LAUSR

This paper derives the declarations for timelike ruled surfaces with stationary timelike Disteli-axis by the E. Study map. This prepares the ability to determine a set of Lorentzian invariants which explain the local shape of timelike ruled surfaces. As a result, the Hamilton and Mannhiem formulae of surfaces theory are attained at Lorentzian line space and their geometrical explanations are examined. Then, we define and explicate the kinematic geometry of a timelike Plűcker conoid created by the timelike Disteli-axis. Additionally, we provide the relationships through timelike ruled surface and the order of contact with its timelike Disteli-axis.