lagrangian mechanics

A particle of mass m slides around in a bowl which is a paraboloid of revolution, z = bp^2 in cylindrical polar coordinates (p, f, z), with z vertically upwards. Using p and f as coordinates, write out the equations of motion using the Lagrange method (don’t forget about the vertical motion). Find the value of f(dot) for which the particle will move in a circle at constant radius p = p 0.

 

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