Rudenko S. Geometric Modeling of shaped surfaces of revolution, reinforced winding

Dissertation is devoted to development of new method of calculating shaped surfaces of revolution, in which the mean curvature varies along the axis for knowingly prescribed by law and subject to the strengthening of these surfaces by asymptotic or geodesic winding yarn. By the main results should include how to determine the variation of the mean curvature along the axis according to the description of the contoured surface of revolution (direct problem) and a way to describe the contoured surfaces of revolution based on the mean curvature along the axis (inverse problem). Written and solved the differential equations to describe the asymptotic curves and geodesics on the contoured surface of revolution. Also developed methods for solving differential equations of the asymptotic curves on a cone-corrugated surface and contoured surfaces of revolution in the condition of elimination of extreme values of the curvature using R-functions, which allow, to describe and make, visible new kinds of pneumatic surfaces of revolution Managed mean curvature. In the language of Maple software package developed geometric modeling or asymptotic geodesic winding. The results of the work put into production in the design of pneumatic rubber lifts corrugated cone-type, as well as in the educational process at the National University of Civil Protection of Ukraine.