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MODEL FOR DETERMINING OF BODY POTENTIAL
Abstract
The task of determining the potential of the field u ( x) of a bodyG , which is limited in space 3 R , is important and well known for solving both theoretical and applied problems of geodesy. The traditional approach to its solution, based on the representation of the potential in the form of series of spherical functions, has well-known advantages and disadvantages. This article discusses another model for solving the original problem in the form of an integro-differential equation u ( x) = K?u ( x), x?G , where K is an integral operator with a symmetric polar core, defined in a bounded domain 3 G?R with boundary S of class 2 C . In the focus of the article is on justifying the suitability of the model for solving the problem and analyzing the conditions for the existence of a solution to the considered equation. Based on the known methods of mathematical physics, in particular, the method of potentials and integral Green formulas, necessary and sufficient conditions for the existence of a solution of this equation are obtained. The results are presented in the form of a theorem on the criterion for the existence of a solution for the problem. It is shown that the solution u ( x) of the equation coincides with the potential of the field of the body G under consideration in the whole space.
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References5
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