Homothetic motions with dual octonions in dual $8-$space

Abstract

In this study, for dual octonions in dual $8-$space $D^{8}$ over the domain of coefficients $D,$ we give a matrix that is similar to a Hamilton operator. By means of this matrix a new motion is defined and this motion is proven to be homothetic. For this one parameter dual homothetic motion, we prove some theorems about dual velocities, dual pole points, and dual pole curves. Furthermore, after defining dual accelerations, we show that the motion defined by the regular order $m$ dual curve, at every $t$-instant, has only one acceleration center of order $\left( m-1\right) .$