loading page

BENDING OF THE SURFACES OF THE BINORMALS OF THE SLOPE LINES
  • +2
  • Tetiana Kresan,
  • Serhii Pylypaka,
  • Zynovii Ruzhylo,
  • Ivan Rogovskii,
  • Oleksandra Trokhaniak
Tetiana Kresan
Separated Subdivision of National University of Life and Environmental Sciences of Ukraine Nizhyn Agrotechnical Institute
Author Profile
Serhii Pylypaka
National University of Life and Environmental Sciences of Ukraine
Author Profile
Zynovii Ruzhylo
National University of Life and Environmental Sciences of Ukraine
Author Profile
Ivan Rogovskii
National University of Life and Environmental Sciences of Ukraine
Author Profile
Oleksandra Trokhaniak
National University of Life and Environmental Sciences of Ukraine
Author Profile

Abstract

The bending of the surfaces of the binormals by deformation of the directing curve, which is the slope line, is considered. Such deformation changes the curvature of the curve, but it remains a slope line. The rectilinear generators of the surfaces at deformation of the curve coincide with the unit binormal of the accompanying trihedral at all its points. Parametric equations of continuous bending of these surfaces have been made by changing the angle of inclination of the directional slope line. The initial slope curve is given by the angle of its rise and the conformity of change of curvature as a function of arc length. The partial case where the curvature of the initial curve is constant is considered. In this case, it is shown that helicoids, including the screw conoid, are the set of surface bends. Specific examples are considered. According to the obtained equations, the surfaces that are the bending of the initial are constructed.