Does anyone know of a valid reference highlighting the proof of the divergence theorem in a strictly coordinate invariant tensor framework? Kellogg is probably the most frequently sited source, however, I find it very difficult to follow for a general region. It relies heavily on lots of geometric constructs which leaves me desiring a more elegant proof. The usage for the proof is for continuum mechanics self study. Thanks.
Dear Courtney, the proof in general coordinates is in the this text. Gianluca
Aldo Bressan, Relativistic Theory of Materials, 1978
Hi Courtney,
I prefer, however, the geometrical approach because it provides the most natural setting of continuum mechanics (a continuous material body is in fact a manifold). Try, for example,
R. Abraham, J. E. Marsden, and T. Ratiu. Manifolds, Tensor Analysis, and Applications. Addison-Wesley, Reading, Massachusetts, 1983
J. E. Marsden and T. J. R. Hughes. Mathematical Foundations of Elasticity. Dover Publications, New York, 1994
G. Romano and R. Baretta. Continuum mechanics on manifolds. Lecture notes, Department of Structural Engineering, University of Naples Federico II, Italy, 2009. http://wpage.unina.it/romano/
Regards
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