On the Construction of Generalized Bobillier Formula

Authors : Tülay ERİSİR, Mehmet Ali GÜNGÖR, Soley ERSOY

Pages : 111-124

Doi:10.31801/cfsuasmas.443657

View : 19 | Download : 14

Publication Date : 2019-02-01

Article Type : Research Paper

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]\kern1pt[kern]\kern1ptp=0,[kern]\kern1pt[kern]\kern1ptp>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.
Keywords : Bobillier Formula, Euler Savary Formula, Generalized Complex Numbers