Integrable Hamiltonian systems on Lie groups: Kowalewski type
The integrability theory of Hamiltonian systems on Lie groups is presented through an extension of the equations of motion of a rigid body around a fixed point. The system of differential equations is reduced by using the integrals of motion and the procedure of integration by quadratures is explained. The cases of elastic equations that admit purely meromorphic solutions when two principal moments of inertia are equal are found to be the well known integrable cases of Euler, Lagrange and Kowalewski. A case of complete Liouville integrability which does not fall in the meromorphically integrable class is presented.
scientific article; zbMATH DE number 1419959