Magnetic trajectories in three-dimensional Lie groups |
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Authors: | Tunahan Turhan |
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Institution: | Isparta University of Applied Sciences, Vocational School of Technical Sciences, Isparta, Turkey |
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Abstract: | We study magnetic trajectories in Lie groups equipped with bi-invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi-invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G. |
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Keywords: | Lie groups Lorentz force equation magnetic flow magnetic trajectory |
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