Euler savary formula for the one parameter motions in the complex plane C

Abstract

Muller (1978), in the Euclidean plane E-2 introduced the one parameter planar motions and obtained the relation between absolute, relative, sliding velocities (and accelerations). During one parameter planar motion in the Euclidean plane E-2, the Euler-Savary formula was expressed by Muller (Blaschke and Muller, 1956). Also Blaschke and Muller (1956) and Tutar et al. (2001) provided the relation between the velocities (and accelerations) in the sense of the complex under the one parameter motions in the complex plane C = {x + iy vertical bar x, y epsilon IR, i(2) = -1}. In this paper we have defined canonical relative system of one parameter motions in the complex plane, C. With the aid of this relative system we have obtained the Euler-Savary formula giving the relation between the curvatures of the trajectory curves of one parameter motions in the complex plane c.