Geometric kinematics of persistent rigid motions in three-dimensional Minkowski space

Kahveci D., Yaylı Y.

MECHANISM AND MACHINE THEORY, cilt.167, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 167
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.mechmachtheory.2021.104535
  • Dergi Adı: MECHANISM AND MACHINE THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, zbMATH, DIALNET
  • Anahtar Kelimeler: Minkowski space, Lorentz group, Poincaregroup, Persistent rigid-body motions, Frame motions, Axode surfaces, SCREW SYSTEMS, CURVES, FRAMES
  • Ankara Üniversitesi Adresli: Evet

Özet

This paper investigates whether Lorentz geometry can be systematically implemented to study the geometric kinematics of persistent rigid motions in three-dimensional Minkowski space. The notion of persistence of a one-parameter rigid motion is identified by the property that the instantaneous twist of the motion has a constant pitch. The main difference between three-dimensional Euclidean and Minkowski spaces is that the pitch of twists will take three different values in Minkowski space depending on the causal character of the curve on which the motions are based. Furthermore, based on the fundamentals of screw theory, the paper establishes necessary and sufficient criteria for modeling the persistence of some significant frame motions, including Frenet-Serret, adapted frame, and Bishop motions. Then, the axode surfaces of these special motions and their geometric concepts are defined. Finally, for a thorough treatment of special frame motions in three-dimensional Minkowski space, this paper reveals some illustrative examples of persistent rigid motions and axode surfaces.