Quaternions and homothetic motions in euclidean and lorentzian spaces

In the present paper, we investigate homothetic motions de-termined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable prop-erties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.