Yaylı, YusufKaracan, Murat Kemal2022-05-312022-05-312004http://hdl.handle.net/20.500.12575/80692ABSTRACT Ph. D. Thesis THE KINEMATIC APPLICATIONS OF THE TWO PARAMETERS MOTIONS Murat Kemal KARACAN Ankara University Graduate School of Natural and Applied Sciences Department of Mathematics Supervisor: Prof. Dr. Yusuf YAYLI This thesis consists of six chapters. The first chapter has been devoted to the introduction. Second chapter is devoted to fundamental notions. In the third chapter, general and special two parameter motions in Euclidean plane are defined. The Sliding velocity, pole line, hodograph and acceleration pole at each (K\i) position of one parameter motion which are obtained from two parameter motion calculated. Some theorems and results are obtained. In the forth chapter, general and special two parameter motions in Lorentzian plane are defined. Sliding velocity, pole line, hodograph and acceleration pole at each (X,u) position of one parameter motion which are obtained from two parameter motion calculated. Correspondence in Lorentzian plane of theorems and results which are obtained in the third chapter are investigated. In the fifth chapter, two parameter motion along a curve in Minkowski space El is defined and some theorems are obtained. Characterizations of some orbit surfaces in E\ are found. In the last chapter, general two parameter motions are given with the aid of rank of the rotation matrix. It is shown that geometric locus of instanteneous screw axis is a ruled surface. 2004, 108 pages Key Words: One Parameter Motion, Two Parameter Motion, Planar Motion, Lorentz Space, Motion Along a Curve.trMatematikdoctoralThesis