Kinematics of dual transformations

This thesis consists of five main parts. The first chapter was arranged as an introduction part, and the concepts of kinematics and dual transformation were mentioned. In the second chapter, the definition of dual transformation is given by presenting the basic concepts used in the thesis. In the third chapter, the relationship between Euclidean space and Lorentz space is discussed with the help of dual transformation. The axes of rotation that remain constant in both spaces have been studied. In addition, the commutative diagram created using the dual transform and Cayley formula is examined. In the fourth chapter, the dual transformation defined between Galilean and pseudo-Galilean spaces is given and its applications are made. The last chapter is organized as the conclusion part of the thesis.