Infinitesimal Rotary Deformations of Surfaces and Their Application to the Theory of Elastic Shells

Abstract

We present a variational generalization of the problem of infinitesimal geodesic deformations of surfaces in the Euclidean space E ³. By virtue of rotary deformation, the image of every geodesic curve is an isoperimetric extremal of rotation (in the principal approximation). The results are associated in detail with rotary-conformal deformations. The application of these results to the mechanics of elastic shells is given.