Consider a particle of mass m at the end of a rod of length l of negligible mass. The particle is free to swing in any direction under the action of gravity. Since the particle is constrained to move on the surface of a sphere, this system is called "the spherical pendulum".

a) Identify the appropriate generalized coordinates for this problem.

b) Find the Lagrangian of the system.

c) Is there a cyclic coordinate?

d) Is the total energy of the system conserved?

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