The two body central-force problem we have been dealing with in the previous two problems also has another unexpected and amazing symmetry. Consider the transformation

Therefore, it's a total derivative and generates a symmetry under our generalized definition of a symmetry.

Data from Problem 6.15

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.

B B , = 2(2xy-yx), dt = 0