Abstract
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, Kötter, and Weber and also the Lax representation obtained by the author.
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REFERENCES
S. Kovalevskaya, Acta Math., 12, 177–232 (1889).
F. Kötter, Acta Math., 17, 209–263 (1893).
G. V. Kolosov, Math. Ann., 56, 265–272 (1902).
A. M. Perelomov, Comm. Math. Phys., 81, 239–241 (1981); math-ph/0111024.
V. Z. Enolsky, Phys. Lett.A, 100, 463–466 (1984).
V. Z. Enolsky, Sov. Math. Dokl., 30, 394–397 (1984).
S. P. Novikov and A. P. Veselov, Proc. Steklov Math. Inst., 165, 53–65 (1985).
H. Dullin, P. Richter, and A. P. Veselov, Regul. Chaotic Dyn., 3, 18–31 (1998).
A. G. Reyman and M. A. Semenov-Tian-Shansky, Lett. Math. Phys., 14, 55–61 (1987).
M. Adler and P. van Moerbeke, Comm. Math. Phys., 113, 659–700 (1988).
A. I. Bobenko, A. G. Reyman, and M. A. Semenov-Tian-Shansky, Comm. Math. Phys., 122, 321–354 (1989).
D. G. Markushevich, J. Phys. A, 34, 2125–2135 (2001).
A. Clebsch, Math. Ann., 3, 238–262 (1871).
Ju. Moser, “Geometry of quadrics and spectral theory,” in: Differential Geometry (Proc. Intl. Chern Symposium, Berkeley, 1979, W. Y. Hsiang et al., eds.), Springer, Berlin (1980), pp. 147–188.
A. M. Perelomov, Funct. Anal. Appl., 15, 144–146 (1981).
A. M. Perelomov, “Integrable systems of classical mechanics and Lie algebras: Motion of rigid body around fixed point,” Preprint ITEP-147, ITEP, Moscow (1983).
A. M. Perelomov, Regul. Chaotic Dyn., 5, 89–91 (2000).
H. Weber, Math. Ann., 14, 173–206 (1879).
K. Weierstrass, Monatsberichte Akad. Wiss. Berlin, 986–997 (1861).
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Perelomov, A.M. Kovalevskaya Top: An Elementary Approach. Theoretical and Mathematical Physics 131, 612–620 (2002). https://doi.org/10.1023/A:1015416529917
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DOI: https://doi.org/10.1023/A:1015416529917