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A particle moves in a potential field V(r,z)=az/r, a is constant. Use the cylindrical coordinates as...

A particle moves in a potential field V(r,z)=az/r, a is constant. Use the cylindrical coordinates as the general coordinates.
1)Determine the Lagrangian of this particle.
2)Calculate the generalized impulse.
3)Determine the Hamiltonian of this particle and the Hamiltonian’s equations of motion.
4)Determine the conserved quatities of this system.
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