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Applications of Potential Theoretic Mother Bodies in Electrostatics
Department of Mathematics, Kansas State University, Manhattan, USA
- 1 Department of Mathematics, Kansas State University, Manhattan, USA
American Journal of Computational Mathematics·Volume 07 (2017)·Pages 481–494·Published 26 October 2017·DOI10.4236/ajcm.2017.74035
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Abstract
Any polyhedron accommodates a type of potential theoretic skeleton called a mother body. The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov [1] and developed by Björn Gustafson and Makoto Sakai [2] . In this paper, we attempt to apply the brilliant idea of mother body to Electrostatics to compute the potentials of electric fields.
KeywordsNewtonian KernelPotentialMother BodyConvex PolyhedronGeometryGeophysicsElectrostatics
- Zidarov, D. (1968) On Solution of Some Inverse Problems for Potential Fields and Its Application to Questions in Geophysics. Publishing House of Bulgarian Academy of Sciences, Sofia (Russian).
- Gustafsson, B. and Sakai, M. (1999) On Potential Theoretic Skeletons of Polyhedra. Geometriae Dedicata, 76, 1-30. https://doi.org/10.1023/A:1005184009159
- Gustafsson, B. (1998) On Mother Bodies of Convex Polyhedra. SIAM Journal on Mathematical Analysis, 29, 1106-1117. https://doi.org/10.1137/S0036141097317918
- Felkel, P. and Obdrzalek, S. (1998) Straight Skeleton Implementation. In Proceedings of Spring Conference on Computer Graphics, Budmerice, 1998, 210-218.
- Savina, T.V., Sternin, B.Y. and Shatalov, V.E. (2005) On a Minimal Element for a Family of Bodies Producing the Same External Gravitational Field. Applicable Analysis, 84, 649-668. https://doi.org/10.1080/00036810500078845
- Griffiths, D.J. (1962) Introduction to Electrodynamics. Prentice Hall, Upper Saddle River, 609.
- Kibble, T.W. and Berkshire, F.H. (2004) Classical Mechanics. World Scientific Publishing Company, Singapore. https://doi.org/10.1142/p310
- Young, H.D. (2008) Sears and Zemansky’s University Physics (Vol. 1). Pearson Education, London.