On the fermi-walker derivative for inextensible flows

Abstract

In this paper, we explicitly determine some curves corresponding to the their flows on the threedimensional space. We construct a new characterisation for inextensible flows of curves by using the Fermi-Walker derivative and the Fermi-Walker parallelism in space. Using the Frenet frame of the given curve, we present partial differential equations. Finally, we construct the Fermi-Walker derivative in the motion of a charged particle under the action of electric and magnetic fields.