Geodesic
Kovalevskaya Top: An Elementary Approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 197-205 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We give an elementary, very short solution to the equations of motion for the Kovalevskaya top, using some results from the original papers by Kovalevskaya, Këtter, and Weber and also the Lax representation obtained by the author. 
@article{TMF_2002_131_2_a2,
     author = {A. M. Perelomov},
     title = {Kovalevskaya {Top:} {An} {Elementary} {Approach}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--205},
     year = {2002},
     volume = {131},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a2/}
}
TY  - JOUR
AU  - A. M. Perelomov
TI  - Kovalevskaya Top: An Elementary Approach
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 197
EP  - 205
VL  - 131
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a2/
LA  - ru
ID  - TMF_2002_131_2_a2
ER  - 
%0 Journal Article
%A A. M. Perelomov
%T Kovalevskaya Top: An Elementary Approach
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 197-205
%V 131
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a2/
%G ru
%F TMF_2002_131_2_a2
A. M. Perelomov. Kovalevskaya Top: An Elementary Approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 197-205. http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a2/

[1] S. Kovalevskaya, Acta Math., 12 (1889), 177–232 | DOI | MR

[2] F. Kötter, Acta Math., 17 (1893), 209–263 | DOI | MR

[3] G. V. Kolosov, Math. Ann., 56 (1902), 265–272 | DOI | MR

[4] A. M. Perelomov, Commun. Math. Phys., 81 (1981), 239–241 | DOI | MR | Zbl

[5] V. Z. Enolsky, Phys. Lett. A, 100 (1984), 463–466 | DOI | MR

[6] V. Z. Enolskii, DAN SSSR, 278:2 (1984), 305–308 | MR

[7] S. P. Novikov, A. P. Veselov, Tr. MIAN, 165, 1984, 49–61 | MR | Zbl

[8] H. Dullin, P. Richter, A. P. Veselov, Regular Chaot. Dynam., 3 (1998), 18–31 | DOI | MR | Zbl

[9] A. G. Reyman, M. A. Semenov–Tian-Shansky, Lett. Math. Phys., 14 (1987), 55–61 | DOI | MR | Zbl

[10] M. Adler, P. van Moerbeke, Commun. Math. Phys., 113 (1988), 659–700 | DOI | MR

[11] A. I. Bobenko, A. G. Reyman, M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 122 (1989), 321–354 | DOI | MR

[12] D. G. Markushevich, J. Phys. A, 34 (2001), 2125–2135 | DOI | MR | Zbl

[13] A. Clebsch, Math. Ann., 3 (1871), 238–262 | DOI | MR

[14] Jü. Moser, “Geometry of quadrics and spectral theory”, Differential Geometry, Proc. of the International Chern Symposium (Berkeley, 1979), eds. W. Y. Hsiang et al., Springer, New York, 1980, 147–188 | MR

[15] A. M. Perelomov, Funkts. analiz i ego prilozh., 15:2 (1981), 83–85 | MR | Zbl

[16] A. M. Perelomov, Integrable systems of classical mechanics and Lie algebras. Motion of rigid body around fixed point, Preprint ITEP-147, 1983 | MR

[17] A. M. Perelomov, Regular Chaot. Dynam., 5 (2000), 89–91 | DOI | MR | Zbl

[18] H. Weber, Math. Ann., 14 (1879), 173–206 | DOI

[19] Monatsberichte Akad. Wiss. zu Berlin, 1861, 986