Geodesic
Integrable Euler equations on Lie algebras arising in problems of mathematical physics
Izvestiya. Mathematics , Tome 25 (1985) no. 2, pp. 207-257

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Complete integrability in the sense of Liouville is established for the rotation of an arbitrary rigid body about a fixed point in a Newtonian field with an arbitrary homogeneous quadratic potential. Explicit formulas, which express the angular velocity of the rigid body rotation in terms of theta functions on Riemannian surfaces, are obtained. A series of cases is found in which the Euler equations on the Lie algebra $\operatorname{SO}(4)$ are integrable. A model of pulsar rotation, the dynamics of which are described by Euler equations on the Lie algebra $\operatorname{SO}(3)\oplus E_3$, is investigated. Bibliography: 53 titles. 
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     author = {O. I. Bogoyavlenskii},
     title = {Integrable {Euler} equations on {Lie} algebras arising in problems of mathematical physics},
     journal = {Izvestiya. Mathematics },
     pages = {207--257},
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     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_2_a0/}
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O. I. Bogoyavlenskii. Integrable Euler equations on Lie algebras arising in problems of mathematical physics. Izvestiya. Mathematics , Tome 25 (1985) no. 2, pp. 207-257. http://geodesic.mathdoc.fr/item/IM2_1985_25_2_a0/