Maksymenko-Sheyko K. Mathematical modeling of physical and mechanical fields having helical symmetry type with the R-functions method

For the first time the R-functions method is applied in mathematical modeling of physical and mechanical fields having helical symmetry type in curvilinear non-orthogonal coordinates. With the help of the R-functions theory the normalized equations of twisted cylinders and coil pipes of nonclassical cross section are constructed for the first time. In curvilinear non-orthogonal coordinates the basic differential invariants and vectorial ratio for coil pipes and twisted cylinders are obtained. It is shown that if there is the conforming geometrical and physical symmetry then the dimension of boundary value problems can be reduced. All constructed differential invariants and vectorial ratio can be used at construction of mathematical models of the different physical nature fields. The necessary condition of decidability of Neumann inhomogeneous boundary value problem for a Poisson equation for pressure is demonstrated, which one is a consequent of Navier-Stokes equations.The influence of a corner of twist and geometrical parameters of the coil pipe on nature of electric potential distribution and incompressible viscous liquid flow pattern is investigated. The implementation is planning. The results can be used in organizations, which ones investigating physicomechanical twisting fields.