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The problems of the mathematical modeling of electrostatic fields in short-range location systems


S.P. Klepka, A.E. Lastovetskiy, G.L. Pavlov

In recent decades, a great progress is achieved the theory and technique of electrostatic fields for problems of short-range aerodynamic marks location. In the development and simulation of short-range electrostatic location systems, accurate and reliable calculation of the electrostatic sensor signals. This problem is essentially reduced to finding the distribution of induced electric charge on the surface of a metallic conductor in an external electrostatic field. Therefore, the actual problem is the improvement of tools calculating electrostatic fields in the presence of conductive metal bodies. One of the most effective methods for calculating electrostatic fields in a linear piecewise-homogeneous media is the method of boundary integral equations. For surfaces with conductive bodies the parameter of the Fredholm integral equation of the 2nd kind  is unity. In the theory of integral equations it is proved that the kernel for the plane problem has an proper number equal to unity. Therefore, the Fredholm determinant of the resulting integral equation is zero and, consequently, this equation is unstable. To understand the causes of emerging computational problems it is expedient to use the results and methods of potential theory. Conducted analysis shows that improvement of the computational stability of the plane model can be made by using the spatial properties. For this purpose, as the calculation we take the classical plane-parallel model of the body in the form of a cylinder of limited length, and obtain an expression for the kernel quasi-spatial model. The stability of the integral equation is proved analytically and confirmed by numerical experiments.

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