In the previous problem show that the conserved Noether charge associated with the symmetry 6.197 is indeed

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In the previous problem show that the conserved Noether charge associated with the symmetry 6.197 is indeed the angular momentum \(|\mathbf{r} \times \mu \mathbf{v}|\), which is naturally entirely in the \(z\) direction.

Data from previous problem

For the two-body central-force problem with a Newtonian potential, the effective two dimensional orbit dynamics can be described by the Lagrangian

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

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

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