The analogy of a ball being put on a hilltop or in a valley certainly applies here. I think what he meant is that such solution never exists in nature, not even classically. On a hilltop it's easy to see why (it's unstable) but in a valley small perturbations will always produce some tiny...
First time poster so I apologize any problems with location or content. By the way, you guys are awesome.
Just some context: last semester I had a theoretical mechanics class and the teacher said, while teaching us about the Lagrangian formulation, that particles cannot, ever, reach a...