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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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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Question Posted: Mar 16, 2024 11:29 AM

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A particle moves in a cylindrically symmetric potential (U(ho, z)). Use cylindrical coordinates (ho, varphi), and (z)

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