Kozlov, V. V. 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 Cited in 2 ReviewsCited in 72 Documents MSC: 70E05 Motion of the gyroscope 70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems Keywords:first analytic integrals; periodic solutions; Poincaré’s small parameter method; variational calculus; splitting of separatrices; Painlevé problem; small ratio problems × Cite Format Result Cite Review PDF