Kepler unbound: some elegant curiosities of classical mechanics
Exactly Solvable and Integrable Systems
2015-06-22 v1 High Energy Physics - Theory
Abstract
We describe two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger ('MICZ') Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of well-separated solitonic ('BPS') monopoles using Taub NUT space. Each system is characterized by the conservation of a Laplace-Runge-Lenz vector, and we use elementary vector techniques to show that each obeys a subtly different variation on Kepler's three laws for the Newton/Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles.
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Cite
@article{arxiv.1406.5866,
title = {Kepler unbound: some elegant curiosities of classical mechanics},
author = {Niall J. MacKay and Sam Salour},
journal= {arXiv preprint arXiv:1406.5866},
year = {2015}
}
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15 pages