A charged particle moves in a plane subject to the oscillatory potential:
There is also a constant EM-field described by:
where B is normal to the plane.
This produces the Lagrangian:
Now my friend says we need to transform this into polar coordinates and that produces:
where $\omega_L$ is the Larmor precession frequency:
My question is, How does he get this transformation? I don't really understand where the second term is coming from in the mechanical kinetic energy.