NAU Harvester System
Research of structure of coefficients’ representation of the potential by everywhere convergent series
Наукові журнали Національного Авіаційного Університету
View Archive Info| Field | Value | |
| Title |
Research of structure of coefficients’ representation of the potential by everywhere convergent series
Исследование структуры коэффициентов представления потенциала всюду сходящимися рядами Дослiдження структури коефiцiєнтiв представлення потенцiалу всюди збiжними рядами |
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| Creator |
Фис, М. М.; Нацiональний унiверситет «Львiвська полiтехнiка», 79013, м. Львiв, вул. Карпiнського, 6
Бридун, А. М.; Нацiональний унiверситет «Львiвська полiтехнiка», 79013, м. Львiв, вул. Карпiнського, 6 Согор, А. Р.; Нацiональний унiверситет «Львiвська полiтехнiка», 79013, м. Львiв, вул. Карпiнського, 6 |
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| Subject |
potential; continuous function; everywhere convergent series; Earth’s gravitational field
521.82 потенциал; непрерывная функция; всюду сходящийся ряд; гравитационное поле Земли 521.82 потенцiал; неперервна функцiя; всюди збiжний ряд; гравiтацiйне поле Землi 521.82 |
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| Description |
This paper offers the representation of the potential of planets by a sequence of non-harmonic continuous functions, whichare determined by direct resolve of the inversion radius in the binomial series. The coefficients of such interpretation are, in essence, the quantities determined by the body’s shape and its filling, generating the potential by the massesand, the refore, taking into account their features. In connection with this, there is a need to study the nature ofthese quantities (for example, the possible connection with the parameters of the external gravitational field) and to develop methods and means for their determination. There are introduced algorithms for finding these elements of suchrepresentation, investigated the character and structure, connected with the harmony in the middle of a bulk body, whatallows to find the coefficients of the resolve of series by means of linear combinations of parameters of the externalgravitational field of the celestial body (Stokes constant), which is confirmed by arithmetical experiment on a concreteexample. On the contrary, according to the known values for the elements in this representation, it is possible todetermine Stokes permanent gravitational fields of planetary bodies. This, in turn, allows us to determine the value ofthe potential of the force of attraction (gravity, if we take into account the rotating component) throughout the space, including at points that are close to the surface or are on it. Obviously, the advantage of this approach consists inthe computational aspect, since such images are not harmonic functions of the external generating body, and the reforethe proposed approximation should be considered as an approximation of the continuous function. But, given the slowconvergence (or even difference) of approaching ball functions in areas close to the surface, such an approach can beconsidered as an additional tool (or even alternative) when studying the representation of a gravitational field by classicalmethods (for example, by means of ball functions). Also the recording of the attraction potential using binomial seriescan be considered as its analytic continuation in the middle of the generating body with the corresponding distribution ofmasses and used in the interpretation of planetary geodynamic processes, which consist precisely in the proposed areas.
Рассмотрены изображения потенциала планеты с помощью непрерывных функций. Исследована структура элементов разложения и возможность их определения. Гармоничность коэффициентов ряда обеспечивает их представление через параметры гравитационного поля и наоборот. Это позволяет находить значения потенциала как непрерывной функции во всем пространстве. Розглянуто представлення потенцiалу планети за допомогою неперервних функцiй. Дослiджена структура елементiв розкладу та можливiсть їх визначення. Гармонiчнiсть коефiцiєнтiв ряду забезпечує їхнє представлення через параметри гравiтацiйного поля та навпаки. Це дозволяє знаходити значення потенцiалу як неперервної функцiї у всьому просторi. |
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| Publisher |
National Aviation University
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| Contributor |
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| Date |
2018-11-22
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| Format |
application/pdf
application/pdf application/pdf |
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| Identifier |
http://jrnl.nau.edu.ua/index.php/ASTRO/article/view/13104
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| Source |
Вісник Астрономічної школи; Том 13, № 1 (2017); 1-4
Astronomical School’s Report; Том 13, № 1 (2017); 1-4 Вестник Астрономической Школы; Том 13, № 1 (2017); 1-4 |
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| Language |
uk
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