One-Parameter Planar Motions in Affine Cayley-Klein Planes

Abstract

In 1956, W. Blaschke and 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, M. Akar and 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 P-epsilon and we will discuss the relations between absolute, relative, sliding velocities and accelerations.