On calculation of the pitch and angle of pitch of a closed ruled surface of dimension (k+1) using a rotation minimizing frame in Euclidean space Double-struck capital Rn

Keskin O., ALTIN A., EKMEKCİ F. N., YAYLI Y.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.8, pp.7004-7016, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 8
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7237
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.7004-7016
  • Keywords: angle of pitch, closed ruled surface, Euclidean space, pitch, rotation minimizing frame (RMF), ruled surface
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, first, the pitch and the angle of pitch of a closed ruled surface of dimension (k + 1) are calculated according to a rotation minimizing frame in Euclidean space Double-struck capital R4. To calculate this pitch and this angle of pitch of the closed ruled surface of dimension (k + 1), three different ruled surfaces are taken according to the rotation minimizing frame. Therefore, for these three different ruled surfaces, three different situations are found. Second, by taking any curve in four-dimensional Euclidean space, the closed ruled surface of this curve, its orthogonal trajectory, the pitch, and the angle of pitch of this closed ruled surface are obtained according to the rotation minimizing frame. Finally, the pitch and the angle of pitch of the closed ruled surface of dimension (k + 1) are generalized to n-dimensional Euclidean space with the help of the rotation minimizing frame.