, Ivo Lilov, Georgi Chamov, Spaska Yaneva FUNCTIONAL TESTING OF THE CAMERA WITH ACTUATOR FOR THE EXPERIMENTAL DETERMINATION OF THE POLARIZATION OF LIGHT BY MEASURING THE STOKES PARAMETERS. ..239 In memoriam 80TH ANNIVERSARY OF THE BIRTH AND 10TH DEATH ANNIVERSARY OF ACAD. DIMITAR MISHEV. .254 С Ъ Д Ъ Р Ж А Н И Е 1. Димитър Димитров АНАЛИТИЧНО ПРЕСМЯТАНЕ НА ДВА ИНТЕГРАЛА, ВЪЗНИКВАЩИ В ТЕОРИЯТА НА ЕЛИПТИЧНИТЕ АКРЕЦИОННИ ДИСКОВЕ. I. РЕШАВАНЕ НА СПОМАГАТЕЛНИТЕ ИНТЕГРАЛИ, ПОЯВЯВАЩИ СЕ ПРИ ТЯХНОТО ИЗЧИСЛЯВАНЕ. 5 2. Димитър Димитров АНАЛИТИЧНО ПРЕСМЯТАНЕ НА ДВА ИНТЕГРАЛА, ВЪЗНИКВАЩИ В ТЕОРИЯТА НА ЕЛИПТИЧНИТЕ АКРЕЦИОННИ ДИСКОВЕ. II. РЕШАВАНЕ НА НЯКОИ СПОМАГАТЕЛНИТЕ ИНТЕГРАЛИ, СЪДЪРЖАЩИ ЛОГАРИТМИЧНИ ФУНКЦИИ В СВОИТЕ ИНТЕГРАНДИ. 35 3. Петър Велинов, Симеон Асеновски, Лъчезар Матеев, Едуард Вашинюк, Александър Мишев ИЗСЛЕДВАНЕ НА ЙОНИЗАЦИЯТА В СРЕДНАТА АТМОСФЕРА ПО ВРЕМЕ НА СЪБИТИЕТО GLE 70 ОТ ДЕКЕМВРИ 2006 ПОСРЕДСТВОМ МОДЕЛА CORIMIA И НОРМАЛИЗИРАНЕ НА СПЕКТЪРА НА КОСМИЧЕСКИТЕ ЛЪЧИ. .62 4. Мария Абунина, Анатолий Абунин, Анатолий Белов, Сергей Гайдаш, Йордан Тасев, Петър Велинов, Лъчезар Матеев, Петър Тонев ГЕОЭФФЕКТИВНОСТЬ СОЛНЕЧНЫХ КОРОНАЛЬНЫХ ДЫР С РАЗЛИЧНОЙ ПОЛЯРНОСТЬЮ МАГНИТНОГО ПОЛЯ. 70 5. Цветан Дачев, Николай Банков, Борислав Томов, Юрий Матвийчук, Пламен Димитров ОСОБЕНОСТИ НА КОСМИЧЕСКАТА РАДИАЦИЯ В ОБКРЪЖАВАЩОТО ПРОСТРАНСТВО НА МЕЖДУНАРОДНАТА КОСМИЧЕСКА СТАНЦИЯ (МКС). 78 6. Цветан Дачев, Борислав Томов, Юрий Матвийчук, Пламен Димитров, Николай Банков, Владислав Петров, Вячеслав Шуршаков, Олга Иванова, Донат-Петер Хедър, Михаел Леберт, Мартин Шустер, Гюнтер Райтц, Герда Хорнек, Ондреж Плоц ПРЕДВАРИТЕЛНИ РЕЗУЛТАТИ ЗА РАДИАЦИОННАТА ОБСТАНОВКА НАБЛЮДАВАНА С ДОЗИМЕТЪРА-РАДИОМЕТЪРА RD3-B3 НА СПЪТНИКА BION-M № 1. .109 7. Татяна Зенченко, Малина Йорданова, Лилия Поскотинова, Анна Медведева, Тодор Узунов, Александра Аленкова, Тамара Бреус СИНХРОНИЗАЦИЯ НА ВАРИАБИЛНОСТИТЕ НА СЪРДЕЧНИЯ РИТЪМ И ГЕОМАГНИТНОТО ПОЛЕ: ПИЛОТНО ПРОУЧВАНЕ. 125 8. Лъчезар Филчев ОТКРИВАНЕ И ОЦЕНКА НА АБИОТИЧЕН СТРЕС, ПРИЧИНЕН ОТ УРАНОДОБИВ, В ИГЛОЛИСТНИ ЛАНДШАФТИ (С ИЗПОЛЗВАНЕ НА СПЪТНИКОВИ СПЕКТРОМЕТРИЧНИ ДАННИ ОТ EO-1/HYPERION). 138 9. Васил Василев АНАЛИЗ НА ЗЕМЕДЕЛСКИТЕ КУЛТУРИ ПО СПЪТНИКОВИ ИЗОБРАЖЕНИЯ СЪС СВРЪХ-ВИСОКА ПРОСТРАНСТВЕНА РАЗДЕЛИТЕЛНА СПОСОБНОСТ ОТ WORLDVIEW-1 И QUICKBIRD-2 ЗА ТЕСТОВИ УЧАСТЪК НА ТЕРИТОРИЯТА НА БЪЛГАРИЯ. .154 10. Васил Василев МОНИТОРИНГ НА ЗЕМЕДЕЛСКИТЕ КУЛТУРИ ПО ВРЕМЕВИ СЕРИИ ОТ ВЕГЕТАЦИОНЕН ПРОДУКТ SPOT-VGT NDVIs S10 ВЪРХУ ОБРАБОТВАЕМАТА ТЕРИТОРИЯ НА Р. БЪЛГАРИЯ. .172 11. Ваня Найденова, Стефан Стаменов КЛАСИФИКАЦИЯ НА ФОРМИТЕ НА ЗЕМНАТА ПОВЪРХНОСТ С ИЗПОЛЗВАНЕ НА ЦИФРОВ МОДЕЛ НА РЕЛЕФА ASTER GDEM И САТЕЛИТНИ ИЗОБРАЖЕНИЯ С ВИСОКА ПРОСТРАНСТВЕНА РАЗДЕЛИТЕЛНА СПСОБНОСТ ЗА РАЙОНА НА ОБЛАСТ СОФИЯ ГРАД. .183 12. Мария Димитрова, Ива Иванова, Мариана Захаринова, Румен Недков ПРИЛОЖЕНИЕ НА АЕРОКОСМИЧЕСКИТЕ МЕТОДИ ЗА ПРОСЛЕДЯВАНЕ НА ГОРСКИ И ПОЛСКИ ПОЖАРИ И ОЦЕНКА НА ИЗГОРЕЛИТЕ ПЛОЩИ В ОБЛАСТ ХАСКОВО ПРЕЗ ЛЯТОТО НА 2011 г. .194 13. Петър Гецов, Зоя Хубенова, Димитър Йорданов, Вилям Попов МОДЕЛИРАНЕ НА ЧОВЕКА – ОПЕРАТОР В СЛОЖНА СИСТЕМА, ФУНКЦИОНИРАЩА В ЕКСТРЕМНИ УСЛОВИЯ. 206 14. Петър Петков, Елисавета Александрова НОВА КОНСТРУКЦИЯ НА АНТЕНА ЗА ПРИЕМНА СТАНЦИЯ ЗА СПЪТНИКОВО ТЕЛЕВИЗИОННО РАЗПРЪСКВАНЕ В KU-ОБХВАТА С ПОДОБРЕНА ДИАГРАМА НА ИЗЛЪЧВАНЕ. .228 15. Живко Железов, Румен Недков, Димитър Теодосиев, Мария Биволарска, Невен Георгиев, Иво Лилов, Георги Чамов, Спаска Янева ФУНКЦИОНАЛНО ТЕСТВАНЕ НА КАМЕРА СЪС ЗАДВИЖВАНЕ ЗА ЕКСПЕРИМЕНТАЛНО ОПРЕДЕЛЯНЕ НА ПОЛЯРИЗАЦИЯТА НА СВЕТЛИНАТА ЧРЕЗ ИЗМЕРВАНЕ НА ПАРАМЕТРИТЕ НА СТОКС. .239 In memoriam 80 ГОДИНИ ОТ РОЖДЕНИЕТО И 10 ГОДИНИ ОТ СМЪРТТА НА АКАД. ДИМИТЪР МИШЕВ. 254 Bulgarian Academy of Sciences. Space Research and Technology Institute. Aerospace Research in Bulgaria. 25, 2013, Sofia ANALYTICAL COMPUTATION OF TWO INTEGRALS, APPEARING IN THE THEORY OF ELLIPTICAL ACCRETION DISCS. I. SOLVING OF THE AUXILIARY INTEGRALS, EMERGING DURING THEIR DERIVATIONS Dimitar Dimitrov Space Research and Technology Institute – Bulgarian Academy of Sciences e-mail: [email protected] Abstract The present work is a part of an extended analytical investigation of the dynamical equation, determining the spatial structure of the stationary elliptical accretion discs, according to the model of Lyubarskij et al. [1]. In the mathematical description of the problem are used as parameters the eccentricity e(u) of the particle orbits, and its derivative ė(u) ≡ de(u)/du ,where u ≡ ln(p), and p is the focal parameter of the considered orbit. During the process of simplification of that equation, there arises 2π the necessity of analytical evaluations of integrals of the following types: Ai(e, ė) ≡ ∫(1 + +ecosφ) – idφ, 0 2π 2π – 1 – k – k (i = 1,…,5), Jk(e, ė) ≡ ∫(1 + ecosφ) [1 + (e – ė)cosφ] dφ and Hk(e, ė) ≡ ∫(1 + ecosφ) × 0 0 ×[1 + (e – ė)cosφ] – 1dφ, (k = 1,…,4). In these formulas φ is the azimuthal angle, over which the averaging is taken. The approach in solving of the task is, in fact, recursive. At first, we evaluate the integrals with the smallest i and k (i.e., i and k equal to unity). After then, we go to the next steps, gradually increasing the integer powers i or k, until achieving the designated values 5 or 4, correspondingly. A special attention is devoted to these values of e(u) and ė(u) (and their difference e(u) - ė(u) ), which, eventually, may cause divergences in the intermediate or the final expressions. It is shown that although such troubles arise, they can be overcome by means of a direct substitution of the “peculiar” values of e(u) and/or ė(u) into the integrals, and after then performing the calculations. Even if the denominators in the final results appear factors equal to zero (due to the nullifications of e(u), ė(u) or e(u) – ė(u) ), the expressions are not
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