Generalized Fermi-Walker derivative of magnetic curves

This study consists of six chapters. The first chapter is the introduction part of the study. First the physical concepts and definitions are given, and then the information in the literature about the studies on magnetic curves in 3- dimensional Euclidean space is given. In the second part, the basic definitions and theorems used in our study are given. In the third chapter, definitions of T-magnetic, N-magnetic and B-magnetic curves are given according to Frenet frame in 3-dimensional Euclidean space. In the fourth chapter, derivatives of T-magnetic, N-magnetic and B-magnetic curves, Fermi-Walker derivatives, Normal Fermi-Walker derivatives, modified (bi-normal) Fermi-Walker derivatives are calculated according to Frenet frame in 3-dimensional Euclidean space. In the fifth chapter, derivatives of T-magnetic, N-magnetic and B-magnetic curves, generalized Fermi-Walker derivatives, generalized normal Fermi-Walker derivatives and generalized modified (bi-normal) Fermi-Walker derivatives are calculated according to Frenet frame in 3-dimensional Euclidean space. In the sixth part, the energies of the derivatives of T-magnetic, N-magnetic and B-magnetic curves, the energies of the generalized Fermi-Walker derivatives, the energies of the generalized normal Fermi-Walker derivatives and the energies of the generalized modified (bi-normal) Fermi-Walker derivatives are calculated according to Frenet frame in 3-dimensional Euclidean space. Keywords: Energy, Frenet Frame, Fermi Walker Derivate, Lorentz Force, Normal Fermi-Walker Derivate, Magnetic Curves