A new integrable system on the sphere (Q1769983)

A Hamiltonian system is called natural if its Hamiltonian is the sum of a positive-definite kinetic energy and potential. Up to now, only the family of systems obtained from the Goryachev-Chaplygin top is known. In this note, the authors present a second, distinct family of natural Hamiltonian systems on \(T^*S^2\) (cotangent bundle of \(S^2\)) with an integrable cubic in the momenta.