Geodesic
Bihamilon structure and singularities of momentum mapping for Lagrange top
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 23-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new approach to the problem of describing the singularities of the momentum mapping for the Lagrange top is presented in the paper. Previous results were obtained with the use of the bi-Hamiltonian structure. A simple and convenient technique for determination of singular points and their type is presented. 
@article{VMUMM_2015_2_a3,
     author = {M. A. Tuzhilin},
     title = {Bihamilon structure and singularities of momentum mapping for {Lagrange} top},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {23--27},
     year = {2015},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a3/}
}
TY  - JOUR
AU  - M. A. Tuzhilin
TI  - Bihamilon structure and singularities of momentum mapping for Lagrange top
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2015
SP  - 23
EP  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a3/
LA  - ru
ID  - VMUMM_2015_2_a3
ER  - 
%0 Journal Article
%A M. A. Tuzhilin
%T Bihamilon structure and singularities of momentum mapping for Lagrange top
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2015
%P 23-27
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a3/
%G ru
%F VMUMM_2015_2_a3
M. A. Tuzhilin. Bihamilon structure and singularities of momentum mapping for Lagrange top. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 23-27. http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a3/

[1] Jacobi C., “Fragments sur la rotation d'un corps tirés des manuscripts de Jacobi et communiqués par E. Lotner”, Gesammel. Werke. Chelsea., 2 (1969), 425–514 | MR

[2] Klein F., Sommerfeld A., Über die Theorie des Kreisels, v. 4, Druck und verlag von B. G. Teubner, Leipzig, 1965 | MR

[3] Bolsinov A.A., Fomenko A.T., Integriruemye gamiltonovy sistemy, v. 2, Izdatelskii dom “Udmurtskii universitet”, Izhevsk, 1999 | MR

[4] Ratiu T., “Euler–Poisson equations on Lie algebras and the N-dimensional heavy rigid body”, Amer. J. Math., 104 (1982), 409–448 | DOI | MR | Zbl

[5] Bolsinov A.V., Oshemkov A.A., “Bi-Hamiltonian structures and singularities of integrable Hamiltonian systems”, Regular and Chaotic Dynamics, 14 (2009), 431–454 | DOI | MR | Zbl

[6] Fomenko A.T., Kunii T.L., Topological modeling for visualization, Springer-Verlag, Berlin, 1997 | MR | Zbl

[7] Brailov Yu.A., Fomenko A.T., Lie groups and integrable Hamiltonian systems, Res. Exp. Math., 25, Heldermann Verlag, Berlin, 2002 | MR | Zbl

[8] Fomenko A.T., Morozov P.V., “Some new results in topological classification of integrable systems in rigid body dynamics”, Contemporary geometry and related topics (Belgrade, 15–21 May 2002), World Scientific Publishing Co., 2004, 201–222 | DOI | MR | Zbl

[9] Fomenko A.T., Konyaev A.Yu., “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topol. and its Appl., 159 (2012), 1964–1975 | DOI | MR | Zbl

[10] Fomenko A.T., Konyaev A.Yu., Algebra and geometry through Hamiltonian systems, Solid Mechanics and Its Applications, 211, Springer-Verlag, Berlin, 2014 | MR | Zbl

[11] Gavrilov L., Zhivkov A., “The complex geometry of Lagrange top”, L'Enseign. math., 44 (1998), 133–170 | MR | Zbl

[12] Bolsinov A.A., “Compatible Poisson brackets on Lie algebras and the completeness of families of functions in involution”, Math. USSR Izv., 38 (1992), 69–90 | DOI | MR

[13] Bolsinov A.A., Izosimov A.M., Singularities of bihamilton systems, arXiv: 1203.3419