The author of the blog post completely misses the point of the problem. The dome is interesting close to the apex. It doesn't matter that the particle would fly

The author of the blog post completely misses the point of the problem. The dome is interesting close to the apex. It doesn't matter that the particle would fly off the surface at some point further down on its trajectory. The real issue is that Newtonian physics just doesn't work for forces that are not Lipschitz continuous (which the author brushes over in a half-sentence). The surprising thing is that a simple dome with an easy to draw shape can produce such a force.