Regular and chaotic motion of coupled rotators

We consider a classical Hamiltonian H = L_z+M_z+L_xM_x, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L² and M². By studying Poincaré surfaces of section, we find that the motion is regular when L² or M² is very small or very large. It is chaotic when both L² and M² have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.