ON THE CONSTRUCTION OF GENERALIZED BOBILLIER FORMULA

In this study, we consider the generalized complex number system C-p = {x + iy : x, y is an element of R; i(2) = p is an element of 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 different methods for one-parameter planar motion in C-p; 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.