Slow variations in continuum mechanics

Publisher Summary This chapter describes the slow variations in continuum mechanics. The hydraulic approximation is a simple and useful idea, which as the quasicylindrical approximation has its counterpart in other branches of mechanics. The key to treating a slow variation is to rescale the coordinates in different directions so that the variation formally becomes normal. This transfers the perturbation parameter from the boundary conditions to the differential equations, which can accordingly be simplified by approximation. It is remarkable that this simplification also renders the approximate solution uniformly valid. The method of slow variations has been applied mostly to thin two-dimensional shapes in the plane, or slender axisymmetric ones in three dimensions.. It is found that axisymmetric problems of slow variation can be treated in exactly the same way as symmetric plane problems, and the results have a similar structure.