A particle moves in a cylindrically symmetric potential (U(ho, z)). Use cylindrical coordinates (ho, varphi), and (z)
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A particle moves in a cylindrically symmetric potential \(U(ho, z)\). Use cylindrical coordinates \(ho, \varphi\), and \(z\) to parameterize the space.
(a) Write the Lagrangian for an unconstrained particle of mass \(m\) (using cylindrical coordinates) in the presence of this potential.
(b) Write the Lagrange equations of motion for \(ho, \varphi\) and \(z\).
(c) Identify any cyclic coordinates, and write a first integral corresponding to each.
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