Hi,
Strong and weak forms are fundamental in theory of FEM. I read many books discussing governing equations and conservation of linear momentum in Cartesian coordinates. However have you seen anywhere a book or an article dealing with strong and weak forms in polar and spherical coordinates? If you have encountered such things, please share it.
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Re: Conservation of momentum in polar coordinates
If you know the weak form in coordinate-free notation, you can use the definitions of gradient and divergence in arbitrary curvlinear coordinates systems to generate the equations you need. I had shown some of these expressions for cylindrical polar cordinates at http://en.wikipedia.org/wiki/Tensors_in_curvilinear_coordinates some time ago (but you will have to recheck these for correctness because of Wikipedia entropy).
-- Biswajit