ABSTRACT
Chapter 14
The Topology of Liouville Foliations
in Classical Integrable Cases
in Rigid Body Dynamics
14.1. INTEGRABLE CASES IN RIGID BODY DYNAMICS
In this chapter, we discuss the results on computing of topological invariants for
the main integrable cases in rigid body dynamics. The bifurcations of Liouville
tori, bifurcation diagrams, and molecules W for these cases were rst calculated by
M. P. Kharlamov [178] and A. A. Oshemkov [277], [278], [280]. Then the complete
invariants of the Liouville foliations (marked molecules W
) were computed
in a series of papers by several authors (A. V. Bolsinov [44], P. Topalov [344],
A. V. Bolsinov, A. T. Fomenko [55], [59], O. E. Orel [270], O. E. Orel, S. Taka-
hashi [275]). As a result, a complete classication of the main integrable cases
in rigid body dynamics has been obtained up to Liouville equivalence. Just this
classication will be presented in this chapter.
