ABSTRACT
Helpful remarks It should be noted that both the plane, Eq. (7.41), and axially symmetric, Eq. (7.49), general solutions to problems contain, in accordance with a classical theory of ordinary differential equations, a pair of arbitrary constants C1 and C2. In both the plane and axial symmetric cases the function p(θ) gives a plane boundary curve. The only difference is that in the case of axial symmetry the boundary curve represents a certain axial cut. In order to determine uniquely the function p(θ) in Eq. (7.49) (as well as in Eq. (7.41) for the plane problem) for a concrete surface S, we need to assign two boundary (or initial) conditions. Usually such conditions are predetermined by a periodicity of the solution.
