The spherical pendulum is a particle of mass m attached to a fixed point by a light inextensible string of length a and moving under uniform gravity. Its Lagrangian in polar angles 8, is given by L=-=-ma (0 + sin 06) + mga cos If p, and p, are conjugate momenta corresponding to and respectively, then Hamiltonian is O O 1 2ma 1 ma 1 2ma 2ma P + Pe Po sin Po sin0 Po sin 8 Po sin +mga cos - mga cos mga cose mga cos