From angular momentum hamiltonian to angles(coordinates)

[jannyhuggy]

I have a Hamiltonian, consisting only of angular momentum components L_x,L_y,L_z. I need to go from it to some coordinate representation. But I don't have derivatives Lx' etc. in H. So, when I'll go to coordinates and momenta I'll have Hamiltonian equations like p_i=0, which doesn't have sense.
How I need to go from H to x,y,z or \phi,\theta,r.
H=-K₁L_x²+K₂L_z²+H_xL_x+H_yL_y+H_zL_z

Going from L to angles can make no problem according to https://www.physicsforums.com/showthread.php?t=161865 in example
But back?

 

[jannyhuggy]

Please, somebody! I need at least the guidance how to go in classical case from H=-K1Lx2+K2Lz2+HxLx+HyLy+HzLz to action-angle variables! I know how to do that in a variety examples having coordinates (i.e. harmonic oscillator or Kepler problem etc.) but I don't know what to do having angular momentum in the Hamiltonian! Rewriting via p\cros r doesn't help either!