Derivation of slant helices on a given surface through new approaches


Duldul B. U. , DÜLDÜL M.

APPLIED MATHEMATICS AND COMPUTATION, vol.366, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 366
  • Publication Date: 2020
  • Doi Number: 10.1016/j.amc.2019.124742
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts

Abstract

In this paper, we provide some methods for generating slant helices lying on a parametric or an implicit surface in Euclidean 3-space. These methods are based on the initial value problems of first order ordinary differential equations. Although analytical solutions of the derived systems are not possible even for simple surfaces, we provide some illustrative examples in which the slant helices have been obtained numerically. The produced slant helices possess the given fixed direction, constant angle, and the curvature function. (C) 2019 Elsevier Inc. All rights reserved.