The Kepler problem for planetary motion is a two-body dynamic model with an attractive force obeying the inverse square law, and has a direct analogue in any dimension. While the magnetized Kepler problems were discovered in the late 1960s, it is not clear until recently that their higher dimensional analogues can exist at all. Here we present a possible route leading to the discovery of these high dimensional magnetized models.
Guowu Meng. "The Classical Magnetized Kepler Problems in Higher Odd Dimensions." J. Geom. Symmetry Phys. 32 15 - 23, 2013. https://doi.org/10.7546/jgsp-32-2013-15-23