On polar moments of inertia of Lorentzian circles
Journal of Applied Sciences, vol.6, no.2, pp.383-386, 2006 (Scopus)
- 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.