On polar moments of inertia of Lorentzian circles

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 ?) 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 = ?ab. 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) - ?ab is obtained. © 2006 Asian Network for Scientific Information.