Existence of angular jerk in Keplerian motion

Abstract

The concept of angular jerk is introduced in angular motion in analogy with the linear jerk in translation. The angular jerk vector is defined as the rate of change of the angular acceleration vector, or the third derivative of the angular displacement vector. The existence of angular jerk is demonstrated in Keplerian motion as an example. The angular velocity, angular acceleration and angular jerk vectors are calculated from the polar equation of the orbit and the conservation of angular momentum in terms of the constants of motion. The variations of the angular quantities as functions of the polar angle are studied. Whereas the angular velocity necessarily remains posigrade, the angular acceleration has both posigrade and retrograde phases, and the angular jerk exhibits two posigrade and one retrograde phases during the course of one revolution. The locations of the extrema of the three angular quantities are determined. This treatment is suitable for upper undergraduate physics majors.