One-Parameter Planar Motion in Affine Cayley-Klein Planes

Abstract

In 1956, H.R. Muller introduced the one-parameter planar motions and obtained the relation between absolute, relative, sliding velocities and accelerations in the Euclidean plane E^2, [3]. A. A. Ergin [4] considering the Lorentzian plane L^2, instead of the Euclidean plane E^2, introduced the one-parameter planar motions in the Lorentzian plane L^2 and also gave the relations between the velocities and accelerations in 1991. In addition to this, in 2013, S. Yuce, [1], introduced the one-parameter motions in the Galilean plane G^2 and gave same concepts stated above.In this paper, we will introduce one parameter planar motions in affine Cayley-Klein (CK) planes Pϵ and we will discuss the relations between absolute, relative, sliding velocities and accelerations.