A Dynamical Approach to Position Vector of Timelike Curve by Vectorial Momentum, Torque and Tangential Dual Curve

Abstract

In this study, the position vector of a timelike curve wp is stated by a linear combination of its Serret Frenet frame with differentiable functions. The definition of tangential dual curve of the curve wp is stated by using these differentiable functions. Moreover, tangential torque curve of timelike curve wp is defined and investigated. New dynamically and physical results are stated depending on the torque of the timelike curve wp and the direction of the tangent vector component of the curve. Then, the position vector of a timelike W curve is again stated by differentiable functions. Therefore, solutions of differential equation of the position vector of timelike W curve with two different types depending on the values of curvature and torsion of timelike curve are obtained. By using the differentiable functions obtained as a result of these solutions, tangential dual and torque curve of the timelike W curve are obtained. Depending on the tangential dual and torque curve of the timelike W curve, results are given for two different cases separately.