SCOPE OF FIELD THEORY IN NORMAL CONIC COORDINATES
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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.
Subject of research. The field of definition of elements of field theory in conic coordinates.
Materials and methods: The main basis of the work is the study of the general field theory in curvilinear coordinates. The main research methods are analytical with the involvement of graphical methods.
Results: The paper describes for the first time the variants of the correct coordination of space when using the normal conic coordinate system. An example is given on the basis of which the mathematical apparatus for visualizing the simulated moles is considered.
Conclusions: the dependence functions of rectangular Cartesian coordinates on normal conical coordinates for both cavities of the determinant cone are obtained.
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References
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