Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)11015Some aspects of the geometry of the surfaces with the system of plane coordinate linesIvanovV Nivanov.v.n@stream.ru15032010361512092016Copyright © 2016, Structural Mechanics of Engineering Constructions and Buildings2016In the article, the geometry of the surfaces with the system of the plane coordinate lines is investigated. The common vector formula of these surfaces is received.
The formulas of the coefficients of the quadratic forms are presented too. The conditions, when of the plane coordinate lines are lines of the principle curvatures of the surface, are received.
The subclass of the surfaces with the system of the plane coordinate lines in the normal plane of the directrix curve is investigated. The formula of the Monge's ruled surfaces is received on the base of the common formula.
The drawings of the Monge's ruled surfaces made in MathСad system are shown.surfaces with the system of plane coordinate linesa vector equationquadratic formslines of principle curvaturesnormal surfacesruled Monge's surfacesповерхности с системой плоских координатных линийвекторное уравнениекоэффициенты квадратичных формлинии главных кривизннормальные поверхностирезные поверхности Монжа