Geodesic
Euler equations on finite-dimensional Lie groups
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 371-389.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1978_12_2_a10,
     author = {A. S. Mishchenko and A. T. Fomenko},
     title = {Euler equations on finite-dimensional {Lie} groups},
     journal = {Izvestiya. Mathematics },
     pages = {371--389},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a10/}
}
TY  - JOUR
AU  - A. S. Mishchenko
AU  - A. T. Fomenko
TI  - Euler equations on finite-dimensional Lie groups
JO  - Izvestiya. Mathematics 
PY  - 1978
SP  - 371
EP  - 389
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a10/
LA  - en
ID  - IM2_1978_12_2_a10
ER  - 
%0 Journal Article
%A A. S. Mishchenko
%A A. T. Fomenko
%T Euler equations on finite-dimensional Lie groups
%J Izvestiya. Mathematics 
%D 1978
%P 371-389
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a10/
%G en
%F IM2_1978_12_2_a10
A. S. Mishchenko; A. T. Fomenko. Euler equations on finite-dimensional Lie groups. Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 371-389. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a10/

[1] Dubrovin V. A., Matveev V. B., Novikov S. P., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, Uspekhi matem. nauk, 31:1 (1976), 55–136 | MR | Zbl

[2] Manakov S. V., “Zamechanie ob integrirovanii uravnenii Eilera dinamiki $n$-mernogo tverdogo tela”, Funkts. analiz i ego prilozheniya, 10:4 (1976), 93–94 | MR | Zbl

[3] Arnold V., “Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits”, Ann. Inst. Fourier (Grenoble), 16:1 (1966), 319–361 | MR

[4] Mischenko A. S., “Integraly geodezicheskikh potokov na gruppakh Li”, Funkts. analiz i ego prilozheniya, 4:3 (1970), 73–78 | MR

[5] Mischenko A. S., Fomenko A. T., “Ob integrirovanii uravnenii Eilera na poluprostykh algebrakh Li”, Dokl. AN SSSR, 231:3 (1976), 536–538 | MR | Zbl

[6] Dikii L. A., “Zamechanie o gamiltonovykh sistemakh, svyazannykh s gruppoi vraschenii”, Funkts. analiz i ego prilozheniya, 6:4 (1972), 81–84 | MR

[7] Langlois Michel, Contribution a Tetude du mouvement du corps rigide a $N$ dimension autour d'un point fixe, These l'universite de Besancon, 1971

[8] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR