ON THE CONSTRUCTION OF GENERALIZED BOBILLIER FORMULA.

In this study, we consider the generalized complex number system Cp = {x + iy : x, y ∈ R, i² = p ∈ R} corresponding to elliptical complex number, parabolic complex number and hyperbolic complex number systems for the special cases of p < 0; p = 0; p > 0, respectively. This system is used to derive Bobillier Formula in the generalized complex plane. In accordance with this purpose we obtain this formula by two di¤erent methods for one-parameter planar motion in Cp ; the first method depends on using the geometrical interpretation of the generalized Euler-Savary formula and the second one uses the usual relations of the velocities and accelerations. [ABSTRACT FROM AUTHOR]