Identifications of paths and curves under the plane similarity transformations and their applications to mechanics

ÖREN İ., Khadjiev D., PEKŞEN Ö.

JOURNAL OF GEOMETRY AND PHYSICS, vol.151, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 151
  • Publication Date: 2020
  • Doi Number: 10.1016/j.geomphys.2020.103619
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Invariant, Plane curve, Similarity transformation, Newtonian mechanics, DETECTING SYMMETRIES, INTEGRABLE EQUATIONS, INVARIANTS, MOTIONS, RECOGNITION, SYSTEMS
  • Karadeniz Technical University Affiliated: Yes


In this paper, global differential G-invariants of paths in the two-dimensional Euclidean space E-2 for the similarity group G = Sim(E-2) and the orientation-preserving similarity group G = Sim(+)(E-2) are investigated. A general form of a path in terms of its global G-invariants is obtained. For given two paths xi(t) and eta(t) with the common differential G-invariants, general forms of all transformations g is an element of G, carrying xi(t) to eta(t), are found. Similar results are given for curves. Moreover, analogous of the similarity groups in the three-dimensional space-time and in the four-dimensional space-time-mass are defined. Finally, applications to Newtonian mechanics of the above results are given. (C) 2020 Elsevier B.V. All rights reserved.