[FEATURE]: Add a Lie Poisson bracket for singular coordinates

[EmilyBourne]

Mathematical operator

$$[F, G] = \boldsymbol{b} \cdot \left( \nabla F \times \nabla G \right) = (1/J_x) \epsilon^{ijk} \partial_i F \partial_j G b_k$$

Implementation Ideas

The Lie Poisson bracket works well except at the singular point. In order to avoid this difficulty it is useful to be able to solve the Lie-Poisson bracket in a different set of coordinates. I.e. (R,Z,phi) instead of (r,theta,phi)

Benefits

• Simplify calculation of advection fields
• Avoid code duplication to handle singular point

Contribution

• I'm willing to work on this issue

[EmilyBourne]

3D tests for this require more coordinate transformation functions