Orel, O. E.; Ryabov, P. E. Topology, bifurcations and Liouville classification of Kirchhoff equations with an additional integral of fourth degree. (English) Zbl 1005.70006 J. Phys. A, Math. Gen. 34, No. 11, 2149-2163 (2001). By means of topological methods and energy surfaces, the authors study the bifurcation set for integrable problem of motion of a rigid body in fluid. In this way, the authors construct integrable Hamiltonian systems for which Lax representation and separation of variables are not known. All bifurcations of Liouville tori and of Fomenko-Zieschang invariant are obtained, and a bifurcation of two tori into four tori is put into evidence. Reviewer: Petre P.Teodorescu (Bucureşti) Cited in 2 Documents MSC: 70E40 Integrable cases of motion in rigid body dynamics 70G40 Topological and differential topological methods for problems in mechanics 37N05 Dynamical systems in classical and celestial mechanics 76E30 Nonlinear effects in hydrodynamic stability Keywords:Kirchhoff equations; Liouville classification; topological methods; energy surfaces; bifurcation set; motion of rigid body in fluid; integrable Hamiltonian systems; Liouville tori; Fomenko-Zieschang invariant PDFBibTeX XMLCite \textit{O. E. Orel} and \textit{P. E. Ryabov}, J. Phys. A, Math. Gen. 34, No. 11, 2149--2163 (2001; Zbl 1005.70006) Full Text: DOI