Quaternions and geometric applications

Quaternions were introduced in 1843 by William Rowan Hamilton. Later, real and dual quaternions have been discussed by many authors. The aim of this thesis is to examine the geometric applications of real and dual quaternions by giving their algebra and matrix representations. Additionally, the relationship between real quaternions, rotational motion and the relation between dual quaternions and screw motions will be investigated. For this reason, real and dual quaternions will be used as rotation and screw operators and kinematics applications of them will be given. This thesis consists of five chapters. The first chapter is arranged as an introduction and W. R. Hamilton's discovery of quaternions is mentioned and the application areas of real and dual quaternions are mentioned. In these condpart, basic concepts are included within four subsections. In the third chapter, algebraic structures, matrix representations and geometric applications of real quaternions will be given. In the fourth chapter, algebraic structures and matrix representations of dual quaternions will be examined and their geometric applications will be given. The last chapter is organized as the conclusion part of the thesis.