On the application of the principle of least action and holditch theorem to the some special curve types under the homotetic motion

This study consist of five chapters. In the introduction chapter, the summary of literature is given. In the second chapter, some basic concepts are given. In the third chapter, some specific cycloid-type curve definitions are given and the principle of least action is expressed. The orginal part of the study are the fourth and fifth chapters. Firstly special cycloid-type curves are expressed under closed planar homotetic motion and the principle of least action is applied to these curves. The principle of least action is applied to these curves and the energies of the points of the moving plane are calculated in order to calculate the minimum action point of these curves. Finally the Holditch theorem are obtained for circle and ellipse closed curves.