REPRESENTATION OF GENERALIZED CIRCULAR SURFACES AS RIGID BODY MOTIONS

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Aslan S., BEKAR M., YAYLI Y.

Miskolc Mathematical Notes, vol.25, no.1, pp.79-91, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.18514/mmn.2024.4311
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.79-91
  • Keywords: circular surfaces, dual quaternion surfaces, generalized tube surfaces, rigid body motions (screw motions), tube surfaces
  • Gazi University Affiliated: Yes

Abstract

In this paper, we introduce generalized circular surfaces, a generalization of generalized tube surfaces and circular surfaces. Moreover, we define a special dual quaternion by using the moving frame along the spine curve of generalized circular surface. We then show that the screw motion obtained by this dual quaternion can be used to construct generalized circular surfaces. We also prove that these generalized circular surfaces can be expressed by homothetic motions. Finally, we provide some examples of generalized circular surfaces with figures.