ON THE CONSTRUCTION OF GENERALIZED BOBILLIER FORMULA

Abstract

In this study, we consider the generalized complex number system Cp =x + iy : x; y 2 R; i2 = p 2 Rcorresponding to elliptical complexnumber, parabolic complex number and hyperbolic complex number systemsfor the special cases of p 0, respectively. This system isused to derive Bobillier Formula in the generalized complex plane. In accordance with this purpose we obtain this formula by two di§erent methods forone-parameter planar motion in Cp ; the Örst method depends on using the geometrical interpretation of the generalized Euler-Savary formula and the secondone uses the usual relations of the velocities and accelerations.