An alternative approach to jerk in motion along a space curve with applications

Abstract

Jerk is the time derivative of an acceleration vector and, hence, the third time derivative of the position vector. In this paper, we consider a particle moving in the three dimensional Euclidean space and resolve its jerk vector along the tangential direction, radial direction in the osculating plane and the other radial direction in the rectifying plane. Also, the case for planar motion in space is given as a corollary. Furthermore, motion of an electron under a constant magnetic field and motion of a particle along a logarithmic spiral curve are given as illustrative examples. The aforementioned decomposition is a new contribution to the field and it may be useful in some specific applications that may be considered in the future.