Euler-Savary formula for the planar homothetic motions

The homothetic motion in 2-dimensional Euclidean space [E.sup.2], the relation between the velocities of this motion and geometric results for the pole curves were studied in ref [1]. In this paper a canonical relative system of any plane with respect to other planes are given. Therefore in a homothetic motion E/E', Euler-Savary formula giving the relation between the curvature of trajectory curves drawn in the fixed plane E' by the points of the moving plane E is obtained. In the special case of homothetic scale h identically equal to 1, we get the Euler-Savary formula which was given by Muller [5]. Finally some geometrical results are reached using Euler-Savary formula. Keywords Euler-Savary formula, homothetic motion, kinematics.
§ 1. Introduction This study deals with instantaneous geometric plane kinematics. Which is the study, for a certain instant during a continuous motion, of the differential geometric properties? So if [...]