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A particle moves in a cylindrically symmetric potential V(p, z). Use cylindrical coordinates p, 4 and z to parametrizat (a) Write the Lagrangian for an

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A particle moves in a cylindrically symmetric potential V(p, z). Use cylindrical coordinates p, 4 and z to parametrizat (a) Write the Lagrangian for an unconstrained particle of mass m using cylindrical coordinates in the presence of this potential. (b) Write equation of motion for p, 4 and z (c) Identify any cyclic coordinates, and write a first integral corresponding to each

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