The problem statement, all variables and given/known data A point particle of mass m is confined to the frictionless surface of a spherical bowl. There are 2 degrees of freedom. 1. Prove that the equilibrium point is the bottom of the bowl. , 2.Does the bowl need to be exactly spherical for this to be true ? 3. Near the bottom of the bowl what is the most general form possible for the shape of the bowl in order to maintain the stability of the equilibrium point at the bottom? I found this problem in analytical mechanics book(Hand and Finch) and was trying to solve it. 2. Relevant equations 3. The attempt at a solution In part one i used the p.e to find the eq point. im not sure about part 2&3 please !