The geometry of line-symmetric rigid-body motions


BAYRIL AYKUT D., Selig J.

Differential Geometry and its Application, vol.100, 2025 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 100
  • Publication Date: 2025
  • Doi Number: 10.1016/j.difgeo.2025.102270
  • Journal Name: Differential Geometry and its Application
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Rigid-body motions, Ruled surfaces, Half-turns, Line-symmetric motion
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this work the kinematic geometry of line-symmetric rigid-body motions is revisited. These motions are produced by reflecting a rigid body in the successive generator lines of a ruled surface. Classical results are re-derived using methods from Lie algebra and new results are found. In particular, results for some of the acceleration properties of these motions are found using the Sannia frame of the ruled surfaces. The ruled surfaces considered are given by the tangent, normal or binormal lines to smooth curves as well as Catalan surfaces and right conoids.