Geodesic
Separation of Variables in Multi-Hamiltonian Systems: An Application to the Lagrange Top
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 226-238 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show explicitly that after the reduction to each symplectic leaf, the vector field of the Lagrange top is separable in the Hamilton–Jacobi sense.
Mots-clés : Lagrange top
Keywords: Hamiltonian formulation, separability. 
@article{TMF_2003_137_2_a8,
     author = {C. Morosi and G. Tondo},
     title = {Separation of {Variables} in {Multi-Hamiltonian} {Systems:} {An} {Application} to the {Lagrange} {Top}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {226--238},
     year = {2003},
     volume = {137},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a8/}
}
TY  - JOUR
AU  - C. Morosi
AU  - G. Tondo
TI  - Separation of Variables in Multi-Hamiltonian Systems: An Application to the Lagrange Top
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 226
EP  - 238
VL  - 137
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a8/
LA  - ru
ID  - TMF_2003_137_2_a8
ER  - 
%0 Journal Article
%A C. Morosi
%A G. Tondo
%T Separation of Variables in Multi-Hamiltonian Systems: An Application to the Lagrange Top
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 226-238
%V 137
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a8/
%G ru
%F TMF_2003_137_2_a8
C. Morosi; G. Tondo. Separation of Variables in Multi-Hamiltonian Systems: An Application to the Lagrange Top. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 226-238. http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a8/

[1] C. Morosi, G. Tondo, J. Phys. A, 35 (2002), 1741–1750 | DOI | MR | Zbl

[2] G. Tondo, J. Phys. A, 28 (1995), 5097–5115 ; Г. Фальки, Ф. Магри, Г. Тондо, ТМФ, 122:2 (2000), 212–230 ; G. Falqui, F. Magri, M. Pedroni, G. Zubelli, Regul. Chaotic Dyn., 5 (2000), 33–52 | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl

[3] F. Magri, C. Morosi, A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson–Nijenhuis manifolds, Quaderno 19/S, Dip. Mat., Università di Milano, Milano, 1984

[4] R. Caboz, V. Ravoson, L. Gavrilov, J. Phys. A, 24 (1991), L523–L525 ; R. Brouzet, R. Caboz, J. Rabenivo, V. Ravoson, J. Phys. A, 29 (1996), 2069–2075 | DOI | MR | Zbl | DOI | MR

[5] C. Morosi, G. Tondo, J. Phys. A, 30 (1997), 2799–2806 | DOI | MR | Zbl

[6] G. Tondo, C. Morosi, Rep. Math. Phys., 44 (1999), 255–266 | DOI | MR | Zbl

[7] F. Magri, T. Marsico, “Some developments of the concept of Poisson manifolds in the sense of A. Lichnerowitz”, Gravitation, Electromagnetism, and Geometric Structures, ed. G. Ferrarese, Pitagora, Bologna, 1996, 207–222 | MR

[8] E. K. Sklyanin, Progr. Theor. Phys. Suppl., 118 (1995), 35–60 | DOI | MR | Zbl

[9] S. Benenti, J. Math. Phys., 38 (1997), 6578–6602 | DOI | MR | Zbl

[10] L. Gavrilov, A. Zhivkov, Enseign. Math., 44 (1998), 133–170 | MR | Zbl

[11] T. Ratiu, Am. J. Math., 104 (1982), 409–448 | DOI | MR | Zbl

[12] C. Médan, Phys. Lett. A, 215 (1996), 176–180 | DOI | MR | Zbl

[13] G. Magnano, Acc. Sc. Torino-Mem. Sc. Fis., 19 (1995) ; 20 (1996), 159–209 | MR

[14] I. M. Gel'fand, I. S. Zakharevich, Selecta Math. (N. S.), 6 (2000), 131–183 | DOI | MR | Zbl