Frictional magnetic curves in 3D Riemannian manifolds

Abstract

In this study, we investigate the special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold. First, we consider a moving charged particle under the action of a frictional force, [Formula: see text], in the magnetic field [Formula: see text]. Then, we assume that trajectories of the particle associated with the magnetic field [Formula: see text] correspond to frictional magnetic curves ([Formula: see text]-magnetic curves[Formula: see text] of magnetic vector field [Formula: see text] on the 3D Riemannian manifold. Thus, we are able to investigate some geometrical properties and physical consequences of the particle under the action of frictional force in the magnetic field [Formula: see text] on the 3D Riemannian manifold.

Magnetic motion of spherical frictional charged particles on the unit sphere

“…Bearing in mind, the importance of the frictional force of the displacement of charged particles in magnetic fields, Coronel-Escamilla et al [16] focused on the fractional dynamics of charged particles in harmonic magnetic fields, ramp magnetic fields, and constant magnetic fields. Körpınar and Demirkol also defined frictional and gravitational magnetic curves together with their energy functionals and uniformity conditions on the 3D Riemannian surface [17,18].…”

“…There also exists another expression for the magnitude of the angular momentum ( L = mvr) that we can take into account to find out the constant function c = Ψ(N) • δ in terms of the geodesic curvature µ of the δ and coefficients of the force fields α, N. If one uses that definition together with Eqs. (15,17), it is yielded that…”

New approach to uniformly quasi circular motion of quasi velocity biharmonic magnetic particles in the Heisenberg space

“…The definition of uniformly accelerated motion (UAM) in general relativity has been discussed many times over the last 50 years 11 . In the pioneering work by Rindler, 12 it was motivated in part by some aspects of intergalactic rocket travel by use of the special relativistic formulas for hyperbolic motion in Körpinar and Demirkol 13 . The notion of a UAM of an observer in a general spacetime is analyzed in detail.…”

On Backlund transformations of surfaces by extended Harry-Dym flow

“…Kwon gave new equations of Evolution of inelastic plane curves, and Inextensible flows of curves and developable surfaces in [1,9]. Additionally, there are many works related to curves [6,[10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”