Geodesic
An integrable system related to the spherical top and the Toda chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 310-322

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We study the integrable motion over the sphere $S^2$ in the potential $V=(x_1x_2x_3)^{-2/3}$ possessing an additional integral of motion that is cubic in the momenta. We construct the Lax representation without a spectral parameter and consider the relation to the three-particle Toda chain. 
@article{TMF_2000_124_2_a8,
     author = {A. V. Tsiganov},
     title = {An integrable system related to the spherical top and the {Toda} chain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {310--322},
     publisher = {mathdoc},
     volume = {124},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a8/}
}
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A. V. Tsiganov. An integrable system related to the spherical top and the Toda chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 310-322. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a8/