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Kepler unbound: some elegant curiosities of classical mechanics

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.

preprint2014arXivOpen access
Niall J. MacKaySam Salour
nlin.SIhep-th
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Niall J. MacKaySam Salour

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