Professional paper

Cyclical Surfaces Created by a Conical Helix

Tatiana Olejníková ; Department of Applied Mathematics, Faculty of Civil Engineering, Technical University in Kosice, Kosice, Slovakia

Abstract

The paper describes cyclical surfaces created by revolution of a circle about an edge of the trihedron of a conical helix that is moving evenly along the helix. This Euclidean metric transformation is composed from revolution about one of the coordinate axes and transformation of the right handed coordinate system to the right handed system of the moving trihedron in every point of the conical helix. This transformation is analytically represented by a functional matrix of 4th order. These surfaces are determined at particular parameter values which have influence on the surface shape. The vector equation of surfaces and some illustrations of this group of surfaces are presented in the paper. The surfaces are illustrated and modelled in the programme Maple.

Keywords

cyclical surface; conical helix; trihedron

Hrčak ID:

19909

URI

https://hrcak.srce.hr/19909

Publication date:

14.2.2008.

Article data in other languages: croatian

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