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Review of Rational Electrodynamics: Deformation and Force Models for Polarizable and Magnetizable Matter

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Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 334))

Abstract

In this paper a rational derivation of Maxwell’s equations is presented in a purely spatial description. On a macroscopic scale this can be done by means of localization of global balance laws. The mathematical tools for the localization in a spatial description are presented. Subsequently the balance laws of electric charge and magnetic flux are discussed and localized in order to obtain Maxwell’s equations. Furthermore, short historical remarks on the origin of the governing laws in mechanics are presented. In order to illustrate the coupling of electrodynamics in matter to mechanics, two exemplary problems are analyzed. The procedure and the arising difficulties are discussed.

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Authors and Affiliations

  1. Institute of Mechanics, Chair of Continuum Mechanics and Constitutive Theory, Technische Universität Berlin, Einsteinufer 5, 10587, Berlin, Germany

    Wilhelm Rickert & Wolfgang H. Müller

Authors
  1. Wilhelm Rickert
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  2. Wolfgang H. Müller
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Correspondence to Wilhelm Rickert .

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Editors and Affiliations

  1. I.Vekua Institute of Applied Mathematics & Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    George Jaiani

  2. Georgian Technical University, Tbilisi, Georgia

    David Natroshvili

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Rickert, W., Müller, W.H. (2020). Review of Rational Electrodynamics: Deformation and Force Models for Polarizable and Magnetizable Matter. In: Jaiani, G., Natroshvili, D. (eds) Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019. Springer Proceedings in Mathematics & Statistics, vol 334. Springer, Cham. https://doi.org/10.1007/978-3-030-56356-1_15

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