Dual Transformations in Galilean Spaces

Abstract

In this study, we define a dual transformation between G n and G n 1. We examine the invariance of the plane where the shear motion is acting in Galilean and pseudo-Galilean spaces. We define a dual transformation between G n and G n 1 as well. We provide applications in G 3 and G 3 1. In addition to applications, we draw their figures in order to reinforce the visualization in both spaces.

Applications of Quaternions in Galilean Spaces

“…where In , shear movement determined with the help of with (6) is also called motion in the meaning of Galilean.…”

“…By using dual transformation which is given in [1], we defined the dual transformation between Galilean and pseudo-Galilean spaces in [6]. where .…”

“…In [5], the geometry of motions in Galilean and pseudo-Galilean spaces was studied. In the light of studies in Galilean geometry and dual transformations, we defined the transition from real Galilean space to pseudo-Galilean space in [6].…”

“…Finally, with a similar method, dual Galilean orthogonal matrices are obtained by using unit dual quaternions. The difference of this work from [6] is that we construct the Galilean transformations using quaternions. We think that the idea of transferring quaternions and dual quaternions to Galilean and Pseudo-Galilean spaces with the help of a dual transformation may be a positive contribution to the literature.…”

Construction of Binormal Motion and Characterization of Curves on Surface by System of Differential Equations for Position Vector

“…Many studies dealing with this problem are also available in the literature. Such as in [5][6][7][8][9][10].…”