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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 2, Pages 396–415 (Mi izv1771)  

This article is cited in 81 scientific papers (total in 81 papers)

Euler equations on finite-dimensional Lie groups

A. S. Mishchenko, A. T. Fomenko


Abstract: In this paper, a special class of dynamical systems is studied-the so-called Euler equations (a natural generalization of the classical equations of motion of a rigid body with one fixed point). It turns out that for any finite-dimensional Lie algebra this system has a large collection of integrals which are in involution. For the class of semisimple Lie algebras and for certain series of solvable Lie algebras these integrals turn out to be sufficient for the complete integration (using Liouville's theorem) of the multiparametric family of Euler equations.
Bibliography: 8 titles.

Full text: PDF file (1977 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1978, 12:2, 371–389

Bibliographic databases:

UDC: 513.944
MSC: Primary 58F05, 34C35, 22E60; Secondary 70B10, 70E15
Received: 22.12.1976

Citation: A. S. Mishchenko, A. T. Fomenko, “Euler equations on finite-dimensional Lie groups”, Izv. Akad. Nauk SSSR Ser. Mat., 42:2 (1978), 396–415; Math. USSR-Izv., 12:2 (1978), 371–389

Citation in format AMSBIB
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\by A.~S.~Mishchenko, A.~T.~Fomenko
\paper Euler equations on finite-dimensional Lie groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 2
\pages 396--415
\mathnet{http://mi.mathnet.ru/izv1771}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=482832}
\zmath{https://zbmath.org/?q=an:0383.58006|0405.58031}
\transl
\jour Math. USSR-Izv.
\yr 1978
\vol 12
\issue 2
\pages 371--389
\crossref{https://doi.org/10.1070/IM1978v012n02ABEH001859}


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    This publication is cited in the following articles:
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