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Methods of qualitative analysis in the dynamics of a rigid body. (Metody kachestvennogo analiza v dinamike tverdogo tela). (Russian) Zbl 0557.70009

Moskva: Izdatel’stvo Moskovskogo Universiteta. 232 p. R. 1.50 (1980).
The monograph is devoted to the motion of a rigid body around some fixed point. The process of investigation is based upon the contemporary methods of the qualitative analysis of dynamical systems. The following problems are reflected: existence of first analytic integrals; determination of periodic solutions with the help of Poincaré’s small parameter method and the variational calculus and splitting of separatrices. The Painlevé problem on the connection between the ambiguity of the general solution and nonexistence of the new univalent first integrals is considered and a number of mathematical problems, which are connected with small ratio problems, are studied.
Reviewer: V.Sobolev

MSC:

70E05 Motion of the gyroscope
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems