The Liouville classification of integrable systems of the Clebsch case

The Fomenko–Zieschang invariants for the integrable Clebsch case in the dynamics of a rigid body are calculated. Thus a complete description of the structure of the Liouville foliations on isoenergy surfaces of this integrable Hamiltonian system is obtained. As a corollary the Liouville equivalence of the Euler and Clebsch cases for certain values of the parameters is established.