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

The jerk is the time derivative of 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 osculating plane and the other radial direction in rectifying plane. Also, the case for planar motion in space is given as a corollary. Furthermore, the motion of an electron under a constant magnetic field and the motion of a particle along a logarithmic spiral curve are given as illustrative examples. 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.