The Field of Attraction of a Polyhedron and Polygonal Plate with Linear Density

Abstract

New representations of the elements of the fields of attraction (potential and its first derivatives) are presented for the important approximating models such as polyhedron and polygonal plates with the density varying by the linear law. It is shown that these elements are determined through the elements of the fields from the models with the known analytical representations (polyhedron, polygonal plate, and material segment with constant densities) and the additional integrals for which the explicit analytical expressions exist.