# A New Expression for Higher Order Accelerations and Poles under the One Parameter Planar Hyperbolic Homothetic Motions

Presenter: Serdal Sahin, Yildiz Technical University, Turkey

Joint work with Salim Yuce

The one parameter planar hyperbolic homothetic motion was introduced via hyperbolic numbers which are the universal Clifford algebra for $\mathbb{R}^{1,0}$. Sahin and Yuce gave a formula for the higher order accelerations and poles under the one parameter planar complex homothetic motion. In this paper, in analogy to Sahin and Yuce, we obtain a formula for the higher order accelerations and poles under the one parameter planar hyperbolic homothetic motion. Also, In the case of the homothetic rate $h\equiv 1$ we obtain the higher order accelerations and poles under one parameter planar hyperbolic motion. Also, the higher order velocities and accelerations are presented by taking the angle of the rotation instead of the parameter of the motion.