I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time.   This leads to some interesting problems with time reversibility, as it implies the ball will spontaneously roll down the surface.  I'm not looking for an explanation, so much as a name and link to study it some more.
This question is in the spirit of , an example of an apparently non-deterministic system in Newtonian mechanics. Under certain restrictions, the  guarantees the existence and uniqueness of solutions to differential equations with initial conditions. However, Norton's dome does not satisfy these restrictions. The ball may sit on top of the dome for an arbitrary period of time before sliding down in a particular trajectory, without violating Newton's laws of motion.    Is there a plausible example of a system of interacting point-particles such that the equations of a point-particle are continuous but not , and therefore fail to have a unique solution?
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