Topological analysis of integrable problems in the dynamics of a rigid body

Abstract

The book contains the results obtained by the author in 1975-1982 and presents new constructive methods of the topological analysis of integrable systems having non-linear integrals in involution. The phase topology of the classical integrable cases of the rigid body dynamics is investigated including the cases of Euler-Zhukovsky, Goryachev-Chaplygin-Sretenski and Kovalevskaya. All types of bifurcations of two-dimensional tori in these problems are revealed.

LaTeX version of the book printed in 1988 in Leningrad, in Russian. In version 2 some mistyping is removed