Snap in Motion Along Plane and Space Curves

The rate of change of jerk or the second derivative of acceleration with respect to time has been called snap or jounce. Snap is an important topic that has many applications in mechanics, acoustics and is used to explain the universe's different phenomena. The main purpose of this paper is to study the snap vector in planar and space motion. For the planar motion, the snap vector is resolved into tangential-normal and radial-transverse components. The oscillation of a simple pendulum and central force proportional to distance are chosen as models for the plane motion to show the several geometric properties of the snap vector. Furthermore, we consider a particle moving in the three-dimensional Euclidean space and resolve its snap vector along the tangential direction, the radial direction in the osculating plane, and the other radial direction in the rectifying plane, respectively. The motion of an electron under a constant magnetic field and the motion of a particle along a logarithmic spiral curve are chosen as models for the three-dimensional motion to show the several geometric properties of the snap vector.