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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 6, Pages 1139–1164 (Mi izv900)  

This article is cited in 1 scientific paper (total in 1 paper)

Integrable problems of the dynamics of coupled rigid bodies

O. I. Bogoyavlenskii


Abstract: Several classical problems of dynamics are shown to be integrable for the special systems of coupled rigid bodies introduced in this paper and called $C^k$-central configurations. It is proved that the dynamics of an arbitrary $C^k$-central configuration in the Newtonian gravitational field with an arbitrary quadratic potential is integrable in the Liouville sense and in theta-functions of Riemann surfaces. A hidden symmetry of the inertial dynamics of these configurations is found, and reductions of the corresponding Lagrange equations to the Euler equations on the direct sums of Lie coalgebras $SO(3)$ are obtained. Reductions and integrable cases of the equations for the rotation of a heavy $C^k$-central configuration about a fixed point are indicated. Separation of rotations of a space station type orbiting system, which is a $C^k$-central configuration of rigid bodies, is proved. This result leads to the possibility of independent stabilization of rotations of the rigid bodies in such orbiting configurations. Integrability of the inertial dynamics of $CR^n$-central configurations of coupled gyrostats is proved.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:3, 395–416

Bibliographic databases:

UDC: 539.2
MSC: Primary 70F99, 70H35; Secondary 70M20
Received: 20.07.1992

Citation: O. I. Bogoyavlenskii, “Integrable problems of the dynamics of coupled rigid bodies”, Izv. RAN. Ser. Mat., 56:6 (1992), 1139–1164; Russian Acad. Sci. Izv. Math., 41:3 (1993), 395–416

Citation in format AMSBIB
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\by O.~I.~Bogoyavlenskii
\paper Integrable problems of the dynamics of coupled rigid bodies
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 6
\pages 1139--1164
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\zmath{https://zbmath.org/?q=an:0799.70003}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..395B}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 3
\pages 395--416
\crossref{https://doi.org/10.1070/IM1993v041n03ABEH002269}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Shamolin M.V., “Variety of the Cases of Integrability in Dynamics of a Symmetric 2D-, 3D-and 4D-Rigid Body in a Nonconservative Field”, Int. J. Struct. Stab. Dyn., 13:7, SI (2013), 1340011  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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