One parameter motions and disteli diagram in dual Lorentzian space

This thesis which is related to the one parameter motions and Disteli diagram in dual Lorentzian space consists of four sections. In the first section, we have given basic concepts and theorems in dual geometry. In the second section, we have given basic concepts and theorems in dual Lorentzian space. Moreover, dual hyperbolic spherical curves and Lorentzian spherical curves in the dual Lorentzian space are brought to mind. In the third section, we have introduced one parameter dual hyperbolic spherical motions and one parameter dual Lorentzian spherical motions in the dual Lorentzian space. This investigation the curves on the sphere corresponding to with Blaschke frame of axodes have been given. By considering Disteli axis on the Blaschke frame we have obtained Euler Savary formulae of hyperbolic and Lorentzian spherical motions. At the end of sections, by obtaining orthogonal rotation matrices in the sense of dual Lorentzian type 3 3 × , we have found real and dual invariants of fixed and moving axodes. In the fourth section, by considering diagram given by Martin Disteli and study of Figliolini, Stachel and Angeles we have introduced this diagram for hyperbolic spherical and Lorentzian spherical motions in the dual Lorentzian space. These diagrams, illustrating the relation between the angular velocities of a pair of skew gears and the position and pitch of their relative screw motion in the dual Lorentzian space. Finally, in the appendix of this thesis we have given basic concepts and theorems in the Lorentzian geometry. Furthermore, differential geometry of curves and surfaces in the Lorentzian geometry are brought to mind.