On the Construction of Generalized Bobillier Formula

Abstract

In this study, we consider the generalized complex number system C_{p}={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,[kern]<LaTeX>\kern</LaTeX>1pt[kern]<LaTeX>\kern</LaTeX>1ptp=0,[kern]<LaTeX>\kern</LaTeX>1pt[kern]<LaTeX>\kern</LaTeX>1ptp>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.