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P: 360
 Quote by garrett $$\xi^-_i{}^B = \delta_{iB} \frac{\sin(r)\cos(r)}{r} + x^i x^B ( \frac{1}{r^2} - \frac{\sin(r)\cos(r)}{r^3} ) + \epsilon_{ikB} x^k \frac{\sin^2(r)}{r^2}$$ And now I have to go figure out what the inverse of that is...
$$\xi_B{}^i = \delta_{Bi} \frac{r \cos(r)}{\sin(r)} + x^B x^i ( \frac{1}{r^2} - \frac{\cos(r)}{r \sin(r)} ) + \epsilon_{Bik} x^k$$

:)

By the way, if you're trying to do this yourself by hand, I calculated the inverse by making the ansatz:
$$\xi_B{}^i = \delta_{Bi} A + x^B x^i B + \epsilon_{Bik} x^k C$$
and solving for the three coefficients.

Now I'm going for a bike ride, then coming back to do rotations.