Geodesic
On one case of reducibility of the equations of motion of a complex mechanical system
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 65-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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A mechanical system, consisting of a non-variable rigid body (a carrier) and a subsystem, the configuration and composition of which may vary with time (the motion of its elements with respect to the carrier is specified), is considered. The system moves in a uniform gravitational field around a fixed point of the carrier. Obtained are conditions for the existence of the integral, which is a generalization of the kinetic moment projection integral in the case of variable mass. The system is reduced to an autonomous type. Case of an algebraic integral of the Kovalevskaya type existence is distinguish. 
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V. Yu. Olshanskiy. On one case of reducibility of the equations of motion of a complex mechanical system. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 65-69. http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a8/

[1] Olshanskii V. Yu., “Lineinyi i kvadratichnyi integraly slozhnoi mekhanicheskoi sistemy”, Prikladnaya matematika i mekhanika, 60:1 (1996), 37–46 | MR

[2] Olshanskii V. Yu., “Svobodnoe dvizhenie slozhnoi mekhanicheskoi sistemy s kvadratichnymi integralami”, Kosmicheskie issledovaniya, 34:2 (1996), 145–149

[3] Olshanskii V. Yu., “O privodimosti uravnenii svobodnogo dvizheniya slozhnoi mekhanicheskoi sistemy”, Prikladnaya matematika i mekhanika, 62:5 (1998), 768–777 | MR

[4] Borisov A. V., Mamaev I. S., Dinamika tverdogo tela, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001, 384 pp. | MR | Zbl

[5] Borisov A. V., Mamaev I. S., Kholmskaya A. G., “Kovalevskaya top and generalizations of integrable systems”, Reg. and Ch. Dyn., 6:1 (2000), 1–16 | DOI | MR

[6] Olshanskii V. Yu., “O dinamike mekhanicheskoi sistemy izmenyaemoi konfiguratsii i sostava v sluchae Kovalevskoi”, Vestn. Sarat. gos. tekhn. un-ta, 2008, no. 4(36), 39–44