The Newtonian potential of a homogeneous cube

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1976 English Publisher:Springer Science and Business Media LLCJournal:Zeitschrift für angewandte Mathematik und Physik ZAMP, volume 27, pages 867-871 (issn: 0044-2275, eissn: 1420-9039,

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Authors: Waldvogel, Jörg;

doi: 10.1007/bf01595137

The Newtonian potential of a homogeneous cube

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Abstract

Closed form expressions for the Newtonian force field and the Newtonian potential of a homogeneous rectangular parallelepiped were given by MacMillan (1930). Here a new concise derivation by means of multiple summations is presented. Each component of the force is written as a sum of 24 terms involving Artanh and arctan functions, whereas the expression for the potential consists of 48 terms. As a new application, the self-energy is represented in closed form, too.

Related Organizations

ETH Zurich
Switzerland
École Polytechnique Fédérale de Lausanne EPFL
Switzerland

Keywords

Integral representations, integral operators, integral equations methods in higher dimensions, Applications to the sciences

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