Motion Caused by Magnetic Field in Lobachevsky Space
V.V. Kudryashov, Yu.A. Kurochkin, E.M. Ovsiyuk, V.M. Red'kov
TL;DR
This paper investigates the behavior of a relativistic particle in 3D Lobachevsky space under a magnetic field, deriving exact solutions and analyzing motion on cylindrical surfaces, revealing unique relativistic effects in hyperbolic geometry.
Contribution
It provides the first exact solutions for relativistic particle motion in Lobachevsky space with a magnetic field, identifying integrals of motion and analyzing specific surface trajectories.
Findings
Exact integrals of motion are derived.
Particle trajectories on cylindrical surfaces are characterized.
Relativistic effects in hyperbolic magnetic fields are elucidated.
Abstract
We study motion of a relativistic particle in the 3-dimensional Lobachevsky space in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in the Euclidean space. Three integrals of motion are found and equations of motion are solved exactly in the special cylindrical coordinates. Motion on surface of the cylinder of constant radius is considered in detail.
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