You can have a sharp corner and you still won’t get a Norton’s dome in every case. There’s definitely something there, but it’s not obvious to me what it is. It

You can have a sharp corner and you still won’t get a Norton’s dome in every case. There’s definitely something there, but it’s not obvious to me what it is. It does sometimes happen in physics that we throw away valid solutions to differential equations that are “physically impossible”, and I guess this falls in that category. Other examples are not immediately coming to mind unfortunately. But yea I don’t think this shows anything general about Newtonian mechanics.