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arXiv · 1406.5866

Kepler unbound: some elegant curiosities of classical mechanics

Niall J. MacKay·Sam Salour
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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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Niall J. MacKay, Sam Salour. 2014-06-23. Kepler unbound: some elegant curiosities of classical mechanics. https://doi.org/10.1119/1.4895393

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