On the Construction of Generalised Bobillier Formula

Abstract

In this study, we consider the generalized complex number system $C_{\mathrm{p}}=\left\{x+iy:x,y\in R,i^2=\mathrm{p}\in R\right\}$ corresponding to elliptical complex number, parabolic complex number and hyperbolic complex number systems for the special cases of $\mathrm{p}<0,\mathrm{p}=0,\mathrm{p}>0$, 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 $C_{\mathrm{p}}$; 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.

15 pages, 5 figures

References in corpus (1)

• One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula