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Integrable Hamiltonian systems on Lie groups: Kowalewski type. (English) Zbl 0953.37012
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.

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
70E40 Integrable cases of motion in rigid body dynamics
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