Kepler unbound: Some elegant curiosities of classical mechanics

Niall J. MacKay, Sam Salour
2015 American Journal of Physics  
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
more » ... for the Newton/Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles.
doi:10.1119/1.4895393 fatcat:b36tjyfjyvcqllseozc7eap4dq