Calculation of nonlinear deformation of a flexible rod

The class of nonlinear tasks for flexible rods, even in the case of flat deformation, is rather complicated. Closed form solutions are possible only for some special cases. An algorithm of numerical integration of the nonlinear equations of equilibrium of a flat rod by a Runge-Kutta method is considered. The boundary conditions on the extremity of a rod are satisfied approximately. The projection equations are obtained from the common vectorial equations of equilibrium. As solving functions the projections of a transition vector and internal forces vector on global axes, angle of a normal's turn to the rod axis, and internal flexing, are chosen.