Chiang Mai Journal of Science

 Müller, H. R. [2], on the Euclidean plane , introduced the one-parameter planar motion and obtained the relation between absolute, relative, sliding velocities (and accelerations). Also, Müller, H. R. [6] provided the relation between the velocities (in the sense of Complex) under the one-parameter motion on the Complex plane . Ergin, A. A. [4] considered the Lorentzian plane , instead of the Euclidean plane , and introduced the one-parameter planar motion on the Lorentzian plane  and also gave the relations between both the velocities and the accelerations. Yüce, S. [12] introduced the relation between the velocities (in the sense of Hyperbolic) under the one-parameter motions on the Hyperbolic plane . Yüce, S. [1] considered the Galilean plane , instead of the Euclidean plane  and Lorentzian plane , and introduced the one-parameter planar motion on the Galilean plane  and also gave the relations between both the velocities and accelerations. In analogy with the Complex numbers and Hyperbolic numbers, a system of Dual numbers can be introduced: . Complex numbers are related to the Euclidean geometry, the Dual and Hyperbolic systems of numbers are related to the Galilean geometry and Lorentz (or Minkowski) geometry, respectively, [9,10]. In this paper, in analogy with Complex motions as given by Müller, H.R. [6] and Hyperbolic motions as given by Yüce, S. [12], one-parameter motion on the Dual plane are defined. Also the relations between absolute, relative, sliding velocities (and accelerations) and pole lines are discussed.