2005/07/05 by Jayme De Luca, De Luca, Jayme
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Metal Forming Simulation Techniques #Metallurgy and Material Forming #physics.class-ph
paper · pdf · doi:10.48550/arxiv.physics/0507033
4 pages, 1 table included in text and 1 postscript figure version 3 includes a minor text melioration, namely; the Z-coorditates are defined to be explicitly real
openalex publication_date 2005/07/05 · arxiv created 2005/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study an orbit of the electromagnetic two-body problem that involves a fast (stiff) spinning motion about a circular orbit. We give a multiscale method of solution that solves for the fast timescale first. The solvability condition of the asymptotic expansion demands resonances for the fast dynamics. The stiff resonant tori are found precisely in the atomic magnitude and agree with many features of the Bohr atom in quantitative and qualitative detail; We calculate every first emission line of the first 13 observable spectroscopic series of hydrogen within a few percent deviation. The resonant orbits have angular momenta that are approximate multiples of Planck's constant and the emitted frequencies are given by a difference of two linear eigenvalues. This Lorentz-invariant two-body dynamics exhibts the phenomenon of resonant dissipation, i.e., the metastable dynamics radiates the center-of-mass energy while the particles perform fast spinning oscillations of small amplitude about a circular orbit, a collective radiative recoil.