An analytic representation for the potential of a uniform elliptic cone

Citation
Va. Antonov et As. Baranov, An analytic representation for the potential of a uniform elliptic cone, TECH PHYS, 46(10), 2001, pp. 1213-1217
Citations number
7
Categorie Soggetti
Apllied Physucs/Condensed Matter/Materiales Science
Journal title
TECHNICAL PHYSICS
ISSN journal
10637842 → ACNP
Volume
46
Issue
10
Year of publication
2001
Pages
1213 - 1217
Database
ISI
SICI code
1063-7842(200110)46:10<1213:AARFTP>2.0.ZU;2-B
Abstract
In view of the fact that various gravitating and charged bodies may have si ngular points on their surface, the problem of the effect of these singular ities in the mass distribution on the behavior of potential arises. The ana lytic representation for gravitational and electrostatic potentials of a un iform elliptic cone in terms of ordinary integrals is derived. Generally, t hese integrals are somewhat more complicated than the elliptic ones; howeve r, they reduce to elementary functions in the case of a circular cone. The arbitrariness in the way of truncating a cone manifests itself in the possi bility of adding various harmonic polynomials. However, the singularity of potential in the vicinity of the vertex of a cone is of an objective and un ique character. (C) 2001 MAIK "Nauka/Interperiodica".