Consider a particle of mass m contrained to lie on the surface of a cone with it's vertex pointing down and half angle alpha.
a) write the equations of constraint.
b) employing cylindrical coordinates, (rho,phi,z) write the equations of motion and reduce them to an equivalent one degree of freedom problem using the radial coordinate rho as the independent variable.
c) sketch the effective potential identified from the equations of motion.
d) find the conditions for a circular orbit (rho=rhozero=constant, rhodot=o). And obtain the frequency of small oscillations about rhozero.