This article is cited in 18 papers

The Liouville classification of integrable systems of the Clebsch case

P. V. Morozov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 515.1+521

MSC: Primary 37J35, 70E17; Secondary 53D20, 70E40, 70H06

Received: 31.10.2001

DOI: 10.4213/sm687

 English version: Sbornik: Mathematics, 2002, 193:10, 1507–1533

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