Application of geometry of curves in Euclidean spaces

Abstract

In this article the so called induced spin velocities are studied, and it is an improvement of the paper \cite{CEJP2013}
using the geometry of curves in 3-dimensional Euclidean space.
Some essential properties of them are given, and they are rather different than the ordinary velocities. Indeed,
the induced spin velocities are non-inertial and instead of the Lorentz transformations
for them the Galilean transformations should be used.
The induced spin velocity is derived in terms of the curvature and torsion of the trajectory.
Two important applications of the induced spin velocities are studied in details.