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

TL;DR

This work provides a comprehensive topological analysis of classical integrable rigid body problems, revealing bifurcation types of tori and introducing new methods for analyzing systems with non-linear integrals.

Contribution

It introduces new constructive methods for topological analysis of integrable systems with non-linear integrals, applied to classical rigid body problems.

Findings

Classical cases of rigid body dynamics are thoroughly analyzed.

All bifurcation types of two-dimensional tori are identified.

The methods enhance understanding of phase topology in integrable systems.

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.