Trajectories with constant acceleration, jerk, etc. in 2D Minkowski spacetime

Abstract

In this work we study one spatial dimension motion kinematics in Minkowski space-time. First, we discuss different approaches to the accelerated observer. Then, we propose a parametrization for the four-velocity and solve exactly the case that describes the asymptotic behaviour for constant higher order derivatives of velocity. Finally, we examine how more general cases change our solution.