On polar moments of inertia of Lorentzian circles


YÜCE S., KURUOĞLU N.

Journal of Applied Sciences, vol.6, no.2, pp.383-386, 2006 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 2
  • Publication Date: 2006
  • Doi Number: 10.3923/jas.2006.383.386
  • Journal Name: Journal of Applied Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.383-386
  • Keywords: Lorentzian circle, Lorentzian motion, Moment of inertia, Trigonometry in Lorentzian geometry
  • Istanbul Gelisim University Affiliated: Yes

Abstract

In this study, we first compute the polar moment of inertia of orbit curves under planar Lorentzian motions and then give the following theorems for the Lorentzian circles: When endpoints of a line segment AB with length a +b move on Lorentzian circle (its total rotation angle is δ) with the polar moment of inertia T, a point X which is collinear with the points A and B draws a Lorentzian circle with the polar moment of inertia Tx. The difference between T and Tx is independent of the Lorentzian circles, that is, Tx - T = δab. If the endpoints of AB move on different Lorentzian circles with the polar moments of inertia TA and TB, respectively, then Tx = [aTB + bTA]/(a + b) - δab is obtained. © 2006 Asian Network for Scientific Information.