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 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 T<inf>x</inf>. The difference between T and T<inf>x</inf> is independent of the Lorentzian circles, that is, T<inf>x</inf> - T = δab. If the endpoints of AB move on different Lorentzian circles with the polar moments of inertia T<inf>A</inf> and T<inf>B</inf>, respectively, then T<inf>x</inf> = [aT<inf>B</inf> + bT<inf>A</inf>]/(a + b) - δab is obtained. © 2006 Asian Network for Scientific Information.