Question

2. (25 points) A s ball bearing slides without friction in a parabolic surface. The parabola is a surface of revolution about the z axis, given by z = 2 where p vy2 is the radial coordinate in the cylindrical coordinate system (a) Calculate the kinetic and potential energy in terms of ρ and φ, where φ is the cylindrical polar angle. Show that the Lagrangian L is given by (b) Calculate the generalized momenta Po and pp appropriate to the nates and ф coordi- (c) Obtain equations of motion for the ф and f) coordinates. Show that mpeg Ξ l-const Use this result to eliminate the φ dependence in the equation of motion for pin favor of 2. There is no need to solve this equation.

Answer 1