Kremets Y. The geodesic lines of surfaces in problems of reinforcement of the shell and the inertial motion of a material point

In a dissertation it is considered two directions of use of properties of geodetic lines of a surface at a problem solving of applied character. The first direction - a reinforcement of shells of their surfaces by reinforcing filaments which work in tension at origin of voltages in a shell. If the filament rule on a surface coincides with its geodetic line in that case there are no gains which shift a filament from the initial rule. As it is convenient to do filament winding on surface of revolutions which are spread in practice the direct problem, that is a problem of determination and construction of geodetic lines on surface of revolutions and partially on the ruled is in-process considered. The known theorem of Clairaut for surface of revolutions not always allows to build geodetic line in a total storage but only its separate fragments, therefore are in-process made differential equations of the second order for a solution of this problem. Parametric equations of a meridian and their derivatives enter into them. By means of a numerical integration of differential equations geodetic lines on various surface of revolutions are built and is studied singularities of their disposition. The second direction - designing of ruled surfaces on the set directing curve, that is the inverse problem solution in comparison with the first direction. It has found the application at designing of soil-cultivating tools отвального type behind the set limiting mechanical trajectory of corpuscles of soil on them. In the basis of this approach property of corpuscles to move on the paths close to geodetic lines of a surface at positive motion on them, especially on the big speeds lies.