INFINITESIMAL BENDING OF CURVES ON THE RULED SURFACES

  • Marija S Najdanović Preschool Teacher Training College
  • Ljubica S Velimirović University of Niš
Keywords: Hyperbolic paraboloid, Cylinder, Ruled surface, Variation, Curve, Infinitesimal bending,

Abstract


In this paper we study infinitesimal bending of curves that lie on the ruled surfaces in Euclidean 3-dimensional space.We obtain an infinitesimal bending field under whose effect all bent curves remain on the same ruled surface as the initial curve. Specially, we consider infinitesimal bending of the curves which belong to the cylinder as well as to thehyperbolic paraboloid and find corresponding infinitesimal bending fields. We examine the variation of the curvature of a curve under infinitesimal bending on the hyperbolic paraboloid. Some examples are visualized using program packet Mathematica.

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Supplementary files
Published
2018/06/30
Section
Original Scientific Paper