- We consider a classical Hamiltonian H = L z + M z + L x M x , where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H , L 2 and M 2 . By studying Poincare surfaces of section, we find that the motion is regular when L 2 or M 2 is very small or very large. It is chaotic when both L 2 and M 2 have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.