We answered the old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie group SO(4) of canonical transformations in some domain of phase space? We presented a system which is not centrally symmetric, but has SO(4) symmetry of canonical transformations. We showed also that not every mechanical system with 3 degrees of freedom possesses such symmetry.
Полезно уже хотя бы ссылками.