Applied Physics and Mathematics Annotation << Back Conformal Mapping Method and Rotationally-symmetric Сoordinates (Boundary Problems of Electrostatics) A.V. Kukushkin The basics are discussed of the invariant method of the curvilinear orthogonal coordinate systems constructing in 3D space by making use of the complex variable theory and conformal plane-to-plane mapping followed by revolving the resulting complex plane about its real and imaginary axes. The method is formulated as general for the case of the coordinate surfaces being axisymmetric. It is shown that the list of successfully soluble problems of analytical geometry with the task of finding the mathematical description of three-dimensional solids with symmetry of rotation can be significantly widened by means of revolving complex membranes containing n-sheeted coordinate functions of complex variable. The method is being tested with electrostatics boundary problems with extremely strict boundary conditions – the Neumann and Dirichlet problems – for solids with rotation symmetry. It is demonstrated that making use of the complex variable theory for solving such problems is restricted to the bodies created by rotating a conic section figure about its symmetry axis. The unified formula is suggested for electrostatic fields generating around the charged perfectly conducting oblong and oblate ellipsoids of revolution, sphere, hyperboloid of revolution of two nappes, and paraboloid. Keywords: coordinate function, n-sheeted coordinate function, complex membrane rotation, boundary problems of electrostatics, invariant electric field formula, sphere, oblong ellipsoid of revolution, oblate ellipsoid of revolution, hyperboloid of revolution of two nappes, paraboloid of revolution. Contacts: E-mail: avkuku @gmail.com Pp. 91-109.