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Notes on Metric Independent Analysis of Classical Fields
Author(s) -
Segev Reuven
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2610
Subject(s) - mathematics , differential form , differentiable function , invariant (physics) , metric space , mathematical analysis , traction (geology) , cauchy distribution , pure mathematics , mathematical physics , geomorphology , geology
A metric independent geometric framework for some fundamental objects of continuum mechanics is presented. In the geometric setting of general differentiable manifolds, balance principles for extensive properties are formulated and Cauchy's theorem for fluxes is proved. Fluxes in an n ‐dimensional space are represented as differential ( n − 1)‐forms. In an analogous formulation of stress theory, a distinction is made between the traction stress, enabling the evaluation of the traction on the boundaries of the various regions, and the variational stress, which acts on the derivative of a virtual velocity field to produce the virtual power density. The relation between the two stress fields is examined as well as the resulting differential balance law. As an application, metric‐invariant aspects of electromagnetic theory are presented within the framework of the foregoing flux and stress theory. Copyright © 2012 John Wiley & Sons, Ltd.