Snap in Motion Along Plane and Space Curves

- Hoda El-Sayied,
- Abdelrhman Tawfiq,
- Ayman Elsharkawy

## Abstract

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.