Burmester theory in Cayley–Klein planes with affine base

In this paper, we study the Burmester theory in Euclidean, Galilean and pseudo-Euclidean planes and extend the classical Burmester theory to the Cayley–Klein planes with affine base by a unified method. For this purpose, we use the generalized complex numbers and define a generalized form of Bottema’s instantaneous invariants. By this way, we expose the instantaneous geometric properties of motion of rigid bodies in the Cayley–Klein planes with affine base.