Area of correct space coordination by normal conic coordinates-Reference-Cited by-同舟云学术

Area of correct space coordination by normal conic coordinates

Published:2023-12-26 Issue:3 Volume:11 Page:3-11
ISSN:2308-4898
Container-title:Geometry & Graphics
language:en
Short-container-title:

Author:

Nesnov Dmitriy¹¹

Affiliation:

1. Samara State Technical University

Abstract

The field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems is well studied. Field sources with more complex structures require new approaches to their study. The purpose of this study is to determine the correct coordination of space by normal conic coordinates. This is necessary in subsequent studies, the task of which will be to simplify the expressions for the characteristics of the field by introducing a special coordination of space, which reflect the shape of the source and/or sink of the field. For example, a field with a rectilinear source is more convenient to refer to cylindrical coordinates, and a field with a point source - to spherical coordinates. Basically, the use of field theory in the study of physical processes by methods of applied geometry is limited to two classical curvilinear systems, although their presentation in arbitrary curvilinear coordinates is known. We will distinguish between global and local coordinate systems. The global system, as well as the coordinates of a point in this system, will be denoted by x, y, z. She is unchanging. The local system, as well as the coordinates of a point in this system, will be denoted by t, u, v. Local system variable. At each point in space belonging to the area of existence of the system, the local coordinate system is defined

Publisher

Infra-M Academic Publishing House

Subject

General Medicine

Reference26 articles.

1. Бердинский В.А. Об ортогональных криволинейных системах координат в пространствах постоянной кривизны [Текст] / В.А. Бердинский, И.П. Рыбников // Сибирский математический журнал. Сибирское отделение РАН, Институт математики им. С.Л. Соболева СО РАН. – 2011 – Т. 52. – № 3 – С. 502-511., Berdynsky V.A., Rybnikov I.P. Ob ortogonal'nykh krivolineynykh sistemakh koordinat v prostranstvakh postoyannoy krivizny [On orthogonal curvilinear coordinate systems in spaces of constant curvature]. Sibirskiy matematicheskiy zhurnal. Sibirskoye otdeleniye RAN, Institut matematiki im. S.L. Soboleva SO RAN [Siberian Mathematical Journal. Siberian Department of the Russian Academy of Sciences, Institute of Mathematics named S.L. Sobolev SB RAS]. 2011, V. 52, I. 3, pp. 502-511. (in Russian)

2. Булах Е.Г. Основы векторного анализа и теории поля [Текст] / Е.Г. Буллах, В.Н. Шуман - Киев: Наукова думка, 1998. – 300 с., Bulakh E.G., Schuman V.N. Osnovy vektornogo analiza i teorii polya [Fundamentals of vector analysis and field theory]. Kiev, Naukova Dumka Publ., 1998. 300 p. (in Russian)

3. Гирш А.Г. Окружности на комплексной плоскости [Текст] / А. Г.Гирш // Геометрия и графика. – 2020. – Т. 8. – № 4. – С. 3-12. – DOI: 10.12737/2308-4898-2021-8-4-3-12., Girsh A.G. Okruzhnosti na kompleksnoy ploskosti [Circles in the complex plane]. Geometriya i grafika. [Geometry and graphics]. 2020, V. 8, I. 4, pp. 3-12. DOI: 10.12737/2308-4898-2021-8-4-3-12. (in Russian)

4. Гузев М.А. Вывод уравнений градиентной теории в криволинейных координатах [Текст] / М.А. Гузев, Q.I. Chengzhi // Дальневосточный математический журнал. Институт прикладной математики ДВО РАН, Дальневосточный федеральный. – 2013 – Т. 13. – № 1 – С. 35-42., Guzev M.A., Chengzhi Q.I. Vyvod uravneniy gradiyentnoy teorii v krivolineynykh koordinatakh [Derivation of gradient theory equations in curvilinear coordinates]. Dal'nevostochnyy matematicheskiy zhurnal. Institut prikladnoy matematiki DVO RAN [Far Eastern Mathematical Journal. Institute of Applied Mathematics of the Far Eastern Federal District of the Russian Academy of Sciences]. 2013, V. 13, I. 1, pp. 35-42. (in Russian)

5. Ефремов А.В. Пространственные геометрические ячейки – квазимногогранники [Текст] / А.В. Ефремов, Т.А. Верещагина, Н.С. Кадыкова, В.В. Рустамян // Геометрия и графика. – 2021. – Т. 9. – № 3. – С. 30-38. – DOI: 10.12737/2308-4898-2021-9-3-30-38., Efremov A.V., Vereshchagina T.A., Kadykova N.S., Rustamyan V.V. Prostranstvennyye geometricheskiye yacheyki – kvazimnogogranniki [Spatial geometric sells – quasipolyhedra]. Geometriya i grafika. [Geometry and graphics]. 2021, V. 9, I. 3, pp. 30-38. DOI: 10.12737/2308-4898-2021-9-3-30-38. (in Russian)