1-2(81) 2014 MATHEMATICS AND MECHANICS
M.A. Cheshkova
A Cylindroid with Circular Helixes as Directing Curves
A ruled surface is called a Catalan surface if its rectilinear generators are parallel to a certain surface. A cylindroid is the Catalan surface formed by a straight-line movement along two directing curves with a rectilinear generator being parallel to a certain surface. In the paper we study cylindroids with circular helixes as directing curves. There are four cases: 1) the two helixes are rightrotary and they have the same screw pitch, 2) the two helixes are right-rotary and they have different screw pitches, 3) one helix is right-rotary, the second helix is left-rotary and they have the same screw pitch, 4) one helix is right-rotary, the second helix is left-rotary and they have different screw pitches. Total and the mean curvatures of the considered surfaces are calculated. The mean curvature equals to zero in the first case only. The only surface is the minimal surface. A helicoid is the only minimal ruled surface. We construct these surfaces with a help of mathematical software package.
DOI 10.14258/izvasu(2014)1.2-11
Key words: cylindroid, helix, total curvature, mean curvature
Full text at PDF, 571Kb. Language: Russian.
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