@article{article_443000, title={On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes}, journal={Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi}, volume={21}, pages={137–148}, year={2019}, author={Gürses, Nurten and Yüce, Salim}, keywords={Cayley-Klein düzlemleri, bir parametreli düzlemsel hareket, hareketli koordinat sistemi, kinematik, Euler-Savary formülü}, abstract={<p>In this present paper, we will take three affine Cayley-Klein planes into consideration: A , P ò ò and  P ò . The plane  P ò is a fixed plane relative to two other moving affine Cayley-Klein (CK)-planes. We will describe one-parameter motions A A / , /  ò ò ò ò P P and /  ò ò P P and discuss the relationship between the motions A A / , /  ò ò ò ò P P and /  ò ò P P by evaluating their derivative formulae, velocity vectors and pole points. Also, we will observe moving coordinate system and after that, we will examine the canonical relative system for one-parameter planar motions in the affine CK-planes by using the notions of moving coordinate system. Moreover, Euler-Savary formula, which gives the relationship between the <br />curvatures of trajectory curves, will be obtained with the help of canonical relative system for oneparameter motions in affine CK-planes planes by using the method given by H. R. Müller in 1956 [1]. <br /> </p>}, number={61}, publisher={Dokuz Eylül Üniversitesi}