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Infinitesimal bending influence on the volume change. (English) Zbl 1335.53017
Summary: Applying tensor calculus we discuss change of the volume under infinitesimal bending of the surface. We obtain that the variation of the volume bounded by the surface \(s\) and the cone joining the origin to the boundary of the surface, under infinitesimal bending of \(s\) with the vector field of translation \(\mathbf s\), equals one third of the flux of the field \(\mathbf s\) through the given surface \(s\). An example is analysed and graphically presented. The paper points to the application of the obtained result in the calculation of the volume of a solid model.
MSC:
53A45 Differential geometric aspects in vector and tensor analysis
52B11 \(n\)-dimensional polytopes
74G60 Bifurcation and buckling
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