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

2014/01/06 by Mikhail P. Kharlamov, Kharlamov, Mikhail P.
Engineering · Mathematics · #37J15 #37J20 #70E05 #70E17 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Elasticity and Wave Propagation #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · pdf · doi:10.48550/arxiv.1401.1015

openalex publication_date 2014/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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