Abstract
Abstract In this paper, we explicitly determine some curves corresponding to the their flows on the three-dimensional 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.
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